help-0

[tulip bone]

what

Also

write down everything

uve learnt

[frozen scarab]

omg

[tulip bone]

@frozen scarab take it from here

oh

shit

ur here

[frozen scarab]

this is still happening

[celest pulsar]

😭

[frozen scarab]

nah bro u got this one

[tulip bone]

naa

u got it

[tulip bone]

solve it

lmk

dont get it wrong

[celest pulsar]

what if i do

[tulip bone]

then

go to sleep

[celest pulsar]

A cuboidal room needs to be painted. The floor and the roof of the room have a total area of 36000cm^2, and the walls have a total area of 56000cm^2. Find the total cost for painting the room, if the painter charges 2$ per m^2 of area.

[tulip bone]

thats what i advice

[celest pulsar]

can i work it out here

[tulip bone]

sure

thats the last question we're doing

[celest pulsar]

The floor and the roof of the room have a total area of 36000cm^2, and the walls have a total area of 56000cm^2.

[tulip bone]

you're going to sleep after this

[celest pulsar]

i can't i'm gonna find someone to help me

i need 30 pages more

[tulip bone]

Nobodys gonna do

30 pages with you

You cant solve every question

Its too late for that

[celest pulsar]

my friends will 🤩

[tulip bone]

good luck then

but really, what i suggest is rest

[celest pulsar]

I had a week to study and i've been procrastinating

[tulip bone]

nothing much u can do

@frozen scarab

do u agree

[tulip bone]

solve it tho

this the last question im doing with u anyways

[celest pulsar]

The floor and the roof of the room have a total area of 36000cm^2, and the walls have a total area of 56000cm^2.

so

Find the total cost for painting the room, if the painter charges 2$ per m^2 of area.

i have to convert both the cm's into m

?

[torn quiver]

easier to just covert the cost to cm

[celest pulsar]

the $2?

[torn quiver]

Eithers fine

Unless they haven’t specified what form to give the ans in

[celest pulsar]

20000

cm^2

if the cost is converted to cm

right

[torn quiver]

How is it more for less area…

[celest pulsar]

I'm sorry i've been here for 3 hours straight my brain can't think straight 🤩

[torn quiver]

Why 💀

[celest pulsar]

i'm punishing myself for not doing the study

i had 2 weeks

and i've been side tracked to unproductivity

OK BUT I NEED TO ANSWER THIS 😭

[frozen scarab]

haha @tulip bone its been like 2 hours i think

[celest pulsar]

😭

[tulip bone]

shit

fr?

[torn quiver]

Divide it by 10k to get the cost per cm squared

[celest pulsar]

i'm so close to giving up

[tulip bone]

Florida

Take a break

20 minutes

or 30

[celest pulsar]

😭 I really do need a break

[tulip bone]

Yep

js relax ur mind

close the channel too

[lone heart]

@celest pulsar Has your question been resolved?

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[subtle lance]

how to solve without calculus

[granite galleon]

Try to use artimetic geometric mean

[subtle lance]

where to use am gm

[granite galleon]

Wait

Let me try

[subtle lance]

$2\sqrt{xy} + 4\sqrt{x} + 2\sqrt{y} + y + 4$

[ocean seal]

matchafrappucino

[subtle lance]

a1, a2 = x4/y, y3/x ?

n then what to do with the inequality?

[lone heart]

@subtle lance Has your question been resolved?

[subtle lance]

Help

[lone heart]

@subtle lance Has your question been resolved?

[subtle lance]

<@&286206848099549185>

[sudden charm]

hey u

what can i do for u

[subtle lance]

This

[lone heart]

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[wet harness]

.reopen

[random beacon]

Im not sure what to do

[violet rapids]

@random beacon close the prev channel

[wet harness]

@random beacon what is tg (2alpha)

[violet rapids]

what is tg? I am sorry but never seen it before

[random beacon]

tangent

[wet harness]

Tan 2@

ok

[violet rapids]

oh tan

[random beacon]

yes

[wet harness]

Cos 2alpha = 2cos²a -1

[violet rapids]

in this one you can construct a right angle triangle with one angle being alpha to do the thing

[wet harness]

tan²a = (1-cos2a)/1+cos2a

[violet rapids]

identities works too

[violet rapids]

it is tan 2a not tan sqr thou?

[wet harness]

no use this to find value and +- according to quadrant

[wet harness]

?

[violet rapids]

you gave the formula to find tan^2(a) but he needs tan(2a)

[tardy tapir]

if you don't know the value of alpha, find cos(2alpha) using double angle identity of cos and construct a right triangle of angle 2alpha and find tan(2alpha) from there.

[wet harness]

oh sry

tan2a = 2tana/(1-tan²a)

You know cosa so can find tan a

[random beacon]

I'm not sure how

[violet rapids]

@random beacon 1st thing to do

[wet harness]

Tan a will be positive as in 3rd quadrant

[tardy tapir]

do you not know the double angle identity or dont know how to find trigonometric ratios from a right triangle?

[wet harness]

...

[violet rapids]

2nd thing to do.
You can find Tan(a) by constructing a right angled triangle using the value of cos(a)

[random beacon]

I dont know how to find trigonometric ratios from a right triangle

[ocean seal]

Dyssrupt

[tardy tapir]

im pretty sure these are taught before anything else

[random beacon]

I just havent used them in a while

[violet rapids]

yes they probably have never really applied this in reverse like from just one value to other values

[tardy tapir]

ah alright

[random beacon]

So alpha would be -9? or something?

