help-0

[rigid wind]

lol

disgusting

[remote heron]

for some ungodly reason

[alpine sable]

here is a better format

it just says a bit less lol

[remote heron]

looks right? id have to sit down and check it

[alpine sable]

its the answer guide

im trying to understand it

[remote heron]

whats your confusion here

oh

which part?

[alpine sable]

well i get the transformation and how to switch things over and set everything to y

and i understand how to set the limits of 0 to z and 0 to z-x

i can do the intergration just fine from there and i get int 0 to z: e^-x-e^-z

but i get lost after that part when it comes to the second intergration

sorry im in zoom university, so im trying to teach myself here and im getting the wrong answer and i cant figure out whats going on after i bought the answer guide even

[remote heron]

it kind of looks like you never evaluated and just dropped the integral?

that part is muddled to me

[glass lichen]

You also factored out something when you couldnt

[alpine sable]

alright. so im just all wrong then. good to know hah

im close to giving up. this is too much trying to do this without a teacher

well thanks for the help.

ill just turn this in and get another awful grade and get the solutions afterwards

¨cant believe im wasting my time with this

[remote heron]

:(

i have to walk to campus

i can try to help after that tho

[alpine sable]

haha no stress about it man. just ping me or dm me 🙂

[remote heron]

maybe talk a walk or make some tea

[alpine sable]

im gonna put my kids to bed 😛

[gray oxide]

Is 3 not considered a function?

Becuase it is a constant

[glass lichen]

It is

[gray oxide]

So where did I go wrong?

[glass lichen]

Used quotient rule on a power function

And 3(3x^2) isn't 3(x^2)

[gray oxide]

Oh I didn't know I wrote that lol srr

[glass lichen]

But yeah 9x^2/9=x^2

[gray oxide]

Which line are you talking about the second or third?

[late ivy]

Can anyone help me w/ this quick proof

[glass lichen]

2nd to last

[gray oxide]

Where did I write 3(3x^2)?

[glass lichen]

2nd to last line...

3x^2*3

[gray oxide]

Yea I can find that

[glass lichen]

Yeah then you only factored one of 3s out and write you had done both

[gray oxide]

But not not the other thing you wrote

Ok thank you cya :)

[alpine sable]

if you can give me some constructive feedback i would greatly appreciate it. 😛

[cyan basalt]

I need help

Prove that for all 𝑎, 𝑏, 𝑐 the inequality
𝑎4 + 𝑏4 + 𝑐4 ≥ 𝑎2𝑏𝑐 + 𝑎𝑏2𝑐 + 𝑎𝑏𝑐2

how to prove it

[crisp grove]

do you mean $a^4+b^4+c^4 \geq a^2bc+ab^2c+abc^2$?

[ocean seal]

Ryuzaki

[cyan basalt]

yeah

I dont understand how to solve it

[crisp grove]

$a^2bc+ab^2c+abc^2 = abc(a+b+c)$

[ocean seal]

Ryuzaki

[crisp grove]

first use GM <= AM on abc

[cyan basalt]

what

[crisp grove]

doing it the other way around

$\sqrt[3]{abc} \leq \frac{a+b+c}{3}$

[ocean seal]

Ryuzaki

[crisp grove]

also I assume a,b,c >= 0

[cyan basalt]

Did you accidentally mix them up?

[rigid wind]

a^4 + b^4 >= 2a^2b^2
then (ab)^2 + (bc)^2 >= 2ab^2c

probably an easier way to go about it

[cyan basalt]

I do not understand the procedure

[rigid wind]

what does $(a^2 - b^2)^2 \geq 0$ tell you (expanding it)

[ocean seal]

Vee

[cyan basalt]

i dont figured it out

[rigid wind]

i'm walking you through it

[elfin talon]

I’m not good at wording proofs but:
Angle bcd = 90 (by definition)
Angle bad = 90 (by definition)
Angle dca = 1/2bcd (given)
Therefore angle dca = 45 ———>(1)
Angle cad = 1/2bad (given)
Therefore angle cad = 45 ———>(2)
So angle cad = angle dca

[rigid wind]

expanding $(a^2 - b^2)^2 \geq 0$ what do you get?

[ocean seal]

Vee

[rigid wind]

since i gtg, another hint for you is notice how you can rewrite $2a^2b^2 + 2b^2c^2 + 2a^2c^2$ as $\left((ab)^2 + (bc)^2\right) + \left((bc)^2 + (ac)^2\right) + \left((ab)^2 + (ac)^2\right)$

[ocean seal]

Vee

[rigid wind]

and $(ab)^2 + (bc)^2 \geq 2abbc = 2ab^2c$

[ocean seal]

Vee

[rigid wind]

@cyan basalt

[alpine sable]

Is this right?

[raw shard]

@alpine sable as someone who only knows the basics of integration i would say yes

since it doesn’t have a variable in its exponent

so it’s not being changed

[alpine sable]

i hope so. i dont wanna get this right by blind luck and wrong assumptions 😆

[raw shard]

no variable means it doesn’t change

[sacred mirage]

Is this right?

[alpine sable]

S_18 = 28 + (28-1) + ... + (28-17) right

you should have d = -1 because when going up, the number of cans decreases by 1

so S_18 = 18/2 times (2*28 - 17)

@sacred mirage

[sacred mirage]

I have 2 answer to that

Is that both correct?

[alpine sable]

everything is correct except for that at first you wrote as if d = 1 even though d = -1

[alpine sable]

What's the question?

besides that

[sacred mirage]

This is the question

[alpine sable]

each of the solutions

[alpine sable]

Yeah, you can do that by that process too.

Just you displaced a + (n-1)d by a n

[sacred mirage]

Wait i can’t understand

[glass lichen]

@shell heron stop shitposting.

[sly mantle]

b&

[sacred mirage]

Omg i cant get it

[alpine sable]

Oof.

You don't need to

[sacred mirage]

What i suppose to write?

[alpine sable]

what you wrote is correct

dw about what the guy is saying

It's just that your answer is correct

Both ways you can follow

[alpine sable]

Hmm I see

[sacred mirage]

Oh okaay should I change anything?

