help-28

[signal thorn]

Thanks and again thanks for the help

i feel like i know what to do now in future

[halcyon tree]

It comes with practice

[signal thorn]

For sure wish u a great evening!

[halcyon tree]

Practice with familiarising yourself with those questions and practice to get faster

[halcyon tree]

You too

[signal thorn]

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[robust slate]

c is the y-intercept, so if it's positive, c>0. Otherwise, less than 0

a is postive means the graph opens up, a is negative means it opens down

for b, note the x coordinate of the vertex is -b/2a. You have the sign of a and the sign of the x coordinate from the graph, the sign of b follows.

[slate pasture]

ohh alr ty!

wait would c be undefined or smth? since its not on the intercept

[robust slate]

edited

[slate pasture]

ohh alr

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[deep pawn]

<@&268886789983436800>

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[barren mural]

Three part question, Find the distance between the points (2,-3) and (4,2) answer is in the form of square root A. I got a = 29 but the second part is find the distance between (-4,-3) and (6,2) the answer is in the form b square root c determine b and c. What does b square root c and how do i find both?

[barren mural]

<@&286206848099549185>

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[rocky vale]

Ahh, related rates

Is there anything you've tried yet?

[stiff swan]

nope we are at absolute extrema

[rocky vale]

Oh you're right, it's optimization lol It looks like a related rates problem

[stiff swan]

I think I'm supposed to form a "formula" first?

[rocky vale]

You're looking for the point where the distance between the vehicles is at a minimum

So yeah, if you can find a function that expresses that distance (as a function of time), then we should be able to find its minimum like any other function

[stiff swan]

okay let me try

hmm

s(t) = 15t - 80t?

[rocky vale]

Are you describing the position of the car? or the distance between the car and the bus?

[stiff swan]

well I want to find the second one (the distance between the car and the bus)

but I'm not sure if this is right

[rocky vale]

did you mean to have t on both these terms?

[stiff swan]

yeah why not

[rocky vale]

Maybe this will help

Let's just focus on the top side of the triangle for a moment

Its length is changing, because of the motion of the car.

Can you write an expression for the length of that side, in terms of t?

[stiff swan]

side = 15t

[rocky vale]

hm

so, the question says that the car starts 15 km west of the intersection point (right angle)

and t is the number of hours past since then

So 15t would imply that the length of that side is getting longer

after 1 hour, 15 km
after 2 hours, 30 km
etc

[stiff swan]

ohh

okay

I think it should be 15-t

because of what you said

[rocky vale]

This is closer

But the car is moving west at 80 km/hr

15-t only gives us 1 km/hr

after 1 hour, 14 km
after 2 hours, 13 km
etc

[stiff swan]

15-80t

?

[rocky vale]

Yes!

That's the top leg of the triangle

it describes the position of the car

So what about the bus?

The vertical leg of the triangle

The bus started at the right angle, and is driving south at 60 km/hr

[stiff swan]

well its getting larger so 60t

[rocky vale]

Yep

[stiff swan]

okay so now I got
15-80t and 60t

now what

[rocky vale]

You tell me. What are you trying to do?

[stiff swan]

I have to find the time where distance is minimum first

then when I get the time, I can just substitute it to find the distance

[rocky vale]

So, you need a function that describes the distance between the car and the bus in terms of t

[stiff swan]

hm

maybe this:

s(t) = sqrt[(15-80t)^2 + (60t)^2]

[rocky vale]

Perfect, looks good to me

[stiff swan]

Because I am basically finding the hypotenuse

[rocky vale]

Yeah, exactly

So you can simplify that a little bit to make the derivative nicer

But then, do you know how to minimize it?

[stiff swan]

maybe I should get the first derivative, find critical points, do the line extrema test thing then whatever the x where absolute extrema is that's the minimum time

[rocky vale]

Sounds good 👍

[stiff swan]

okay i'll try it

hey I forgot I had class rn

please don't close this

[rocky vale]

The bot might close it if you don't respond for a while

But you can dm me later if you want

[full forum]

@stiff swan Has your question been resolved?

[stiff swan]

wait bro

[stiff swan]

okay im back

gonna do this quick

[stiff swan]

hey I got a question, why should it be 60t instead of -60t

[rocky vale]

You said it yourself

That distance is growing with time

The other distance is getting smaller

[stiff swan]

yeah but it's moving south right?

in the first one I use 80t since it's moving west

[rocky vale]

First one the rate of change is negative because the car is moving toward the intersection

So that distance is shrinking

The distance from the right angle to the car is shrinking

The distance from the right angle to the bus is growing

[stiff swan]

ohh okay my bad I thought we base the sign depending on the direction

[rocky vale]

I'm hesitant to say you'll never have to do that

but I can't think of any reason to

In this case, we wanted to use the pythagorean theorem

So our expressions were for the lengths of the legs of the triangle

We don't really care about direction

[stiff swan]

ohh okay

aight that works

[stiff swan]

and its a rel min

so its also an absolute min

substitute that to the original function and we get the answer to the 2nd question

right?