[violet rapids]

its alr

[random beacon]

or wait no

[violet rapids]

you dont have to find alpha

you just need to find opposite

[tardy tapir]

dont guess, do it somewhere and show your working

[random beacon]

opposite is -9

[tardy tapir]

sides cant be negative

[violet rapids]

the length can't be negative

[random beacon]

I was thinking because -(4/5) but I see

[tardy tapir]

i would recommend you to go through your notes/videos on this topic atp

[violet rapids]

that is just because the angle lies in some other quadrant

[wet harness]

@tardy tapir is.the teacher 🙂

[violet rapids]

@tardy tapir wait the value of cos being negative can only happen is an angle is more than pie/2 and less than 3pie/2 right?

[random beacon]

so I found opposite is 9 from pythagora theorem, and I replace it in the tangent formula?

[violet rapids]

his recommendation is valid thou

[tardy tapir]

yeah

[violet rapids]

yeah

[violet rapids]

but constructing a right angle triangle with an obtuse angle seems quite confusing thou

[random beacon]

So tan(x) = -(9/4) ?

[wet harness]

No it will be positive

As tan is +ve in 3 rd quadrant

[random beacon]

Do I just replace the values in? ( I used tan 2a formula)

[wet harness]

Val

[random beacon]

Yes?

I don't know what to do 😭

[wet harness]

Wait

See this bro

2a in 1st and 2nd quadrant so tan 2a can be negative and positivs

you take the positive value i wrongly wrote negative only

@random beacon ?

[random beacon]

Ah I see

What now? Do I replace tan(2a) and use the cos(2a) formula?

and then replace that too?

[wet harness]

Yeah

Find cos 2a value using the formula

And use them in your equation

[random beacon]

Like this?

[wet harness]

Yeah

Use positive value of tan2a

[random beacon]

Why?

[wet harness]

It can be both positive and negative

if you use -ve we will have to check for cos 2a too

So its better we consider 2a is in first quadrant

A generalization only

[random beacon]

Alright I see
Thank you so much for helping

🙏

[alpine sable]

well

[wet harness]

@random beacon anytime bro

[lone heart]

@random beacon Has your question been resolved?

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[lone heart]

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[frosty sparrow]

@wispy geyser hey remember the question I asked earlier, no matter how I try it it becomes quartic

[frosty sparrow]

Try rearranging for theta from the x equation then subbing into y, after all expansions it’s quartic

Same if the other way around

Same if I equate arcsin(…) = arccos(…)

[wet harness]

Bro

[frosty sparrow]

Yeah

I’ll repost the context

“Hi there, does anyone know the procedure to find the intersection between two parametric curves, where the time of intersection (the parameter t) is also equal?

My idea is, equate the x(t) and y(t) of both curves. Now we have to equations involving only t as the unknown. Rearrange both equations for t, then set those equal. Then solve.

Specifically, I am looking to approach the problem where we have the curves:

Curve 1:
x(t) = x_0 + V_x * t
y(t) = y_0 + V_y * t

Curve 2:
x(t) = V cos(theta) * t
y(t) = V sin(theta) * t - g t^2

Which makes curve 1 a simple line with an origin and direction, and curve 2 a parabola tracing the curve of projectile launched with velocity V from the origin at a given angle theta.

All quantities are known except theta. I want to solve for theta such that the parabola is guaranteed to intersect with the straight line at some t>0.

Without the gravity term this is doable, but when I add gravity in, making it a parabola, the resulting equations are exceedingly complex.”

I don’t know why this seemingly simple question becomes so hard

[lone heart]

@frosty sparrow Has your question been resolved?

[frosty sparrow]

I ended up doing it numerically, few iterations of newtons method makes it doable

.close

[lone heart]

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[lavish cave]

Where are you stuck?

[novel mesa]

number 4 didnt make sensee

or its my solution that is wrong😭

[lavish cave]

Start from cos 45 = 1/sqrt(2) and sin 45 = 1/sqrt(2)

[novel mesa]

i alreadyy know the phrasee. it's "SPECIAL YOU". i dontt know how to do the solutions

[lavish cave]

So sec 45 = 1/(cos 45), csc 45 = 1/(sin 45)

[lavish cave]

Yeah I'm telling you right now

So we have $\frac{1}{1/\sqrt 2} \frac{1}{1/ \sqrt{2}}- 1 = \sqrt{2} \sqrt{2} - 1 = 1$

[ocean seal]

south

[novel mesa]

its 1 right??

[tidal lichen]

Yes

[novel mesa]

but on C its 3

the answers key didnt make sensee

[novel mesa]

that's what i thought

[tidal lichen]

If I had to guess you match the answer with the letter and it spells something?

[novel mesa]

yeahhh that's the direction

[tidal lichen]

Cuz these letters seem random otherwise

[lavish cave]

Well it is 1, just try your calculator

,calc sec(pi/4) * csc(pi/4) - 1

[ocean seal]

Result:

1

[novel mesa]

got itttt, maybe it's the letter placement tgat's wrong

thankk youu

.close

[lone heart]

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[lavish cave]

npnp

[lone heart]

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[slender nest]

can someone explain to me how its not 27

[slender nest]

so i know that EF is 6 and GF is 3 so i did b*h and got 18 for the rectangle

then for the triangle i did half of 3 - 1.5 and then did b*h so 9 i wouldny have to divide by 2 cuz thats for a right traignel

i know i have to split it down the middle but evn if i did that i would get 4.5 for one side and then again 4.5 for the other side

still 9

[fleet crown]

For the traingle it's 6 * 1.5 / 2 = 3 * 1.5 = 4.5

This is the surface of the whole triangle

not just one side

[slender nest]

4.5?