[alpine sable]

yes, one small detail

in the first picture, when you wrote S_18, there should be (18-1) times -1

[alpine sable]

The 1 in the second row will be -ve

other than that it's good

[sacred mirage]

Okaay thank you!

[marble sparrow]

hi could someone help me with discrete mathematics?

i'm having trouble understanding how we arrived at the 4th bullet point

how did we get 2 r_i+2?

and r_i+1 + r_i+2

[dreamy cedar]

Ignore whatever ping you just got

was a troll

[marble sparrow]

yeah it's alright

[small bear]

Your question is how did they set up the inequality?

[tight sonnet]

Can someone remind me how changing the bounds of the integral works and how we know what to change them to?

[marble sparrow]

yes

[small bear]

r_i = k * r_(i+1)  +  r_(i+2)
   >= r_(i+1)  +  r_(i+2)          (since k >= 1 from bullet point 3)
   > r_(i+2)  +  r_(i+2)           (since r_(i+1) > r_(i+2) from bullet point 2)
    = 2 * r_(i+2)

In other words,

Since k >= 1, we can multiply by r_(i+1) to get
      k * r_(i+1) >= r_(i+1)    must be true

[marble sparrow]

ohh okay now that makes sense

[small bear]

Another note would be that r_(i+1) is positive, but that is obvious

[marble sparrow]

okay i get it now

how do we use that fact above to reach this conclusion?

[void patio]

can someone help me with a real life problem im trying to figure out?

we have a lawnmower thats about 75 pounds, my brother wont mow the lawn for my mom because he says it's too heavy even though i've seen him lift stuff that's about 25 - 30 pounds, the lawnmower has wheels and he's not lifting it so i figured he'd have the ability to, i just need to know how i would do the math to figure out how to prove that he can do it and is just being lazy

[wary stream]

You don't need math to prove it. Just observe if he can push it. Experimental data. Set up the mower, tell him to push it, if he can you proved your point, if he can't he proved his point

[void patio]

he could easily just not put effort into pushing it and i cant prove it that he's lying about it

[jolly stone]

you need to find coefficient of friction between lawnmower and the floor, and calculate the how much static friction it is

given that you know that your brother can lift 25-30 pounds, what's the acceleration of the stuff when he lifted? you can calculate the required force to list 25-30 pounds of object with acceleration: so brother's minimum force F = mg [object] + ma [with acceleration a] = m(g+a)

then for the lawnmower of mass M, find out coefficient of static friction mu_s (by actually trying to push that horizontally), so minimum force to move lawnmower F_min = mu_s * N = mu_s * M * g

but note that there is an actual angle of the handle of lawnmower to consider: pushing lawnmower with angle theta from ground, so F_min_angle = F_min * sec(theta) = mu_s * M * g * sec(theta)
angle of 90 degrees mean you're pushing vertically to make your lawnmower move horizontally, which is weird
so if your brother complains that it's too heavy, try making less angle

[brave drift]

need help with this geometry question

Suppose r(140°, P)(A) = B and (R←→∘R←→)(A) = B, what is m∠CPD?
PD PC

[unkempt thorn]

please help

[oak chasm]

@unkempt thorn Sorry, this channel is busy.

[brave drift]

u have any idea to that question rex

[oak chasm]

I don't know what the notation means.

[urban lily]

channel free?

can someone tell me how to work with graphs like these to get eqns of tangents/normals to the curve given?

[dire whale]

so first, which expression is the gradient of the curve at point C

and what expression would describe line L

[dusty willow]

Is this TFTT?

Just intuition here

[placid zinc]

Not certain what you're asking. What's TFTT?

[dapper spear]

@placid zinc u good at finance maths

@placid zinc can u help me out

Plz

[topaz scaffold]

Please don't ping people, just send the question and wait to see if anyone knows the answer

[granite lily]

Can someone verify if I did this correctly

[placid zinc]

Gotta hate when they do stupid stuff like ReAcTiOn TiMe

I don't know what physics you learn by including that

[granite lily]

Idkk man haha just my physics teacher said it would help so I won’t include it for time

[placid zinc]

I think you can break it into two parts:

• Before reacting, they drive a constant 95km/h for 1s
• After reacting, where they start to decelerate

I say I think because it isn't super clear how the reaction time should be included

[granite lily]

Dw about it brother lol just my process of thinking it’s not mandatory

[placid zinc]

I'm not super clear on what you did. Did you leave the reaction time out?

[granite lily]

And I didn’t include it for my equation

Nope the reaction time is not in my equation

[placid zinc]

Gotcha. Yeah the logic looks good

[granite lily]

Make sense that it would take 43.5m to stop eh?

[placid zinc]

,w 26.39^2 / 16

[ocean seal]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Kaynex#7520

[placid zinc]

Yeah that's right

[thorn forge]

Hey, if any of you is good with kinematics, can you help me solve this problem, I'm only given 2 values and need to solve the problem but I don't know how

If you can just point me in the right direction that would be great

[abstract fractal]

Do you know the formula for projectile motion?

[thorn forge]

No but we should be able to solve it with just the kinematic formulas

[abstract fractal]

That's what I mean

The formula for y(t) or s(t) or however you denote it

[thorn forge]

I'm trying to find either the time it takes to reach velocity of 0, or initial/final velocity and the rest will fall into place, the formulas I have are those

[abstract fractal]

The third formula was the one I was thinking of

[thorn forge]

Problem is we do not have all the values to derive the formula

The 40m isn't the total distance

And the 5 seconds aren't what it takes for one part

So we don't know the delta x nor the t

[abstract fractal]

Δx is x_f - x_0. x_0 is 40, do you know what x_f is when it hits the ground?

[thorn forge]

No, all the information I have is that the starting position for the throw upwards is 40m above ground and that it takes 5 seconds for the whole thing

No other information apart that, if I knew the final velocity it would have helped

[abstract fractal]

What is the x value when the ball hits the ground?