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[stiff swan]

solved

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[atomic vortex]

is that a typo "y(pi/6)"

[atomic vortex]

or do I have to plug

in that

and the x

in my function to find the actual y value?

[jade estuary]

yeah seems like you have to plug it

[atomic vortex]

so like

y(pi/6) = sin(3pi/6)+cos(4pi/6)?

to find y =

[dense oriole]

@atomic vortex take the derviative first

[atomic vortex]

derivate is 3cos(3x)-4sin(4x)

and then plug in x to get slope

right

but then again

when I plug in my point intercept form equation

i still need the y

and I followed all that. and my answer is still wrong

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[short ferry]

Hello I'm just looking for some help with a spreadsheet formula for a game.

Basically my friends and i sell runs and get gold.
Person 1 gets 16800
Person 2 gets 16800
Person 3 gets 8400

There is a flat tax of 0.05% so we at the end of the run we get
Person 1 = 15960
Person 2 = 15960
Person 3 = 7980

For a total of 39900 gold.

Once we're done with all of our runs we figure out what the split of gold is which for this example is 13300.

Person 3 puts an item on the Auction house for both person 1 and person 2 which incurs it's own 0.05% tax.

How can i figure out in my spreadsheet the equation to solve it

[short ferry]

to make sure everyone gets an even split

[balmy peak]

what are you trying to solve for exactly ?

I dont understand the auction house bit

[young robin]

The stuff all makes sense to me

until the auction house

do u mind explaining a bit more mate?

[short ferry]

Um so in order for us to split the gold evenly, Person 3 needs to put an item in the auction house for us to buy in this case, if there was no tax, 2660

i would send 2660, person 2 would send 2660

we all get an event split of 13300

However, there will be a tax of (0.05) to the 2660 which will make it 2527 person 3 would get

so the total wont come out equal

I will get a total of 13300, person 2 will get 13300.

Person 3 will get (2660*.95) + (2660*.95) +their gold (7980)

which comes out to 13034

[young robin]

this seems like a bunch of arbitrary rules tbh

what game is this where this is relevant?

bc there is probably a way to get around this stuff

[short ferry]

It's Lost Ark

[balmy peak]

where does the 2660 come from?

[young robin]

ill be honest i havent played it so idk how it works

but seems like some really random calcs for no reason

when u could just have it being uneven

[short ferry]

2660 = (13300-7980)/2

which is the amount we give person 3 so our gold is equal to 13300 each pretax

i know for this example Person 1 and Person 2 give examtly 2752 which gives person 3 13208g and person 1 and 2 13208g

but thats by forcing it

[balmy peak]

So (starting value A) - (amount) = (goal)
(starting value B) + (1.05 * amount) = (goal)

you could solve for the amount using that in excel

[short ferry]

Thanks, i got it @balmy peak

i appreciate the help ❤️

[balmy peak]

🙂

[short ferry]

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[delicate snow]

i need help

[delicate snow]

what type of function is this?

<@&286206848099549185>

[woven snow]

looks like quadratic

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[raw maple]

Need help

[full forum]

Please don't occupy multiple help channels.

[raw maple]

So

Pls explain this chart

[onyx glen]

@raw maple alright so let's just stick to this channel for now

there are multiple things you could potentially want explained for this chart

[raw maple]

simple

Explanation

[onyx glen]

1. What do the arrows on this chart mean?
2. Why is the chart accurate?
3. How do I use the chart to solve problems?

which of these do you want

[raw maple]

3

[onyx glen]

right

[raw maple]

wait first

[onyx glen]

...

[raw maple]

Let’s say

I give a description of a parallelogram

And description is sometimes true

What other shapes can the description be to make that statement sometimes true

[onyx glen]

...i'm afraid i don't follow, sorry.

"I give a description of a parallelogram, and this description is sometimes true" is not something i am able to conceptualize

[raw maple]

I give a description

Here

Number 3

[torn jolt]

,rotate

[raw maple]

1 pair of parallel sides *

He forgot to type sides

[onyx glen]

so you are asked to say whether this is always true, sometimes true or never true?

[torn jolt]

Are u asking something like what other shapes can be defined by the "description" Of a parallelogram?

[raw maple]

no

What’s is the answer to 3

[raw maple]

Yes

Based on this chart

If it’s always true

Shapes below it always fit it

[onyx glen]

it's not always true

[raw maple]

Ok

[onyx glen]

and idk how you're expected to get any use out of that chart for these problems

[raw maple]

As a general rule

If it’s sometimes true

It’s the shapes that are not below it on the chart

So like above beside

[onyx glen]

...