[fleet crown]

Yes

if you split the triangle in 2

You have opne being width 3, height 1.5

[slender nest]

ohhh yea

i keep forgeting that

alrigt yea that makes sense

forgot to split the 6 to 3

thanks

.close

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[rotund crater]

help

[rotund crater]

why this graph?

[lone heart]

@rotund crater Has your question been resolved?

[lone heart]

@rotund crater Has your question been resolved?

[lone heart]

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[fervent berry]

hi how do i solve this using ruffinis method 😭

[fervent berry]

i tried googling tutorials on ruffinis rule but couldn’t understand nun 😞

[wary root]

Is it similar to factoring or no

Looked it up, and it seems ruffini rule is for dividing polynomials

And this looks like a factoring problem

[fervent berry]

uhhh give me a second

[candid harness]

can someone help with this problem i don't know how to solve it

[wary root]

Have you tried substitution to find possible x and y

[candid harness]

i substituted but where the hell does the "a" go

why is there a random letter in my damn equation

[wary root]

I just did it by dropping the a, and I got x={8,4} so I’m assuming x = 8 since 4 isn’t an option

[fervent berry]

LMFAO

[fervent berry]

basically this is what ur supposed to do, but with all the divisors of the number in circle if that makes sense???

[misty jewel]

they tell u it only intersects at one point

[fervent berry]

and i’m confused what do i do

when i don’t get 0

[wary root]

I guess use this as a base and plug in your numbers

[candid harness]

how do i utilize that information

[candid harness]

oh yeah i can use desmos on the sat #l

[wary root]

Well, use it on your homework to help understand if you’re doing it correctly

[candid harness]

yeah i'm just doing sat prep

rnn

[wary root]

What does it mean by a is a constant

[candid harness]

Idk

it's constant

single number doesn't change

whatever a constant is

[wary root]

So if it’s 0, then x = 8 by factoring

[lone heart]

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[sudden musk]

Can someone check if my answer is correct? Thanks

[lone heart]

@sudden musk Has your question been resolved?

[misty jewel]

sorry for the late reply

but

you can set them up to equal each other to find the intersect

you can evaluate it so it equals 0

then u got a quadratic equation again

which only has 1 root

thus you know the discriminant is 0 and then you can both solve a to -8 and at last the root to be 6

[sudden musk]

would be nice if you dm him

[misty jewel]

oh yea sry

just seemed like he went with 8 which would be wrong given the question

[candid harness]

Thanks i appreciate the response

[candid harness]

it's sat prep anyway so right or wrong i just need to learn how to solve those

[misty jewel]

👍

[sudden musk]

.close

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[barren hazel]

need to find if theres a vertical asymptoe, I think that theres a hole at x = 0, correct?

[jagged cobalt]

si

[barren hazel]

muchas gracias!

.close

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[calm kiln]

hi

[calm kiln]

needed help with this

is this correct way to set it up?

[lone heart]

@calm kiln Has your question been resolved?

[calm kiln]

<@&286206848099549185>

[acoustic tangle]

Not exactly, when using the method of cylindrical shells you got to consider the radius which is rotating, imagine how is the green line rotating, the distance to x axis is the radius and the distance to the sqrt(x) function is the heigh in this case

[calm kiln]

so would the radius be sqrtx?

[calm kiln]

not sure what the height would be

[acoustic tangle]

it depends on how you consider the heigh, if you consider the heigh being x, then yes the radius is sqrtx

you can either think about the radius depending on the heigh or the opposite, the heigh depending on the radius, if you set your heigh being 4 for example, then your radius should be 2, sqrtx

but in that case, the limits where you consider x are from 0 to 9

[calm kiln]

so it would look like this?

[acoustic tangle]

Not actually, sorry I can see why you got confused, the 2-4 thing was just an example of a specific case, what I mean is, if you consider heigh as your independent value, then radius is the sqrt of heigh, that means if you note heigh as x, radius is sqrtx. But in that case the integral limits should be 0 and 9, since your taking the heigh in the interval [0,9]

[calm kiln]

so here I can keep everything the same but change the bounds to 0 and 9?

[acoustic tangle]

yes, you change the bouds, but more importantly, you erase 2, and 4, those were merely examplex, what I tried to tell you is that in the specific case where heigh is 4 then radius is 2. But when you write the integral what you said is for any value of heigh x between 0 and 9, then the radius is sqrtx

[calm kiln]

so I still need to figure out the height

[acoustic tangle]

you dont exactly figure out heigh, you set heigh to be your variable, heigh goes from 0 to 9, the important thing is that for any given heigh the radius is its square root

[calm kiln]

im still confused

[acoustic tangle]

give me a sec

[acoustic tangle]

Basically, when you are writing the integral you are saying you want to add up all these small cylinders, with volume approximately (2pi)(f(x))xdx. Notice that if you consider heigh in the x axis as a variable x, then the radius is a function of x, in this case sqrtx, also in this case that heigh variable goes form 0 to 9

[calm kiln]

so it it just this?

[acoustic tangle]

yes, times another x inside the integral

[calm kiln]

this?

[acoustic tangle]

yes

[calm kiln]

says its wrong again

[acoustic tangle]

Sorry I think I miss explained myself a bit, It is my first time helping here

[calm kiln]

i got 972pi/5

[acoustic tangle]

is the answer 81/2 pi?