[thorn forge]

Ground = 0

[abstract fractal]

That's x_f

[thorn forge]

But we don't know from what height the ball is dropping nor in how much time

If I had the time I'd find the height using g, or if I knew the height I'd find the time using g again

[abstract fractal]

The ball is being thrown upwards at some velocity from a height of 40 m. We know the total trip is 5 seconds. We know that the Δx from those 5 seconds is 0 - 40 = -40. Plug those in, and there's only one unknown: the initial velocity, and you can solve for it

[thorn forge]

Isn't the delta x supposed to be from top to bottom, and not from 40 to 0?

Wait let me at least give it a try

What I got is that initial velocity is -16.525m/s

I think I messed up somewhere

[abstract fractal]

Let me work it out myself real quick

In the meantime, can I see your working?

[thorn forge]

I scratched up most things

I can tell you what I tried though

[magic badger]

Hello, i'm new for this server
i want a help with this exercise
Z = {w ∈ ℤ : w ≥ - 5 y w < 7 y (w)² is par}
Please

[abstract fractal]

Try asking in another channel, this one's currently active rn

[thorn forge]

I tried working it from down upwards trying to find how much time it'd take it to freefall 40m, and the rest of the time divided by 2 for the upwards and downwards motion but I don't think that works

I also tried to write it as one single formula

Where you have the up motion, the down motion to the same height, then the rest of the freefall

[abstract fractal]

If you plug in Δx = -40 and t = 5, you should get -40 = -4.9(5²) + 5v0

[thorn forge]

((Vo-9.81t) + (0+9.81t)) + (-Vo+9.81(5-2t)-40)

I plugged in 40 instead

Then it should be 16.525m/s

[abstract fractal]

Yes

[thorn forge]

So that's the velocity upwards when we throw the ball?

Wait let me try to work it up from there and I'll tell you how it goes

The maximum height I submitted was wrong

What I did is find the time it takes the initial velocity -9.81t to become 0

[abstract fractal]

What did you submit?

[thorn forge]

Then I searched the distance it would travel with the initial veloicty and -9.81 times that time

I wrote 59.57 (40+19.57)

m

But just by looking at it it doesn't feel right

[abstract fractal]

I didn't get that. Here's what I did. You know v² = v0² - 19.6 Δx. v = 0 at the max, so you can solve for Δx

[thorn forge]

Did you get a meter and something?

Or did I do something completely wrong

I'm either really bad at this or just tired from doing different physics problem all day and I'm getting tired

19.6x=16.525?

[abstract fractal]

0² = (16.525)² - 19.6 Δx --> 0 = 273.076 - 19.6 Δx. What do you get when you solve for Δx?

[thorn forge]

13.92?

Oh okay that's right

Oh I think I just understood things now

Let me do the second part and that will confirm if I understand

[abstract fractal]

Be careful, that's not the max height above ground, that's the max height above your initial position. You need to add an extra 40 to get the height above ground

[thorn forge]

Yeah I did

My problem was in the calculation I didn't square the initial velocity

[abstract fractal]

Pog

[thorn forge]

And before that I was confused at why delta x would be 40, because in my head the delta x would have been from highest point to 0, with the highest point unknown back then

[abstract fractal]

Δx is the final x minus the initial x. The final x is 0 and the initial x is 40, so you have 0 - 40 = -40

[thorn forge]

The way I saw it at first was I had to divide the problem into segments, and find the freefall first and thus from 0 to the highest point

[spice oyster]

Hey I can't figure out why I got this wrong
-20x^(5)y^(4)
-4x^(3)y^(7)
I got this
5x^(2)
y^(3)
Can anyone help?

[abstract fractal]

That looks right to me

[spice oyster]

That's what I thought, but it was marked wrong so I'm probably just going to email my teacher

[vestal hollow]

Can someone explain where this ln(C) came from?

Shouldn't it just be +C?

ln(C) is still a constant so I guess it doesn't really matter but idk

Just feels weird

I guess the reason theymay have done it was so they can get the solution to look nicer

Since instead of a +C at the end the C is inside the ln

Is that why or is there a better reason for why the ln is there?

[dusty willow]

1. T
2. F
   Etc

[fresh relic]

Anyone know how to solve this?

[small bear]

What have you tried?

[fresh relic]

I tried to find C

and I think it is 1

but then from there I get lost

[small bear]

How did you arrive at that?

Can you perhaps show the work you did?

[fresh relic]

Well because if y =1

and ^x=1

then a would get canceled out

and then c = 1

[small bear]

Sorry?

Why would it cancel out

[fresh relic]

im so confused man

i dont know what im doing

i need some help

[small bear]

No you are on the right track

so we substitute x=1, y=1

[fresh relic]

yeah

[small bear]

we get 1 = c*a^1

[fresh relic]

Yeah

thats where I think I mess up

[small bear]

but why do you think a^1 = 1 ?

a^1 = a

[fresh relic]

so then its just 1 = ca?

[small bear]

Yes, that is our first clue

[fresh relic]

alright

[small bear]

What would we get for the other point?

[fresh relic]

3 = ca^2

[small bear]

Alright, so now we need to solve

1 = ca
3 = ca^2

do you notice anything similar, maybe a way to solve for one of the variables?

We can also rewrite the second equation like this

1 = ca
3 = ca^2 = ca*a

Any ideas?

[fresh relic]

I am drawing blanks

[small bear]

1 = (ca)
3 = ca^2 = (ca)*a

look what I put in brackets

[fresh relic]

a = 2?

[small bear]

No, not quite

See how the (ca) terms are the same

we can substitute that value in, ca=1 into the second equation

3 = ca^2 = ca*a = (1)*a = a

Does that make sense?

[raw shard]

@small bear i found the answer, can i try to explain it by any chance?

i won’t give it away instantly

[small bear]

Go ahead

[raw shard]

ok

[alpine sable]

I can prove that anything divided by 0 isn’t undefined

[raw shard]

so we have f(x) = y = ca^x, and this has to satisfy (1,1) and (2,3)

so for x=1, we have f(1) = ca = 1

[fresh relic]

none of this makes sense to me

[raw shard]

this means that either c = 1/a or a = 1/c

@fresh relic what do you need help on?