[raw maple]

So is kite a rectangle

Always sometimes or never

[onyx glen]

...sometimes, but i think i can't say anything else here that would not confuse you or me or both

[raw maple]

Why is it a sometimes using this chart

Also read the test

Text on top and bottom

[onyx glen]

all squares are kites and all squares are also rectangles

[raw maple]

ok?

I know?

Why sometimes

[onyx glen]

because there exist kites that aren't rectangles

so kites are not always rectangles

and kites are not NEVER rectangles because there exist kites that are

who knows how you're expected to derive this from that chart though

[full forum]

@raw maple Has your question been resolved?

[raw maple]

Ur not

This is for quick stuff

U have to know there’s

These

Chart is to visualize

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[torn jolt]

Are these correct

idk about the bottom one

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[torn jolt]

Are these correct

I took picture after quiz was done

Just checking early marks

not cheating

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[torn jolt]

These correct

Help

!helpers

#helpers

[pliant crown]

I think q.3 is wrong

Q.2 is correct

Q.4 is correct

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[pliant crown]

Can't see q.1 properly

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[silver moss]

how to show that for the field $F:={(a,b)|a,b\in\mathbb{R}}$
$$\cdot:((a,b),(p,q)\mapsto (ap-bq,\ aq+pb)$$
has a neutral element

[glossy valve]

Kedi

[fast peak]

you could explicitly give it

[silver moss]

I couldn't find it

[fast peak]

ok so you want that $(a,b)(p,q) = (ap-bq, aq+pb) = (a,b)$, yes?

[glossy valve]

Denascite

[fast peak]

for (p,q) to be the neutral element

[silver moss]

yes

[silver moss]

the only solution I thought of was $((1,0),(0,1))$ but it is not in $F$

[fast peak]

K?

[silver moss]

sorry I mean $F$ 😅

[glossy valve]

Kedi

Kedi

[fast peak]

so lets compare the coordinates. we want that ap-bq=a and aq+pb=b

and some things should be 0 or 1. which ones

[silver moss]

$(1,0)$

[glossy valve]

Kedi

[fast peak]

yes

and that's it

[silver moss]

thanks alot
Gracias

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[supple token]

How did they get this answer?

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[supple token]

@supple token

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[tawdry acorn]

How do I find speed when given only a position function?

[tawdry acorn]

I took the derivative to find velo, and the second derivative for accel, but without a point for t how would I go about it

[wild sleet]

average speed?

[tawdry acorn]

yeah

I know speed is |r(t)| but I don't have a t value

[wild sleet]

what function though

[tawdry acorn]

r(t)=<-4cost,2t,-4sint>

[wild sleet]

and the derivative?

[tawdry acorn]

<4sint,2,-4cost>

[wild sleet]

hm

well it's like a helix or something, so that's constant speed

but i don't know how to find it

it's not 2

although average is maybe 2

no idea

[tawdry acorn]

isn't it wacky lol

like v(t)=<4sint,2,-4cost> but then like |v(t)|...?

[wild sleet]

if you're looking for like, scalar it's gotta be 2

[tawdry acorn]

that's what I'm rocking too

in case I'm missing something

[wild sleet]

what else would it be, it does 2 meters per second generally

[tawdry acorn]

couldn't tell you lol

[wild sleet]

no okay, that's not average

they are looking for the constant that isn't 2

[tawdry acorn]

gotcha

so how would we find that?

originally I thought I needed to add everything up and take the square root. So I tried 6 earlier but idk if I'm thinking of something else or if i'm on the right track

[wild sleet]

ima guess 2sqrt(5)?

[tawdry acorn]

i'll try it

correct lol

how'd you get there?

[wild sleet]

i thought like, if you're going in a circle, you do 2pi distance per 2pi seconds

and it has 4

so it's 4

,calc abs(2+4i)

[glossy valve]

Result:

4.4721359549996

[wild sleet]

lol

[tawdry acorn]

for what tho lol

like wdym 2pi/2pi? Like for a t value?

And like if these are dumb questions I'm sorry lol

[wild sleet]

no, it's not dumb, i can't explain my solution it's on me

it's just, you're going in a unit circle if your position is sin(t) and cos(t)

clearly with speed 1

because in 2pi seconds you cover 2pi distance

[tawdry acorn]

right

[wild sleet]

and then i assumed that if it's multiplied by 4 it just makes your speed 4

[tawdry acorn]

and we assumed that bc the radius of our circle is 4?

[wild sleet]

no, i just only relaised how it works

correct, the multiplier is the radius of the circle

[tawdry acorn]

cool cool

[wild sleet]

you constantly move at speed 4 orthogonally to your other speed 2, so your speed is constant sqrt(2²+4²)

[tawdry acorn]

Gotcha

Good stuff good stuff

I really appreciate your help!! I’m gonna do some more practice problems later

Keep ur fingers crossed for me lmao

[wild sleet]

on it

[tawdry acorn]

.close

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[queen glacier]

Hey, sorry if this is not how you ask questions around here but I'm pretty bad at math, so I have these two

x = 190
y = 8%

and I'm trying to figure out what's the number from which 8% is 190

[atomic notch]

set that number ur trying to find as A, then A * 8/100 = 190, solve for A

[queen glacier]

what's a good place on the internet where I can do that

[atomic notch]

err an online calculator

[queen glacier]

okay, ill google around, havent used ones with formulas , thanks a lot

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[pearl shuttle]

can someone explain how this is 6 and 3?