[calm kiln]

oh yea that worked

how did u get that

[acoustic tangle]

when you use the method of cylindrical shells rotating about the x-axis, you have to consider the heigh as a function of radius, the opposite to what we did, the radius is a variable y that goes from 0 to 3 (in this case), and the heigh in this case would be f(y) = y^2, which is the inverse function of the one we had before

If you set the integral like you did before I guess you'll get the volume of the revolution about the y axis

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[pliant cloud]

I don't know where to start with this problem

[pliant cloud]

do I need to find tan^-1

[acoustic tangle]

I'm pretty sure, you can't solve that with standard algebra, can you use numerical methods?

[lone heart]

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[lone heart]

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[silver knot]

hey! this isnt something id usually do but its like 3am and i just wanna sleep 😭 this questions really bugging me though, help would be appreciated....

[tough badge]

ignore the hexagon. the angle is the same if the bottom is the bottom of the pentagon rather than the hexagon

i believe…

[raven geode]

Adding on, you can draw the right triangle formed by cutting the pentagon (and hexagon) in half. Then you can use the interior angle of the pentagon

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[noble tide]

i do that with ln?

[limpid turret]

where do you see ln?

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[dire cloud]

Hey, can anyone help me figure out this problem?

I'm unsure as to how to find the correct answer.

[merry iris]

do you know how to find the error for an alternating series?

[dire cloud]

isnt that the n+1th term?

[merry iris]

yeah

just set up an inequality and solve for k

|a_n+1| <= |error| i believe?

[dire cloud]

okay

thanks!

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[floral swan]

hi can someone please help me with the unit circle, like what does it mean and what is its purpose?

[mortal trellis]

well its a circle

circles are useful

[floral swan]

umm

what correlation does it have to the trig ratios

[cosmic whale]

ok the unit circle is useful as u can correlate trig ratios to a sin of an angle etc

[versed lake]

The unit circle helps you visualize trig ratios. It doesn't need to be done on a unit circle since no matter the radius the proportions are always the same, but the unit circle is just a simpler way of doing it since the radius is defined as 1

[floral swan]

but what si the values of sin, cos and tan

[floral swan]

like pi is 3.1415

[mortal trellis]

if you draw a triangle like that on the unit circle

you'll notice that the hypothenuse has length 1

so the ratios of sin and cos simplify

and it turns out that the other two sidelengths are equal to sin and cos of the relevant angle

[floral swan]

but why would the bottom base be cos theta

[mortal trellis]

cos theta is adjacent/hypothenuse

the hypo is 1

so cos theta = adjacent

sin theta is opposite/hypo. but hypo=1. so sin theta = opposite

[floral swan]

ok that makes sense

so basically the unit circle is visual aid for understanding trigonometric functions

[mortal trellis]

among other things, yes

[floral swan]

but what are the coordinates thing i dont understand that

why does cos theta= x and sin theta=y

[hearty quartz]

That is the unit circle definition of the trig function

[mortal trellis]

well those are the coordinates of the point

the coordinates tell you how far you go left/right and up/down

[hearty quartz]

There is SOHCAHTOA but that only holds for 0<theta<90 degrees

[mortal trellis]

which are exactly the sides of the triangle

[hearty quartz]

The unit circle definitions holds for all theta

[floral swan]

so any angle between 0-369

360*

[hearty quartz]

No all real numbers

So there are two definitions 1) SOHCAHTOA 2) unit circle definition

[floral swan]

ok

[hearty quartz]

So at 90 degrees we have the point (0, 1) in the unit circle. So we get sin(90) = 1, cos(90) =0 from the definition

[floral swan]

OHHHH

gotchu

[hearty quartz]

Similarly at 180 degrees we will be at the point (-1, 0) and we will get sin(180) =0, and cos(180) =-1 because sin(theta) = y so the y-coordinate is the value of sin(theta). Similarly, the x-coordinate is the value of cos(theta). And this comes directly from the definition

[floral swan]

one last question

for this image

how would we know what the P value is

like what would sin and cos be for this image

[hearty quartz]

You would use a calculator

x = cos(200)

y = sin(200)

[mortal trellis]

(you arent asked for the actual values)

[floral swan]

this is the whole exerpt

but is says find it by measuring it

does it mean with a ruler etc.

[hearty quartz]

You don't need to use a ruler

[floral swan]

"measuring the distance along the y-axis"

[hearty quartz]

If you want you can though

[floral swan]

aight thank you guys for all the help

helped a lot

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[hardy steppe]

Hi guys I need help with this

I dont get quesiton b how to do

I am getting answer as 2.9m but the book answer is 2.5m

[hearty quartz]

pythagoras theorem

!show

[lone heart]

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

[hardy steppe]

ok

my working out above

[hearty quartz]

should be (1.7/2)^2

in the first line

[hardy steppe]

why tho?'

[hearty quartz]

the 2.3^2 is good

You can only apply pythagoras theorem on a right angle triangle.

The triangle you have applied it on is not a right angle triangle

[hardy steppe]

can you call em

?

explain

[hearty quartz]

?

[hardy steppe]

can you call me?

[hearty quartz]

no

[hardy steppe]

alr

[hardy steppe]

is it cuz a cone and they halfing it>

?

[hearty quartz]

yep When we construct a line from the tip of the cone is the base. We end up a right angle and the line bisects the triangle cross section

So in the first image there is clearly right angle triangle

[hardy steppe]

yes

I get it

if i have more quesiton can I ask

?

[hearty quartz]

In contrast the triangle for b looks like this and clearly none of the angles are 90 degrees

[hearty quartz]

yep

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[hardy steppe]

ok the third one

[hardy steppe]

I did 1.5 squared divided by 2 plus 3 squared

can you show working out for this?