[fresh relic]

i just dont get anything ur saying

[raw shard]

how should i explain this simpler?

oh

well we start with the equation f(x) = ca^x, right?

[fresh relic]

why are these terms the same?

[fresh relic]

yeah

[raw shard]

this has to be valid for (1,1) and (2,3)

so this has to mean that f(1) = 1

and f(2) = 3

do you get it so far?

[fresh relic]

yeah

[raw shard]

ok so we start with f(1)

f(1) = ca^1 = ca

this means that either c = 1/a, a = 1/c, or a and c = 1

do you want to know why a and c = 1 will not work?

should have said do you know

[fresh relic]

so wait

why isnt it a and c = 1

[raw shard]

i will explain that now

so f(2) = 3

remember that f(x) = ca^x

if a and c = 1, f(2) = 1*1^2 = 1

so a and c = 1 won’t work

[fresh relic]

Alright

[raw shard]

ok

so now we will assume that either a = 1/c, or c = 1/a

[fresh relic]

Alright

[raw shard]

when i did this on paper i assumed that c = 1/a, so we will start with that

f(1) = ca^1 = ca = 1, f(2) = ca^2 = 3

so f(1) now equals a^1/a

which equals 1

so this works so far

now for f(2)

f(2) = a^2/a = 3

can you take a guess on the value of a?

[fresh relic]

so it would be 4

[raw shard]

no

4^2/4 = 4

[fresh relic]

3

[raw shard]

what value of a satisfies a^2/a = 3

yes

so now we test these on f(1) just in case

also this means that c = 1/3

f(1) = ca = 3/3 = 1

f(2) = ca^2 = 3^2/3 = 3

therefore a = 3 and c = 1/3

sorry if i confused you anywhere

@fresh relic did you get the answer?

[fresh relic]

so its 1/3(3)^x?

[raw shard]

yes

f(x) = ca^x = (1/3)*3^x

a = 3 and c = 1/3

or i guess you could say c = 1/a

[fresh relic]

still a little confusing but

it helps a llittle

thank you

[elder viper]

Hmmm ok

so it's more of a physics question but the other server is just not where it's at

"Coming back from the donut merchant, a policeman overhears a thief sitting behind the wheel of his police car. The criminal flees by activating the siren, the frequency of which is 400Hz: at 36 km / h, he goes directly towards a wall which reflects sound waves very well. The policeman remains motionless and quietly eats his donut. Determine the two frequencies received by the police officer as well as the beat frequency."

This is all I have so far,

the answer should be

f' = 388.6 Hz and 412.1 Hz; f_b = 23.5 Hz

I just have no idea how to find the two other numbers

uh.... I think that I just need to do it in three steps but that's kind of dumb, I'll try something

weird emoji
anyway

<@&286206848099549185>

[elder viper]

Yea I think I found my mistake smh

yep

[quiet onyx]

143*879+ (763 times 496)-2

[fresh relic]

This is false right?

[oak chasm]

@fresh relic Why is it false?

[soft zodiac]

How can I solve this? I have a TI-84. I know there's more than one answer so I can't use arcsin

[oak chasm]

Yes, you can use arcsine.

That will give you the reference angle.

Then you can get the other angle from that.

@soft zodiac

[soft zodiac]

yeah but how do I get the other angle?

[oak chasm]

sin(π - θ) = sin(θ)
cos(2π - θ) = cos(θ)
tan(θ - π) = tan(θ)

Take the arc functions of both sides, leave the work undone on the right.

π - θ = arcsin(sin(θ))
2π - θ = arccos(cos(θ))
θ - π = arctan(tan(θ))

Solve each for θ.

θ = π - arcsin(sin(θ))
θ = 2π - arccos(cos(θ))
θ = π + arctan(tan(θ))

So, the arcsine will give you both θ₁ and π - θ₂.

The arccosine will give you both θ₁ and 2π - θ₂.

So, let's say you get 0.3 as the arcsine.

θ₁ = 0.3
π - θ₂ = 0.3

So, θ₁ is 0.3 and θ₂, after a bit of algebra, is π - 0.3.

But the arcsine is probably not 0.3, so use what you actually get.

[soft zodiac]

okay

and i can use the same logic for arctan to say it's arctan(0.3) and pi + arctan(0.3)?

[oak chasm]

No, it's a bit different.

Here's more in detail.

Oh, yes, you're right.

tan(θ - π) = tan(θ)
arctan(tan(θ - π)) = arctan(tan(θ))
θ - π = arctan(tan(θ))
θ = arctan(tan(θ)) + π

tan(θ) = tan(θ)
arctan(tan(θ)) = arctan(tan(θ))
θ = arctan(tan(θ))

[raw shard]

@oak chasm i really like how in depth you’re going with your explanation

[soft zodiac]

ah okay i see thank you for explaining

[oak chasm]

It ate what I typed.

Oh, never mind, I edited instead of copied.

sin(π - θ) = sin(θ)
cos(2π - θ) = cos(θ)
tan(θ - π) = tan(θ)

Take the arc functions of both sides, leave the work undone on the right.

π - θ = arcsin(sin(θ))
2π - θ = arccos(cos(θ))
θ - π = arctan(tan(θ))

Solve each for θ.

θ = π - arcsin(sin(θ))
θ = 2π - arccos(cos(θ))
θ = π + arctan(tan(θ))

So, if you know the formulas at the top, you can get what the other angle is.

Hmm, it's simpler than that even.

Let's see.

@soft zodiac Here's a simpler way:

sin(π - θ) = sin(θ)
cos(2π - θ) = cos(θ)
tan(θ + π) = tan(θ)

The arc function will get you θ. So, then you do:

sin(π - θ) = sin(θ)
The other angle is π - θ.

cos(2π - θ) = cos(θ)
The other angle is 2π - θ.

tan(θ + π) = tan(θ)
The other angle is θ + π.