[pearl shuttle]

what did i do to get that result

because i dont understand this

[twin wolf]

Which one? The numbers 3 and 6?

[pearl shuttle]

yes

i just want to know how i got those values

[twin wolf]

Well the easiest way is counting the squares beneath the triangle

You see that there are 6 squares beneath the length of the triangle

Therefore length is 6

And the triangle goes up 3, therefore height is 3

[pearl shuttle]

yeah but if i didnt have the squares

[twin wolf]

Are the green and yellow numbers coloured that way purposely?

Then if so; because the x value at point E corresponds with the other x value at point F, you would simply move them into a simple addition equation

For example

Point E value for x is 2

And point F value for x is -4

[pearl shuttle]

im just studying for a test tmrw

[twin wolf]

Moving the -4 over you get 2 - - 4

[pearl shuttle]

and going over the thing i dont know

[twin wolf]

Which equals to 6

[pearl shuttle]

huh?

[tight dock]

@pearl shuttle distance between 2 points formula

[pearl shuttle]

ok i forgot i could use that

tanks

thanks

how do i know what to rearrange

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[pearl shuttle]

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[north nacelle]

need some help for trigonometry test review

[north nacelle]

how do i do number 7?

i am having trouble with the opposite

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[charred meadow]

how can i prove this using trig identities

[boreal stump]

try replacing cot with tan

[charred meadow]

i did, I also then changed tan into sin/cos but it just seems like the process is too long and wrong

[boreal stump]

no dont change tan

[charred meadow]

yeah when i just change cot to tan it still doesn't prove it

[boreal stump]

it does

do it carefully

[charred meadow]

yeah im trying, i dont really know what im doing wrong, could it be possible for you to do it please

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[charred meadow]

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[drifting thorn]

I'm trying to use two X and Y (and maybe Z) co-ordinates, the mass of the object, the speed in every direction and the mass of a planet (or other body) to find orbit paths, and I'm just really confused...

[wild sleet]

last time no one answered

could be super hard

[drifting thorn]

ah

[wild sleet]

but not necessarily

[drifting thorn]

ok*

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@drifting thorn Has your question been resolved?

[drifting thorn]

<@&286206848099549185>

:(

[drifting thorn]

aaa

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[grim kestrel]

someone explain what happened

how does bottom line make sense

(-3)^1(-1)^n = (3)^n+1

[ivory cairn]

-3 = 3(-1)

[grim kestrel]

ah

thanks

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[slate reef]

Hello, it is I once more

I can’t tell how to get from 2 to 3

Associative and Distributive laws have failed me

I did try:

Terribly sorry for my horrible handwriting

I use the distributive laws twice

p AND p is p

Am I supposed to use another law?

Is there another law?

[slate reef]

That applies here*

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[slate reef]

Nevermind, the answer in the class notes was wrong... whoops

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[sacred sparrow]

Hi I'm currently intending to find extrema for f(x)=x^(n)*e^(x) for any n

[vast fossil]

And what are you having trouble with?

[sacred sparrow]

I have the extreme points at (0;0) and (-n;(-e/n)^(n)) and I intend to find the functions that contain all extreme points of the above function f

[vast fossil]

So, a point which is a common extrema for all those f?

[sacred sparrow]

No a function that contains the extreme points of f(x)

for instance if f(x) = (x+n)²
then the function g(x)=0 contains all extrema of f(x)

maybe the term for it is locus curve but I'm not sure regarding the translation

[vast fossil]

So let's say P is the set of extrema points of f, you wanna find g such that P is a subset of the range of g?

[sacred sparrow]

exactly, I'm not too familiar with sets or subsets but it sounds intuitively right

[vast fossil]

I mean for this one you could simply pick g(x) = -(-e/n)^n/n * x

I guess

[craggy depot]

Can someone help with my engineering maths test

[vast fossil]

Or define it piece-wisely

[vast fossil]

Post it in an available help channel

[craggy depot]

Alright cheers

[sacred sparrow]

Hm I have
x = -n
y = (-e/n)^n
for the extreme points, so if I rewrite the first equation to n = -x and insert n into the original function f(x), it becomes x^(-x)*e^x which is (e/x)^x

[vast fossil]

Mb, should be a minus sign in front

[sacred sparrow]

this has to be part of the solution, since the function g(x)=(e/x)^x contains these extreme points but only for x>0

not for x<0

😦

I can plot it in desmos if it helps

[vast fossil]