[hearty quartz]

order of operations

Use ^ for power

[hardy steppe]

I have scienitific calculator tho

[hearty quartz]

I meant this "1.5 squared divided by 2 plus 3 squared"

not correct

This (1.5)^2/2+3^2

should be (1.5/2)^2+3^2

[hardy steppe]

no shit you too good

[hearty quartz]

!done

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[hardy steppe]

can you add me so I can ask questions?

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.reopen

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✅

[hardy steppe]

helllo

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[bold silo]

How do I do this q? I split x into $2\sqrt{3}sin(t) + 2cos(t)$ but idk what to do now

[ocean seal]

morphine_addiction

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[bold silo]

<@&286206848099549185> 🙏🙏

[crisp fulcrum]

dy/dx = (dy/dt)/(dx/dt) try that

[runic isle]

think u mean dy/dt * dt/dx

but yeah

chainz rulez

[grizzled flower]

Bro what you guys want

[crisp fulcrum]

i did not mean that, and it has the same outcome

[crisp fulcrum]

??

[runic isle]

oh.
my bad

[crisp fulcrum]

you're not wrong but it's easier to diffferentiate x w.r.t. t than first rewrite t in terms of x and then differentiate t w.r.t. x

[bold silo]

$-\frac{6sin(2t)}{4cos(t+ \frac{\pi}{6}}$

[ocean seal]

morphine_addiction

[bold silo]

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[idle jackal]

Hi, I have a question about solving linear differential equations, so when dealing with a differential of the form $Ly = f$ where the sum of all $L = a_0D^n$ of the n-th order, we can find the homogenous solution $y_h$ by setting f equal to zero, and then solve for the $f_p$ by substituting the constant iinside $f_h$ with a function of our variable
my question is, is this allowed because we use superposition or... how does this work?

[ocean seal]

Mephisto

[idle jackal]

I'm referring to variation of parameters I think

and let's say we have a diff eq of the form
a0y'' + a1y' + y = 10x or smtg like that,
can we find our both particular solution by solving for f_p1: a0y'' + a1y' + y = 0 first and then for f_p2: a0y'' + a1y' + y = 10x? because is f_p1 is a solution to Ly = f1 and f_p2 is a solution to Ly = f1, their sum should be the solution to Ly = f1 + f2, right?

[charred flint]

yea when you find a solution to =0, by linearity you can add as many of those as you want for a solution

you can sort of think of the solutions as a line that doesn't go through 0, so to express it you need a red dot particular solution, then a general solution that you can scale however you want to get the whole line, like a vector

[idle jackal]

ah alright, and does this mean that a 2nd order linear diff eq, would only have one particular solution?

bcs when adding up these f_h terms, it generally changes nothing, but how are the particular solutions influenced by this when dealing with variation of parameters

[charred flint]

there'll always be just one particular solution yea

with variation of parameters that's just a trick to find a particular solution

[idle jackal]

oh alright so the amount of homogenous solutions is always equal to the order of the differential

and the particular would be some function + one of the homogenous solutions ?

[charred flint]

yea that's a theorem

it's just some function as your starting red dot

technically there are a billion choices for yp because you can add the y_h's to it and it's still a solution, but usually there's a simplest one, like the one you get with variation of parameters

[idle jackal]

ah alright, are there any other methods besides variation of paramteres and undetermined coeffecients?

[charred flint]

I think those were the only ways in my diffeq class

[idle jackal]

alright, thanks, one more question, is undermined coefficients always a guess game?

[charred flint]

yea lol I think it's just random guessing, usually it's pretty clear though

[idle jackal]

okay, thanks

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[meager locust]

how do i solve this when the two initial conditions a0 and a1 are both 1?

[meager locust]

to solve this, i tried to solve for t in the equation t^2 - 6t + 9, and t = 3, but a solution of the form a_n = B * r^n + D * r^n with those initial conditions doesnt work because the system of equations i get becomes 3B + 3D = 1 and B + D = 1, which has no solutions

[pseudo ice]

Be careful when you have a repeated root: tl;dr your solution should be something like a_n = B * r^n + Dn * r^n

[meager locust]

oh theres an extra n in the second term for a repeated root? i didnt know that

mustve accidentally skipped it over during lecture, my bad. ill try resolving now, thanks for the help

[pseudo ice]

yep they should hopefully have told you somewhere how to deal with your characteristic equation having repeated roots (and if you're lucky, provided an explanation as to why you multiply by n)

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[austere charm]

what are the steps for doing a question like this

first should i see if i can dived everythign by a specific number?

then what

[fallen verge]

it tells you its a square

whenever you have (ax+b)^2
the x^2 term is (ax)^2
the constant term is (b)^2

the x term is (2ab)x

you can figure out a and b from there

there are two solutions

[austere charm]

i dont get it

nvm

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[placid zinc]

If it's easier, use < instead of U

[left wharf]

<= would make more sense to me since a partial order is reflexive

[placid zinc]

Yep, that's a good call

Well, let's figure out what you're forced to set

For example, if a≤b and b≤c, then a≤c

And we can make a hasse diagram to capture this info

Yeah basically

So you'll have one that goes
d
c
b
a

[rich summit]

Hi can someone Help me with this:

[placid zinc]

#❓how-to-get-help

[rich summit]

How?

[placid zinc]

Yeah, fair. We can also include a branch that goes from a to e

But it's a bit less obvious than I'm making it out. For example, is b≤e?