[soft zodiac]

That makes sense thank you 🙂

[stiff eagle]

Can someone explain why this is the case

The irreversible step part

Not sure if that’s the right answer but I believe the claim is true

[raw shard]

@alpine sable channel already has a question asked

aka channel is currently in use

[alpine sable]

my bad, already took it down thank you

[raw shard]

@alpine sable it’s fine, #help-6 seems to be open

[alpine sable]

ye i posted in #7

[raw shard]

ok

[arctic panther]

good evening, can someone help me with my homework?

they are set problems

[placid zinc]

That's a very odd way to write them. Did you write them yourself?

A = {x/3 | -3 ≤ x ≤ 15, x ∈ Z}

[arctic panther]

I speak Spanish so I translated some parts haha, that's how it is in the book

[fierce fossil]

idk man, this is insane

[placid zinc]

Gotta get those FBDs going

It's just a lot of steps. They're all simple, but there's a lot of them

[alpine sable]

why are these red ones switched for product of sums

for example shouldnt it be X11X instead of X00X?

[night sigil]

1/125

[gloomy wharf]

im so confused

on this

[placid zinc]

Start writing everything in P() notation

Note that 620 shoe laces doesn't matter

[quartz prawn]

1/2 are flat, but we want to only have the flat black ones, so subtract out the flat white ones (1/4*3/5)

so G

[steady meadow]

?

[raw shard]

@steady meadow 2x = 75+y

you’re given 2x = 96

so if 96 = 75+y, what’s y?

[steady meadow]

21?

[raw shard]

yes

[steady meadow]

i already submitted it

thank you thoo<3

[raw shard]

you’re welcome

[alpine sable]

need help

[karmic yarrow]

let's say I have the number n which is any natural number

a factor of n could only be a number that is less than or equal to n right?

the reason I ask this is cause I know for any number, 1 is a factor but idk if it works the other way around.

[strong furnace]

ye

[karmic yarrow]

so the only number that 1 has a factor for is itself then

[strong furnace]

that sentence don't make sense to me, are you saying that the only factor for 1 is 1 or are you saying the only numbers for which factor is 1 is 1 ?

[karmic yarrow]

the only factor for 1 is 1

[strong furnace]

sure that is true

[karmic yarrow]

okay, thanks

[rugged elbow]

the answer is 240 right?

[hybrid moon]

What’s ur work

[fierce bluff]

can someone help with this question?

[solemn juniper]

@fierce bluff what's giving you issue?

[fierce bluff]

i just dont know how to approach this

[solemn juniper]

Do you know how to represent a 3.5% increase?

[fierce bluff]

yeah its just 1.035 of A

[solemn juniper]

Ok, so after 1 year it's 1.035A. To increase this by another 3.5%, you just multiply it by 1.035 again

So after 2 years the salary is 1.035^2 * A

Does that make sense?

[fierce bluff]

yeah

so doubling time formula

[solemn juniper]

So after 6 years, how much will it be?

[fierce bluff]

i got 1.229

[solemn juniper]

,calc 1.035^6

[ocean seal]

Result:

1.2292553263445

[solemn juniper]

Seems good

But remember this is all multiplied by A

[fierce bluff]

yeah

thx

[solemn juniper]

Np

[mint eagle]

could someone explain how {∅} is a subset of {{∅}}} is false

[marble sparrow]

{∅} basically means that you have an empty set. Think of this set like a box. And your box contains nothing. But {{∅}} basically means, you have a box and inside that you have another box. But that second box is empty.

A box which is empty --> {∅}
A box containing another box which is empty --> {{∅}}

Since they aren't the same, it's false

[mint eagle]

cool thx

[marble sparrow]

https://youtu.be/GqvX4Fi0jbM

you could watch this video as well about empty sets

[ancient bear]

what am I doing wrong?

ah I found it. 4th line from bottom, 27u^3 instead of 9u^3

[flat vale]

what do we call the lowest value of a domain?
e.x. [5, inf), 5 is the lowest value here

[placid zinc]

There is no common term for "minimal value of a set" since most don't have one

We often use "Infimum" for the "lowest that any real set tends toward"

So the infimum of [5, inf) is 5
And the infimum of (5, inf) is also 5

If there is an obvious smallest element, could just say "smallest element"

[flat vale]

@placid zinc thanks!

[stark trail]

$\sum_{n=a}^bk=k(b-a+1),b>a\text{ for }k\text{ constant}$

[ocean seal]

Muzan Jackson

[flat vale]

@placid zinc infimum of a function is the lowest value of the range?

not the domain?

[placid zinc]

Infimum of a set is the lowest value that set "tends toward"

[amber iron]

why is the derivative of a smooth curve always positive?

[placid zinc]

Infimum of a function doesn't make sense

[placid zinc]

It is not. Consider 1/x

[raw shard]

@stark trail the user left so no need in answering the question

[flat vale]

is there a common word for lowest value of x for the function?

[placid zinc]

Infimum of the domain of f

[amber iron]

I don't get why x(t), y(t), z(t) can't be something like t^2 (smooth) and thus have a derivative 2t, which means at t = 0 ds/dt = 0

[stark trail]

oof

[placid zinc]

Why not?

[flat vale]

ight, thanks

[amber iron]

coz it says this

??

[placid zinc]

I agree with you. "Resting" is an acceptable curve

[timber wren]

With steps guys

[amber iron]

yeah maybe ds/dt being 0 at a certain point is irrelevant

coz its only 1 infinitely small point

[placid zinc]

I think an important thing to realize is that ds/dt is never negative

[timber wren]

..

[placid zinc]

Your particle moves, ds/dt is positive.

[latent gulch]

How this equation can be solved? I know how to solve it if I have only x but I am not sure how it solved when there is more than one variable

$\nabla^2 \phi(r) = B^2 \phi(r)$

[ocean seal]

Nada

[sly mantle]

expand lhs using the expression of the laplacian in your coordinates

[alpine sable]

(x+4)² + (x-1)(x+2) = ?
how do I solve (x-1)(x+2)

[vale wigeon]

do you mean simplify?

perhaps you could expand it using something called the distributive law.

[alpine sable]

how

[cerulean wolf]

double brackets stuff in primary

[alpine sable]

Someone tell me how can I crack advanced questions.