You could put |x| instead of x

So that the values for x < 0 are the exact same as for x > 0

[sacred sparrow]

but it's not the case, the function isn't symmetrical at the y-axis

[vast fossil]

It'll be symmetrical once you put |x| instead of x

[sacred sparrow]

this is for n=3 for example

now I added the function g(x)=(e/x)^x I found in green and changed n to n=-1.1

as you can see the extreme point lies on it, and it does for any n but only for x>0

or well n>0, it's the same in this case

for n=4 the green curve doesn't intersect the maximum at (-4,4.689)

If I add the function h(x)=(-e/x)^x however, it does work, but I don't get how one can find this function

I hope I made it somewhat understandable and not too clogged 😅 @vast fossil

[vast fossil]

Yeah I'm slightly struggling to catch up xd

Couldn't we just pick a linear function though?

[sacred sparrow]

As you can see the extreme points lie on a very specific curve

the purple+green curve in the last image

and I intended to find the function that describes this curve

I found the green part through calculation, the purple part by accident and am wondering how to get it normally

[vast fossil]

Sure, but as far as I'm concerned there should be infinitely many functions on which those extreme points lie

[sacred sparrow]

I just need to find one with calculation :)

Wait I'll rephrase the entire question to make it simpler

@vast fossil ok, I want to solve this equation for n

[vast fossil]

Yeah, that results in x = 0 (unless n is 1) or x = -n

[sacred sparrow]

exactly, but now with x e R and n e C

which seems to yield at least one more result

[vast fossil]

Doesn't seem to be the case (as long as x is a real number)

[sacred sparrow]

hm and if x e C?

[vast fossil]

Then there may be more solutions to x^(n - 1)

[sacred sparrow]

because in order for this equation to work (the left is the function f(x) and the right is the g(x) I'm searching for) n needs to be complex

[sacred sparrow]

Yeah the other factors are probably irrelevant

Do you know how to solve an equation of such type for complex numbers?

x^(n-1) = 0

[vast fossil]

Well if a complex number is 0, it only means that the modulus of that complex number is 0

x^(n - 1) = e^(n-1)lnx = e^Re((n-1)lnx) * e^iIm((n-1)lnx)

As far as I'm aware it means that x^Re(n - 1) = 0

[sacred sparrow]

oh ok so it boils down to only the real part of n mattering

[vast fossil]

The only solution to x^Re(n - 1) = 0 is x = 0, unless Re(n) = 1

[vast fossil]

Here I'd first cancel out the e^x

x^n = (-1/x)^x

So we have x^n = (-x^(-1))^x

[sacred sparrow]

can we divide by e^x if x is complex?

[vast fossil]

e^x is never 0 so sure

x^n = (-1)^x * x^(-x)

And x^(n + x) = (-1)^x

[sacred sparrow]

understandable

and e^((n+x)*ln(x)) = e^(x*ln(-1)) if that helps at all

(n+x)*ln(x) = x*ln(-1)

n = x*ln(-1)/ln(x) - x assuming ln(x) can't be 0

[vast fossil]

There seem to be no analytical solutions for that

[sacred sparrow]

should I be concerned about this

[vast fossil]

Oh you wanted to solve for n, not x

Then ye that's n

[sacred sparrow]

ok but then my question is how does one find this n from the formula

[vast fossil]

Depends on what property do you want n to satisfy

[sacred sparrow]

do you mean n e C for instance?

[vast fossil]

Ah, wait

So yeah n = -x and n = the thing we found I guess

[sacred sparrow]

yes, but the mathematical approach is unclear to me

should I open a new channel since people will probably pass by as it's already somewhat flooded with unnecessary information from before

[atomic blade]

.close

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[atomic blade]

.reopen

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✅

[atomic blade]

Back on top

[atomic blade]

I mean, what happens if x < 0

That's something you'll have to consider

[sacred sparrow]

Hallu, I'd like to solve this equation for n with n ∈ ℂ (for people who just arrive)

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[wise hazel]

Can someone show me how to do this question

[torn jolt]

Do what with it

[wise hazel]

Solve it

😶

Its a simultaneous equation gotta find all variables

So x and y

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[smoky wing]

write n as a product of primes

[ivory moon]

Can you elaborate?

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[robust oracle]

I need to differentiate h(x)=1/sqrt(x^2+2)

[robust oracle]

how can i do this without the use of a calculator and just the rules for differentating like the power rule

[torn jolt]

<@&286206848099549185>

[thick mountain]

$\frac{1}{\sqrt{a}} = (a)^{-\frac{1}{2}}$

[lyric plover]

I believe it's this formula but someone correct me if im wrong

[glossy valve]

Larry the Cucumber

[thick mountain]

just use power rule from there (and chain rule)

[robust oracle]

can you show me step by step?