I think it can be, yeah. So that's an example of a choice you're able to make, when you're counting how many order relations you get

It means that there must be at least one pair that isn't comparable

Actually, maybe that does mean you can't just have a straight line haha

So it isn't the case that d≤e

And that e≤a

Consider one where a branches off to e, then e goes back at d

[placid zinc]

Heyo back

I like those and I think that's it

yeye, just swapping e with any of those is still the same diagram

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[proud wyvern]

I have no idea what to do

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[topaz nacelle]

m1*v1x + m2*v2x = (m1 + m2)Vfx

same for y

[proud wyvern]

Is that just applying conservation of momentum

[topaz nacelle]

for inelastic collisions

im guessing that's the key here

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[cobalt obsidian]

Can someone help me with a word problem in basic calculus?(Specifically about Areas between two curves)

[small fog]

Sure

Ask away

[cobalt obsidian]

I have tried to look up on youtube on any similar problems like this and I really dont know where to start with

[subtle light]

this is the graph that the swimming pool creates

if we want the area, how would we represent that with an integral?

btw i used 6 as r since it said so

[cobalt obsidian]

So its something like this? ∫(from 0 to 6) √36-x^2

[subtle light]

why 0?

we want the entire area

[cobalt obsidian]

oh

[subtle light]

going from 0 to 6 would only give us half

[cobalt obsidian]

-6 to 6 then?

[subtle light]

yep

[cobalt obsidian]

So ill be integrating this and thats the area right? ∫(from -6 to 6) √36-x^2 dx

[subtle light]

yep exactly

[cobalt obsidian]

ohh alright thanks!!

[subtle light]

yw!

[cobalt obsidian]

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[tranquil crown]

I do not understand how this approximation was done.

[tranquil crown]

i dont even know what this method is called where the alphas and betas came about

<@&286206848099549185> throw out any ideas i am very open to them

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[tired trout]

hi, can someone help with this?

[alpine trench]

!status

[lone heart]

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

[tired trout]

I dont know where to begin

[alpine trench]

ok

[tired trout]

I know that i is part of the complex numbers

[alpine trench]

can you subsitute the given information into the formula

[tired trout]

and i am not that good with exponential functions

[alpine trench]

i is a complex number but in this case it stand for the annual interest rate

[alpine trench]

first start by substituting given information into the formula

[tired trout]

Ko = K*(1+i)^n

Ko = K*(1+8.62)^6

or

8,62= K*(1+i)^6

this is the assigment that I translated to english:

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[proud mortar]

Well, hey there can somebody teach me this part ?

I just calculated wrong by the terms

<@&286206848099549185>

[frosty geyser]

Yes, what do you need help with ?

@proud mortar

[proud mortar]

hello

as i sent

[frosty geyser]

Yeah

[rotund bear]

You can't just subtract ratios they are not equal the are proportional

[proud mortar]

oh i see

[frosty geyser]

Yeah, he's correct

[proud mortar]

then what do ya think then ?

[frosty geyser]

@rotund bear You're correct]

[proud mortar]

so either multiple or division ?

[frosty geyser]

no

Addition

[proud mortar]

both equation as i express just now ?

[frosty geyser]

Yes

[rotund bear]

No bro can't add it too @frosty geyser

[frosty geyser]

Dude yes he can

[proud mortar]

huh

when i add it up still unsolvable too for sure

[frosty geyser]

You add then subtract

[proud mortar]

so my a (firsty term)and common diff is doesnt affected ?

[rotund bear]

Ok just for example

$x/y =1/1$
It doesn't mean $x=1$ , $y=1$
And $x+y=2$ it just means $x=y$

[ocean seal]

Dank_Ninja

[rotund bear]

X and Y can be 3

Or any number and x/y=1

[rotund bear]

I would first suggest you to cancel the n from both equations first then multiply the RHS of both equations with a variable like k to make it correct

Yep it's correct

[proud mortar]

what then ? the 439n : 136n duh ?

cant simplify

[rotund bear]

Ho sorry you can't do it like that the you get things like n=0

[proud mortar]

ouh okay nvm as long as you take me to 4:3 lastly

@rotund bear hey u still here ?

<@&286206848099549185>

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[cold panther]

what is this

[cold panther]

π

[frozen scarab]

You're asking what π is?

[cold panther]

,calc π * 1

[ocean seal]

The following error occured while calculating:
Error: Undefined symbol π

[cold panther]

yes

i know what is the value of PI, but i dont know the definition of PI

or from where did it come

[frozen scarab]

Pi is related to the ratio of circumference and diameter

[cold panther]

very thank you

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[raw tartan]

help...

[frozen scarab]

This is a linear relationship

With number of times Eva pedalling being x and the number of times the wheel rotates being y

So when Eva has pedalled 0 times, the wheel has rotated 0 times

Thus, you know (0, 0) lies on the curve

The wheels rotate 1 time for every time Eva pedals, so when Eva pedals once, the wheel rotates once

So (1, 1) is on the curve

Connect (0, 0) and (1, 1) and you will get a straight line

Ask if you have any questions

[raw tartan]

so slope is 1

[frozen scarab]

Yes

This is just the graph y = x

But x is greater than or equal to zero

[frozen scarab]

Yeah that's right

[frozen scarab]

Okay, so what do you know about angles on straight lines?

[raw tartan]

uhm

[raw tartan]

im not even sure

[frozen scarab]

Angles on a straight line add to 180 degrees

[raw tartan]

oh

[frozen scarab]

So what is the angle adjacent to 10b equal to

Adjacent means "next to"

[raw tartan]

OH

erm

8b - 12 + 3b = 10b

[frozen scarab]

I said the angle next to 10b

It would be 180 - 10b

As angles in a straight line add to 180

So now you know the three interior angles of the triangle are 180 -10b, 3b, and 8b - 12

The interior angles of a triangle add to 180

So you can make an equation and solve

[raw tartan]

soo 12

[raw tartan]

?