I have been trying for 2 months but nothing is working out for me.

[alpine sable]

how

[vale wigeon]

...wait, do you not know what the distributive law is?

[alpine sable]

yes

[vale wigeon]

"yes i know" or "yes i don't know"

[alpine sable]

yes i know but how do I get rid of the • in the middle

[vale wigeon]

what do you mean

okay, let's try this

how would you expand a*(x+2)?

[alpine sable]

(ax+2a)

[vale wigeon]

great

how replace a with (x-1).

[alpine sable]

(x2-2)

?

[vale wigeon]

no

do you know what the word "replace" means?

all i want you to do is to replace a with (x-1) in the expression ax + 2a.

[alpine sable]

idk

but is (x-1)(x+2) = (2x-2)?

[vale wigeon]

no it isn't.

this will be a long shot, but maybe you have seen that dreaded FOIL mnemonic before?

[alpine sable]

no

[vale wigeon]

skittlechan please do not do this

do not give out answers and especially do not give out blatantly wrong answers

no, the answer is not +2.

the answer is not even a number

but an expression

[cerulean wolf]

what on earth is going on here

[vale wigeon]

what's going on here is i'm running up against clar's ignorance of such basic things as the distributive law or even the word "replace"

[cerulean wolf]

ikr its depressing

[vale wigeon]

no, 2x+1 is not the answer either.

please stop.

@alpine sable it sounds as if you're overthinking things here, or you really genuinely do not know what the word "replace" means

i was expecting you to write x(x-1) + 2(x-1)

[cerulean wolf]

do u guys not know what a quadratic is

[vale wigeon]

or (x-1)x + 2(x-1)

to be more literal

it really isn't rocket science at all like

one would've thought replacing something with something else is not any harder than fitting a round peg in a round hole

[alpine sable]

ok now what

[vale wigeon]

expand again

twice this time

you were able to do it once, so you should be able to do two more times

[cerulean wolf]

Solving the riemann hypothesis and evaluating the zeta function is not cool

@vale wigeon do u know how to find the range of the possible values of c when the range of this rational function is for all R: (x+c)/(x^2-3x-c)

[alpine sable]

(2x-1x) + (2x-1)

??

I need help with this problem...

[crisp grove]

,rccw

[supple tundra]

shouldn't have shown them that one

[alpine sable]

Someone tell me how can I crack advanced questions.

I have been trying for 2 months but nothing is working out for me.

[crisp grove]

hmm

[crisp grove]

practice ig

[ancient magnet]

is it ok if i ask a question?

[alpine sable]

I'm practicing for 2 months but nothing's changing.

;__;

[crisp grove]

well ask for help or look rss that can help u

if you are really stuck

[supple tundra]

What kind of advanced questions?

JEE?

[alpine sable]

Rss?

[crisp grove]

resources

[alpine sable]

No, ISI, INMO

[crisp grove]

ISI admission? for Bmath?

[alpine sable]

Yep

Isi Kolkata aspirant

[silver current]

split the denominator

[crisp grove]

nice

[supple tundra]

olympiaders never share their secrets they just say "jUst PrActIce BrO"

[alpine sable]

Oh lmao

[crisp grove]

ISI do share their solutions

so you can look there

[alpine sable]

Imma ok with everything but my geometry sucks

[ancient magnet]

like how? if i split it then it becomes 2-x^2/1 right?

[crisp grove]

or maybe post your question here

someone might be able to help

[silver current]

youre right by 2- x^2/(...)

check this (...)

what would be there

[ancient magnet]

it would be 1 right?

[silver current]

No

[ancient magnet]

coz 100 is 2 times of 50

oh

[silver current]

tell the answer of this (200+100)/100

by spliting

[ancient magnet]

300/100

how do u split?

[silver current]

try to split your way

how do you do it

[ancient magnet]

3/1

[silver current]

that is the answer for this correct

[silver current]

but what about this

dont add them first

[ancient magnet]

oh i make it 2 and 1/3?

is splitting a method or concept? i dont think i know it

what chapter/topic do i find it under

[silver current]

howd you get 1/3

[ancient magnet]

the 100/300 thats left

[silver current]

umm

theyre in addition in the numerator right?

so can i write (200+100)/100 as 200/100 +100/100?

will they give me the same result?

[ancient magnet]

Ohhhh

like thattt

so u separate a whole from it

and write the remaining

[silver current]

basically (a+b)/c = a/c + b/c

[ancient magnet]

OHHH OMG thanks a ton-

ive always had trouble with splitting , is that an identity?

[silver current]

Nope

Just if its in multiplication like (ab)/c = a/c *b

the denominator will be in either of the terms but for addition/subtraction the denominator goes to the each term in the numerator

[ancient magnet]

like distribution?

is this what the distributive property is?

[silver current]

kinda

basically that yeah

[ancient magnet]

thnxx

[silver current]

sure

[crisp grove]

for multiplication, no it's not distributive

[silver current]

yep

[alpine sable]

what is (x-1)(x+2) simplified

[vale wigeon]

clar there's no two ways about it you need to learn more about the distributive law

as-is you seem unable to apply it properly

[alpine sable]

I can do it if there is only a number

on the left

but now there's a parantheses with 2

x•x x•2 -1•x -1•2

is this how it's done??

[alpine sable]

just tell me the results and I'll figure it out

[vale wigeon]

we don't give out answers here so no

I can do it if there is only a number
on the left
but now there's a parantheses with 2

this shows you don't understand it fully then

it doesnt matter if whats on the left is a number or a parenthesis or a scary complicated expression in its own right

[vale wigeon]

yes, but you add these four terms together

[alpine sable]

2x+2x-1x-2?

[vale wigeon]

no

x * x is not 2x.

[alpine sable]

ah yes oops

so x²+2x-1x-2

👍

[silver current]

you can do one more step

[alpine sable]

x²+1x-2

[silver current]

great

[vapid swift]

for 2nd , consider a set A_k which contains all the multiples of k that are less than 400 , to find the primes , first we'll find the non primes that's at most 400

we also know that every non prime less than 400 is divisible by a prime less than sqrt{400} , so here k would be every prime less than 20

now find the union of all these sets and subtract it from the total

[crisp grove]

T is always perpendicular to dT/ds

[leaden isle]

Does anyone know how to get from step one to step two?