[thick mountain]

I’m on mobile so no keyboard :/

you can use symbolab.com tho

[lyric plover]

@robust oracle

[robust oracle]

just use the power rule from here?

so h'(x)=-1/2*(x^2+2)^-3/2

[lyric plover]

almost

you would solve it just like that if there wasn't a (x^2+2)

you also need to multiply the answer you gave by (x^2+2)'

[lyric plover]

look at the formula here

[robust oracle]

i dont quite understand that formula

[robust oracle]

why is that?

[lyric plover]

it just is

the u(x) in that formula is your (x^2+2) and the N is your -1/2

[robust oracle]

so u=2?

[lyric plover]

no. u(x) is a function

like f(x)

[robust oracle]

ohh

[lyric plover]

in this case your u(x) = (x^2+2)

Look at this. hopefully it makes sense

[robust oracle]

so according to the formula it would be: h'(x)=-1/2*(2x)*(x^2+2)^-3/2

[lyric plover]

correct

[robust oracle]

okay perfect

and what is that formula called?

[lyric plover]

i have no clue

[robust oracle]

okay thanks

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[torn jolt]

So divergent test states that when the limit as n approaches infinity is not equal to 0, the series is divergent. Geometric series is when |r| => 1. P-Series is when p < 1.

However, I do not really understand telescoping series-when does it diverge? What value from the limit would I get to show that it diverges?
0? +/- infinity?

[torn jolt]

Telescoping series is a special case of a convergent series where every element except the first and last gets eliminated by the succeeding/preceding one

also if you can figure out that whatever "Telescoping series" you are looking at is divergent, then it is not a telescoping series to begin with

[eager violet]

What if the first term is infinite

[torn jolt]

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[torn jolt]

Correction; in fact, a telescoping series can still be divergent, the name is just a bit deceiving since you wouldn't call a divergent telescoping series telescoping usually

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[magic rover]

how would you come about solving

[magic rover]

|x^2-1|-|x-1|>:0

with intervals

because i get the intervals

(-00 to -1)

[-1,1)

[1;+00)

and then i start solving

for interval (-00;-1) you would get the equation x^2-1-(-x-1) from what I understand

then for [-1;1)
x^2-1-(x-1)

and then for the final interval

x^2-1+x+1

and then I get the wrong anwser

[eager violet]

Why did x - 1 become -x - 1

[magic rover]

well because I have negative x's, so...

[eager violet]

And why did |x² - 1| stay as x² - 1 in [-1, 1)

[eager violet]

x - 1 is negative on (-∞, -1)

[magic rover]

OH IT SHOULD BE 1-x^2

[eager violet]

So |x - 1| becomes -(x - 1)

Not -x - 1

[magic rover]

right

I think I just forgot about how the absolute value switches the sign if the value is negative

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[magic rover]

the intervals for an equation such as |x^2-4|+|x^2-9|=5 would like such as:
(-00;-3), <-3;-2); <-2;2); <2;3); <3;+00)?

[magic rover]

if I understand correctly...

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[bleak pier]

can someone help me with quadratics it shouldnt take very long

[harsh carbon]

Sure

[calm steppe]

fire away

[bleak pier]

ok hold on

lemme get thte problem

Sorry for the blurry picture my phone would focus on my screen

[calm steppe]

looks like completting the square

[bleak pier]

I have to convert it to standard form

Then graph it and I tried It and it wrong every time

[calm steppe]

oh well sorry thats way beyond me i've never lerant that

[bleak pier]

dang

[calm steppe]

Amason might me able to help

[bleak pier]

@harsh carbon can you help?

[harsh carbon]

Well standard form is ax^2 + bx + c = 0 if I remember correctly

So I believe we just solve the bracket

And simplify

[bleak pier]

every time i try its incorrect

[calm steppe]

oh that standard form XD i was thinking 5.7 x10^12 stuff XD

[bleak pier]

idek what that is lol

[harsh carbon]

That's scientific notation

[bleak pier]

oh right

i can see that

[harsh carbon]

Do you know the vertex formula?

[bleak pier]

yes

y= a(x-h)^2 + k

[harsh carbon]

Or just -b/2a in this case

[bleak pier]

uh

ok

[harsh carbon]

So the bottom of our graph is at?

[bleak pier]

the vertex?

[harsh carbon]

Yh

[bleak pier]

the vertex is -4

[harsh carbon]

No

Or yh

Y = -4

X = 2

[bleak pier]

oh yeah

2,-4

[harsh carbon]

So draw a Cartesian plane and mark that

[bleak pier]

done

[harsh carbon]

And then find the roots by using the quadratic formula

I don't think we can factor

[bleak pier]

the quadratic formula uses ab and c

we dont have that yet

[harsh carbon]

Well we do expand the brackets

And since the roots will be found when y=0

We want to find x when 1/2(x^2)-2x-2=0

[bleak pier]

ok so i expanded the brackets and multiplied and got

x^2-4x+4

is that right?