[frozen scarab]

180 - 10b + 3b + 8b - 12 = 180

[raw tartan]

oh 180

so b=180?

[lone heart]

@raw tartan Has your question been resolved?

[raw tartan]

<@&286206848099549185>

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@raw tartan Has your question been resolved?

[fallen linden]

Look at y as x doubles from 3 to 6

What happens to y?

[raw tartan]

oh dw I got it

[left isle]

if you're done, go ahead and close the channel please

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[gentle jay]

I need help with a question with this if that’s okay

[gentle jay]

Actually it’s okay I got it how do I close it 😭

[thick lynx]

.close

[thick lynx]

you can just ask right away

[gentle jay]

Oh yeah here

I’m not sure if it’s

3F or 9F

Nvm I’m outta time 😭 I got it

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[tall oyster]

Close ur thing if ur done

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[alpine sable]

i need help on number 22

i cannot figure it out

at all

[rich mirage]

i'll help you

oh wait, i misread it, lemme read again

could you take a clearer picture, I can't seem to make out some characters

[shrewd prism]

What have you done

Rewrite the roots as fractional exponents

That’s what I would do first

[alpine sable]

i don’t know what it is

so nothing

[rich mirage]

here you go

[limpid turret]

!nosols

[lone heart]

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

[rich mirage]

oh, sorry, didn't know

[alpine sable]

i don’t think thts right

[rich mirage]

why wouldn't it be?

[alpine sable]

uhm

because

that’s not what the question asked

[rich mirage]

ummmm, then what did it ask?

i might be wrong since idk math terms in english that well

[alpine sable]

do u want me to translate it

[rich mirage]

sure, in romanian

if possible

[alpine sable]

i’ll try

Expresia 6/3x2"x este echivalentă cu ax", unde a și b sunt constante pozitive și x>1. Care este valoarea lui a+b?4

@rich mirage

i think that’s right

[rich mirage]

that's definetly not right

but i checked again

and the ideea is good

i might have made mistakes in basic operations

but besides that, it seems ok

[alpine sable]

oh

.close

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[normal cairn]

my friend is making me doubt myself over this lol

[normal cairn]

The answer is no right?

Theorem: The class of Turing recognizable languages is not closed under complementation.

this is the theorem i used in my answer

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@normal cairn Has your question been resolved?

[normal cairn]

<@&286206848099549185>

[normal cairn]

anyone?

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[normal cairn]

<@&286206848099549185>

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@normal cairn Has your question been resolved?

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@normal cairn Has your question been resolved?

[sick igloo]

hello, can someone teach me how to do question 7c? thanks

[primal fox]

for the first one use the form root B times root B is root A time B

it also applies for secount one

** secound

for third one we can write fourth root 64 as 64 power 1/4 do the same for the denominator

if you know exponents and powers

thier is a rule a power m / a power n is equal to a power m - n remeber the base should be same

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[finite swift]

I'm trying to complete this Optimization exercise but I'm failing somewhere, trying to understand where I made the mistake(s)...

[vapid shuttle]

SDP

[finite swift]

max: 10 x1 + 13 x2 + 27 x3 + 8 x4 + 14 x5 + 20 x6 + 42 x7 + 32 x8 + 60 x9 + 35 x10;

// Resource Limits Constraints
4 x1 + 4 x2 + 4 x3 + 5 x4 + 6 x5 <= 100000;                           // Wheels Constraint
12 x1 + 22 x3 + 8 x4 + 12 x6 + 8 x7 + 4 x8 + 2 x9 + 10 x10 <= 100000; // Bolts Constraint
2 x4 + 4 x5 + x6 + 4 x7 + 7 x8 + 4 x9 + 8 x10 <= 90000;               // Metal Constraint
20 x1 + 13 x2 + 2 x3 + 8 x4 + 5 x5 + 2 x6 <= 200000;                  // Plastic Constraint

// Minimal Production Constraints
x1 >= 200;
x2 >= 135;
x3 >= 270;
x4 >= 80;
x5 >= 45;
x6 >= 120;
x7 >= 420;
x8 >= 72;
x9 >= 460;
x10 >= 83;

// Models Constraints
x4 + x5 + x6 <= 2; // These 3 models cannot be produced together
x1 <= x3;          // Model 1 can be produced only if model 3 is too
x7 + x8 = 1;       // Either model 7 or model 8 must be produced, not both

This is my solution but apparently the model isn't feasible

I'm not really sure about the "Minimal production constraints" TBH because they're not even seen as constraints at all... But I have no idea how I could write those otherwise

[finite swift]

?

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[alpine sable]

so i was solving this problem but im stuck on that step idk what should i do about |x| !!

so

x/|x| is between -e-1 and e - 1

@sour verge

[sour verge]

First off, if you did that, you would need -e-1 < x/|x| < e - 1.

[alpine sable]

yes

[sour verge]

But it's not really necessary, what's the value of x/|x| on like (a,0)?\

[alpine sable]

right

-1

wait im confused

which interval is

(a,0)

[sour verge]

Any interval before 0

[alpine sable]

one moment

having food 😅 sorry hard to type lmao

[sour verge]

Ok, so you want to be sure that given some epsilon, you can always find some interval (-delta, 0) such that your function is close to -1

But in any such interval, what is the value of x/|x|?