[crisp grove]

divide by e^n

[leaden isle]

Oh my god, Im fucking stupid

thank you

[crisp grove]

lol

[verbal ermine]

how can i prove

that the line tangent

has gradient -1?

i know it does

but how do i prove it

@ me if u knoiw

[rigid wind]

what is given?

only radius?

[verbal ermine]

circle radius 1

and i need to find the point where the two lines intersect

and i found it assuming that the line is y=x

but how do i prove that the other line is y=-x

then i know that the line is y=x

[rigid wind]

2 lines intersect?

what 2 lines are they

[verbal ermine]

y=-x (i need to show this) and then the other one would obvs me y=x

but my solution isnt fully done if i just assume that its y=-x

just wanted to know why

[devout sigil]

gradient of tangent=-(gradient of normal)^(-1)

normal is perpendicular to the tangent

[verbal ermine]

yeah yeah i got that

but without using y=x

how do i show that the tangent line is y=-x

because im not given that line is y=x

i just assumed it

[rigid wind]

missing some info

[devout sigil]

do u have the full question?

[rigid wind]

with the picture those 2 could be anything

[verbal ermine]

nvm i got it. we can call the line tangent x+y=k so the gradient is y=k-x

was this q

[alpine sable]

v2 + v2 = v4?

[granite raptor]

is the answer (a). if then how?

[verbal ermine]

(1+1/2)/2

[devout sigil]

cos 60deg=1/2

[granite raptor]

yes

[verbal ermine]

sqrt(3/4)

[devout sigil]

numerator=1+(1/2)=3/2

[verbal ermine]

=sqrt3/2

[granite raptor]

well how

[devout sigil]

so u have √(3/4)=√3 / √4=√3/ 2

[granite raptor]

but why

[devout sigil]

it’s a radical law

√(a/b)= √a / √b

[granite raptor]

no not that

i mean why did he take

(1+1/2)/2

[granite raptor]

this one

[verbal ermine]

1+1/2=3/2 right

[granite raptor]

yes

no

[verbal ermine]

3/2/2

flip it

[granite raptor]

3/4

[verbal ermine]

yes

then square root

[granite raptor]

rt 3/2

[verbal ermine]

thats just a surd law

[granite raptor]

got it thank u

[verbal ermine]

np

[digital hearth]

with these numbers: 4-7-10-25-75, I have to find 490 as the result using
I can use as many operators as I like.
Can anyone help me?

[verbal ermine]

ye i can

[digital hearth]

I would like the sequence of operations that solves the problem

please

[verbal ermine]

do i have to use them all?

so u only want to know the operators?

not the numbers?

[digital hearth]

not necessarily

[verbal ermine]

i used them all

wanna see?

[digital hearth]

yes

tanks

[verbal ermine]

$\frac{75}{25}=3
\[5pt]4+3=7
\[5pt]10\cdot7\cdot7=490$

[ocean seal]

Aerials

[verbal ermine]

bit easier to see

[digital hearth]

ok

tank you very much

[verbal ermine]

np

[hexed yoke]

@quaint narwhal @alpine sable T

[silent wraith]

Hi guys how do I find the Beta and Gama angles, and length or arm if all the points are isosceles with same angle and know their height?

[compact vault]

help please

[verbal ermine]

find an eqn for the surface area

[compact vault]

What’s an eqn

[cerulean wolf]

Is that gcse stuff

does anyone know how to find the range of the possible values of c when the range of this rational function is for all R: (x+c)/(x^2-3x-c)

[dim acorn]

anyone knows vivani theorem

[wind kindle]

Need help:")

[cerulean wolf]

is that a test

[alpine sable]

use similiar triangles

[wind kindle]

so which sides are the same?

[alpine sable]

ratio of length of A to the mans feet and AC is equal to the ratio of length of the mans height and the lamppost's height

[merry umbra]

@alpine sable so a and b the different prime numbers less than 12 as the numbers shown I am pretty sure you are doing the even numbers

You did didn't you

Hold on

Yes

Look at the answers

You see how there 3 of a and b

You have to find 3 pairs I think of that

[merry umbra]

Um

[alpine sable]

@daring roost what have you tried so far?

[daring roost]

By parts

[merry umbra]

What does that x sin of x mean

And other shit

[daring roost]

@alpine sable have you tried it?

[quaint narwhal]

OMG!

[sly trout]

How can you figure out the perimeter of a square when we know that all 4 of the sides are equal and the smallest diagonal is 7cm, and the blunt angle is 120*

[orchid python]

how can I evaluate this limit?

[placid zinc]

What happens if you plug 8π in?

[orchid python]

let me try

it gives me ~0.46

[obsidian crane]

wait

8pi is equal to 0

just like 360 degrees = 0 degrees

the whole thing should be zero if im not wrong

sin (0 + 6sin(0)) = sin (0) = 0

[placid zinc]

I think you did degrees on your calculator haha. This should be done in radians.

This should be done without a calculator

[alpine sable]

u get 0 right

sin(8pi) = 0, 8pi isnt though

sin 8pi = 0

sin ( 8pi + 6 sin(8pi)) = sin (8 pi + 6*0 ) = sin 8 pi =0

[obsidian crane]

8pi is equal to 0 radians actually

if you think of it like this

2pi is 360 degrees

keep minusing 2pi from 8pi

you eventually get 0

the trick is

if an even number is being multiplied by pi, it means it's equivalent to 0 (in a way that it will give the same result for the trig functions as 0)

0, 2pi, 4pi, 6pi ...

[hexed yoke]

@alpine sable

[alpine sable]

8pi rad is 0 rad, or 8pi is 0 mod 2pi, i was just trying to make sur to avoid and oversimplification, as "8pi = 0" is wrong per se

yeah

sin 8pi = sin 0
not 8 pi = 0

[sturdy grail]

is this channel free?