[harsh carbon]

Yh same thing

Then solve for the roots

[bleak pier]

with the quadradic formula?

[harsh carbon]

Yh

[bleak pier]

ok

i got

4+- 2{sqrt}3 /2

[harsh carbon]

I get it to be 2-2√2 and 2+2√2
or roughly √2 = 1.41. so 2-2.82 and 2+2.82. so we get roots -0.82 and 4.82.

[bleak pier]

how

[harsh carbon]

Wait

You expanded the brackets

And got x^2-4x+4

That's wrong

[bleak pier]

i said that in the begining

i needed help with that and graping

[harsh carbon]

Ah okay

Sorry

Skipped ahead

So (x-2)^2 = ?

[bleak pier]

?

[harsh carbon]

Expand the brackets

[bleak pier]

(x-2) (x-2)

[harsh carbon]

Yeah

And do you know foil?

[bleak pier]

im not familiar with that term

multiply them?

[harsh carbon]

First outer inner last

Yh

[bleak pier]

yeah

i did that and got x^2 -4x+4

[harsh carbon]

Then multiply that by 1/2

[bleak pier]

omg

im an idiot

[harsh carbon]

You forgot pemdas

[bleak pier]

i over thought this

its litterally just half them

[harsh carbon]

Half them

Then minus 4

So you get (1/2)x^2-2x-2

[bleak pier]

wait i wouldnt be 1/2x^2 -2 +2 -4

[harsh carbon]

From there you should get everything right

[bleak pier]

oh wait im supposed to minus 4

[harsh carbon]

Yeah

2-4 = -2

[bleak pier]

ok so 1/2x^2 -2x - 2

[harsh carbon]

Yeah

[bleak pier]

alright

awesome

gimme a sec ro write this all down fresh

ok on to the graphing

[harsh carbon]

So the vertex is still -b/2a

[bleak pier]

2,-4

[harsh carbon]

Or -(-2)/2(1/2)

Yeah

And the roots

?

[bleak pier]

uh i have to calculate that

[harsh carbon]

Do so

[bleak pier]

so far i have the 2 +- square root of 0 divided by 1

is that a correct step?

[harsh carbon]

No this quadratic does not have a repeated root

Let's go through it.

-(-2) = 2

[bleak pier]

yea

[harsh carbon]

So 2 +- √b^2-4ac

b^2 = 4

-4(1/2)(-2)

-4(1/2) = -2

-2(-2) = 4

4+4 = 8

[bleak pier]

oooo

i did -4 on accident

[harsh carbon]

2+-√8 / 2(1/2)

2(1/2) = 1

√8 = 2√2

So we end up with 2+-2√2

[bleak pier]

wher did the 2(1/2) com from

[harsh carbon]

2a

And a = 1/2

[bleak pier]

2 times .5 is one right?

[harsh carbon]

Yh

So we don't have to care about it

[bleak pier]

oh i read that wrong

[harsh carbon]

No worries

We know √2 is roughly equal to 1.41

So that means we have 2 + 2.82 and 2 - 2.82

So our roots become 0.82 and 4.82

We don't need much more precision than that for the graph

Unless you have a calculator

[bleak pier]

i do

but the graph needs to be hand drawn

how would i get 1.41

when i do the square root of 2

[harsh carbon]

You just learn it

[bleak pier]

it just shows the square root of 2

[harsh carbon]

By doing math enough

Try doing 2^1/2

See what it shows

[bleak pier]

1.41

nd other numbers but i get the point

[harsh carbon]

Yh

So then mark those

Now we plug in some integers for x and we what we get for y value

And then we should be done

And connect the dots

[bleak pier]

ahh i see

thank you soo much for your help

[harsh carbon]

No worries!

[bleak pier]

ive been stuck on this for hours

do u mind if i do one more myself and ask you questions if i run into a road block

and then im done

[harsh carbon]

It's easy to get stuck on these things that seems trivial. Like pemdas but they are important

[harsh carbon]

Try one out yourself. Unfortunately i have to go to sleep. But there are many knowledgeable people around here. Or just look back at what I have written and it might help you.

[bleak pier]

dang

alr thanks for the help and have a nice sleep

[harsh carbon]

Good luck!

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[bronze iron]

You roll five dice in Yatzy, what is the chance of all of them landing on the same number?

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@bronze iron Has your question been resolved?

[bronze iron]

<@&286206848099549185>

[gritty rose]

do you know the probability of two dice landing on the same number?

[bronze iron]

I thought the formula was (n+k-1) / k

[gritty rose]

that doesn't look right

that's probably some other thing you're confusing with

[bronze iron]

Yeah probably

What would the right formula be

[gritty rose]

do you know the answer to this?

or how to reason about it

[bronze iron]

Wouldnt that be 6x6?