[lone heart]

@alpine sable Has your question been resolved?

[alpine sable]

ughh like depends on the possible values of x ig 😅 can't think of anything else

wait

$x/|x| = x|x|/|x|^2$

[ocean seal]

Gary

[alpine sable]

$x/|x| = x|x|/x^2$

[ocean seal]

Gary

[sour verge]

Just as a function, what does it look like?

[alpine sable]

$x/|x| = |x|/x$

[ocean seal]

Gary

[sour verge]

I mean the graph

[alpine sable]

let me graph this i have not worked with this function

before

oooo

thats interesting

[sour verge]

Ok, so now if you consider an interval (-delta,0), does it really matter what x is?

[alpine sable]

nopeee

[sour verge]

So that means that whatever delta you choose, |f(x) + 1| = 0, since f(x) is always -1 on (-delta, 0)

[alpine sable]

yess

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[jovial ferry]

What does it actually mean to "multiply" vectors?
Because in the usual sense, multiplication is the number of times you add something to itself right? Like 2*3 = 2+2+2..
But what does it mean to multiply vectors. (I'm talking about the cross product.) How can you add something with a direction to itself n number of times where n also has direction??

[unborn plover]

i mean
all operations are somewhat nonsensical when you think about it
the idea that multiplication is repeated addition starts to break down when you consider multiplying by decimals

[jovial ferry]

I dont think it does, could you please provide an example?

wait nvm

[unborn plover]

oh sorry multiplication isn't too bad actually

but think of exponentiation

what does 2^e mean, really

it's not multiplying 2 by itself 2.718 times

[jovial ferry]

huh..

[mortal trellis]

well I mean, tell a child that you are adding something 1.2472847294... times to itself and it will also tell you that makes no sense

you are just very used to that idea

[jovial ferry]

What do operations mean then?

Oh god

[unborn plover]

they have very terse formal mathematical definitions that aren't useful for most people🤷‍♀️

we just accept they work and do useful things

[jovial ferry]

I mean- they kinda are useful

[mortal trellis]

that being said, the cross product does have some kind of intuitive understanding

it just has nothing to do with the usual multiplication

we just call it a product because it has some of the same properties as multiplication

[unborn plover]

oh true i kinda took this in a strange direction

[jovial ferry]

Could you please explain the intuitive understanding?

[unborn plover]

but yeah the cross product is just another operation

[unborn plover]

of what exactly

[mortal trellis]

if you have two vectors it gives you an orthogonal vector to both of them

[jovial ferry]

of this message

yeah and why does that happen

[mortal trellis]

well thats a different question

[jovial ferry]

I console myself by telling myself that there are infinite operations out there, but we've only discovered/invented the ones which humans are capable of understanding and which we find use of in our lives.

[mortal trellis]

pretty much

[unborn plover]

there are absolutely infinitely many functions

and an operation like a x b is just a weird notation for f(a,b)

[jovial ferry]

Hmm

And cross product is also a function that we found out to be useful hence we gave it a name?

[unborn plover]

pretty much

[jovial ferry]

makes sense

[unborn plover]

but yeah this is a good question to have lmao
i remember not really enjoying linear algebra becuase i was very caught up with things like "what the (&3&?9 is a determinant?"
before accepting it just sorta does stuff

[mortal trellis]

the determinant is a pretty crazy thing tho

[unborn plover]

oh you probably haven't done lin alg yet mb

[jovial ferry]

I was always in trouble in high school for asking "why" or "how"

Math is my fav subject and I can't help wanting to question everything and dive deeper ig

Math is the only subject that allows that imo

[jovial ferry]

I didnt yet, its on my schedule but not yet 😅

Anyway, thank you @mortal trellis and @unborn plover

Had fun talking to y'all :D

Ok how to close

/close

[unborn plover]

,close i think? idk lmao

!close

!done

[lone heart]

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

[unborn plover]

ah

[jovial ferry]

ty m8

.close

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[fallow wadi]

https://media.discordapp.net/attachments/903463352582434866/1232729054877188198/image.png?ex=662b2ca5&is=6629db25&hm=c833b4726e0a824a27274f9622fc5467c7afdbcbd7a6c08f7c772d99a3731576&=&format=webp&quality=lossless

[fallow wadi]

need help w this

i got eigen valujes n vectors

[valid merlin]

Pretty sure u just shove it into the formula. x’(t) = e^(\lambda t)v

Sorry about no typesetting, I’m typing on an iPad and it would take forever to typeset it lol. I hope it makes sense

[fallow wadi]

:D it doesnt really help me

[valid merlin]

My bad, this explains it better than I can type on an iPad lol

I have the link if you want

It’s fairly straightforward to dedicate using I think it’s called Euler form of complex numbers

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[lone heart]

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[granite iron]

I need help with a down payment and savings math problem

[granite iron]

2. At this savings rate, will you have accumulated sufficient funds to purchase a $500,000 house within the next 5 years? Please keep in mind that this would include obtaining a mortgage, and a 20% down payment is typically required. Explain your reasoning by calculating the amount of savings in the 5 years, then comparing it with the required 20% down payment.
   690 is put into savings ever month

total after 5 years is 41,400

[gritty bramble]

what 💀

[granite iron]

soory wrong paste

[gritty bramble]

💀

[granite iron]

thats for a college assay i'm struggling with

[gritty bramble]

ah

[near temple]

Well what is the down payment?

[granite iron]

wouldnt the math be %20 x41,400

%20 percent

[near temple]

Not quite, that's 20% of your savings

[granite iron]

oh

would it be %80