@alpine sable @alpine sable @obsidian crane

[alpine sable]

yes ig

[covert breach]

idk what im doing wrong here? can someone help?

[mint bronze]

How do I solve it

[covert breach]

bruh im asking a question here

the only thing that would satisfy integral of f'(x) = integral of x would be e^x, right?

[mint bronze]

Bro stop being annoying

I asked way before you

[covert breach]

<@&268886789983436800>

u didnt

[mint bronze]

It's not even allowed to get help in ur hw or quiz

[covert breach]

if u asked hours ago, that doesnt count

[covert breach]

its not quiz, and u are allowed to help with hw

[alpine sable]

@mint bronze

[covert breach]

thats most of what this discord does

[alpine sable]

stop fighting

[night geyser]

molotov did indeed interrupt

[night geyser]

move to a different channel

[alpine sable]

i will tell how to solve @mint bronze

[covert breach]

please help me with this problem if anyone can

[alpine sable]

integral of x dx is x^2 / 2 + c

[covert breach]

what? sorry?

[alpine sable]

what?

[mint bronze]

Come to 1

Pla

Pls

[flat crane]

can't you just remove the integral, so the question becomes f'(x) = x

[covert breach]

u were saying something here, im just asking what u are saying

[covert breach]

well, theres still something wrong in the page

if i choose x

[night geyser]

this doesnt quite work 100% but it does help identify potential candidates.

[alpine sable]

integral of xdx is (x^2) / 2 + c udk that?

[covert breach]

oh yeah, so only e^x would work, but there is no such option

so i chose none of the above

[alpine sable]

$$\int f'(x)dx = f(x) = \int x dx$$
$$f(x) = \frac{x^2}{2} + C$$
see which equation satisfies this format

[ocean seal]

Spica

[night geyser]

for example, it immediately shows that B, D, H are correct answers.

[night geyser]

???

e^x solves f'(x) = f(x)

but thats not what youre solving

[covert breach]

how odes that work?

[night geyser]

youre solving f'(x) = x

[covert breach]

ohh ok

hmm

[night geyser]

in other words, functions that, if you take the derivative, you get x.

[covert breach]

ohh ok

thnx

[alpine sable]

anti derivative of f'(x) will give you f(x)

[covert breach]

finally got it

fuckin hell 😂

10 tries

read the question wrong i guess

mb

so with first order linear equations

its basically any differential equation that doesnt have y^2?

[alpine sable]

it can have y^2 if its linear in terms of x

[covert breach]

wdym?

[alpine sable]

like $\dv{x}{y} + Px = f(y)$

[ocean seal]

Spica

[covert breach]

yeah

oh

[alpine sable]

where f(y) or P can be y^2

[covert breach]

bruh ofc i mean dy/dx

or dy/dt

wouldnt this be any value then?

[alpine sable]

you said first order linear diffeq

[covert breach]

ohh sorry fuck man

i keep reading questions wrong

mb

also i have a doubt, is something like cos(x)y' + y= f(x) LDE?

probably not

[alpine sable]

yes it is

[covert breach]

wait whatt?

how?

[alpine sable]

its 2nd order in terms of x if x is not in power of anything so a = 2

[covert breach]

im not sure how u got that 😂

man im bad at DE..

imma fail

[alpine sable]

divide whole equation by cosx so you'll get that its linear with y

[covert breach]

ohh

damn

bigbrain move

[alpine sable]

see in right hand side

x is in power of e

[covert breach]

yeah

[alpine sable]

which'll make it non-linear

[covert breach]

why?

and u cant solve nonlinear DE?

[alpine sable]

but as its e^(a-2)x when a = 2 x is no more in power of e

[alpine sable]

you can but that's not part of question

[orchid python]

thanks, but why do you know it

[covert breach]

so how does that help?

its just asking if its a DE

not if its a linear DE

[alpine sable]

at bottom

[covert breach]

bruhh

so i did read it write the first time

[crisp grove]

x=0

[covert breach]

wait why is e^x nonlinear?>

i need like a personal tutor for DE man legit

[alpine sable]

cause linear doesn't mean in form of exponential, degree of variable must be 1 and it should not be in composition with any other functions

[covert breach]

A bacteria culture starts with 280 bacteria and grows at a rate proportional to its size. After 3 hours there will be 840 bacteria.

so initial value problem and f'(x) = e^x?

or am i wrong?

[covert breach]

hmm

so would 3 work?

[alpine sable]

3 what?

[covert breach]

a=3

doesnt work

but i dont understand why

so wait

e^y just doesnt work

for linear?

is that how it is?

if its dy/dx

[alpine sable]

yeah cause it'll give e^x and x is still in exponent so it doesn't work

[covert breach]

hmm ok i think i got it

thnx bruv

but im still fucked

idk DE well 😭

[alpine sable]

for 2nd order linear diffeq it must be in form of
$$y'' + f(x)y' + g(x)y = h(x)$$

[covert breach]

and the prof makes no sense, the board is blurry af, and the audio is crap

in online learning

[covert breach]

ahh ok

[ocean seal]

Spica

[formal fossil]

hi guys, i need help with this question. part c.

[covert breach]

wait

ok

[alpine sable]

rationalise the numerator

[covert breach]

so the problem is, we are getting a h(x) * i(y)?

if its not 2?

[alpine sable]

yes

[covert breach]

ahh gotcha

ill try to find more of such problems to solve

[alpine sable]

gl

[dapper patio]

bit lost on how they got d=1 as when i typed it into my calc i got d=0....?

[covert breach]

thnx bruv

legit there are so many ways to solve DEs and some of them just make my brain melt

others take 2 days and 10 pages to solve

like. the fuck is an exact DE

and how the fuck u solve em

i mean i have read it 4 times

still doesnt stick and i mess up when the equation looks complicated

i should probably just give up

i have no hope of scoring well in this class

and my GPA is gonna tank

[rapid hazel]

heeyey i need help

why -96? its evaluating function. I understand the substitution process but I just can't understand why the answer is -96

[alpine sable]

why