[gritty rose]

that's not a probability

[bronze iron]

so 1/36

[gritty rose]

that's the probability of a given number

[bronze iron]

ah true

[gritty rose]

but you don't care that it's (1,1) or (2,2) or ... (6,6)

[bronze iron]

so then 1/6

[gritty rose]

right

Can you do 3 next? (1,1,1) , (2,2,2), ..., (6,6,6)

[bronze iron]

Hmm not quite sure

I just end up with 6

[gritty rose]

6 what

[bronze iron]

like 1/6

[gritty rose]

the question is about the probability

[bronze iron]

but thats not correct

so Im not sure how to go from 2 in a row to 3 in a row

[gritty rose]

how did you go from 1/36 to 1/6 here

[bronze iron]

I knew there was 6 possibilites

but now there are more

But im not sure what formula I should use to calculate how many

[gritty rose]

there are the same number of outcomes

[bronze iron]

wait thats true

[gritty rose]

(1,1), (2,2), ...., (6,6) is 6 outcomes and so is (1,1,1), (2,2,2), ..., (6,6,6)

[bronze iron]

so 1/36 is the answer?

[gritty rose]

nope

where did 1/36 come from?

oh wait sorry yes

[gritty rose]

for 3 dice to be the same number yes

[bronze iron]

yea

[gritty rose]

4 and 5 should be a piece of cake for you now

[bronze iron]

so then for 4 it would be 1/216

[bronze iron]

and 5 would be 1/1296?

[gritty rose]

,calc 6 / 6^5

[glossy valve]

Result:

7.716049382716e-4

[gritty rose]

,calc 1/1296

[glossy valve]

Result:

7.716049382716e-4

[gritty rose]

[bronze iron]

it says its wrong :/

[gritty rose]

maybe it was a rounded decimal

[bronze iron]

Ive tried a few things but its not working

Ill ask my teacher kinda hard for u to answer

thanks for the help 😃

.close

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[cedar monolith]

Hello, i know it has nothing to do with the channel but is there someone good at maths history to explain me some things? I will DM you 🙂

[gritty rose]

just ask your questions in #discussion or #math-discussion h

[eager violet]

#❓how-to-get-help

[cedar monolith]

it's pretty long

that's why i want to talk in private

[gritty rose]

that's creepy

[cedar monolith]

it's basicaly just history actually

[gritty rose]

don't be creepy

[cedar monolith]

ok lol

bye

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[torn jolt]

Hi

[torn jolt]

I don't like algebra

[runic bloom]

we can help

[torn jolt]

?

Hello

Is anyone here?

[runic bloom]

question 1?

[stuck island]

can u go to help 49

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[hollow moth]

are these all the requirements for a probability density function for the continuous type?

1. It must strictly be positive
2. It must be 0 at -infinity
3. it must be 1 at +infinity

[hollow moth]

please @ me if anyone responds

[topaz valley]

thats not a density

thats a distribution function

[hollow moth]

the textbook says it's the probability density function

i was just wondering if i had the correct criteria

[topaz valley]

theres no way a density is 1 at infinity

you need the integral of the density to be 1

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[stiff musk]

moreover, every distribution function, not just those of continuous type, must satisfy those criteria (among others)

with the following correction: "strictly" positive is not required

another requirement which is not stated above is that a distribution function must be right-continuous at every point

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[torn jolt]

idk how I would go about this

[cold quarry]

the turbine completes 4 revolutions per minute i guess

4 rev/min

you can have to convert units to radians/second

1 revolution = 2pi radians

1 minute = 60 seconds

when you multiply 4 rev/min * 2pi rad/rev then the revolution unit (rev) cancels out and your left with radians / minute

from there you can figure out how to convert minute to second

[torn jolt]

ok

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[worthy bridge]

hi

[worthy bridge]

help

[slate hemlock]

Have you tried anything?

@worthy bridge

[worthy bridge]

not atm

im not sure where to start

since altitude is a perpendicular line extended from a vertex ik what that is

but im not sure where or how to use it

[slate hemlock]

The shape you need to calculate the area of is a triangle, right?

[worthy bridge]

yeah

the obtuse one

[slate hemlock]

So A=base*height/2

You said you have the height, right?

[worthy bridge]

i dont have the height

i only have the measurements shown rn

[slate hemlock]

Wait a sec

Take this as the base of your triangle

[worthy bridge]

so

4.5in?

[slate hemlock]

Yes

What's the height of this triangle instead?

[worthy bridge]

like the whole thing?

[slate hemlock]

Wdym

[trail oasis]

do the area of the big right triangle minus the area if the little right triangle

[slate hemlock]

You need to use the line extended from the base to find the height

[worthy bridge]

OH

[trail oasis]

It'll give you what u want

[slate hemlock]

That's a way to do it, you can calculate the area immediately anyways bu finding the height; give me a sec, I'll highlight it

[trail oasis]

I think its easier this way

To understand

[slate hemlock]

Thanks to the extension (yellow) of the base (blue), you can find the height (red)

So the height is the same as the big triangle