help-23

[wise hill]

But evidently Im wrong so I may as well try -1, 0, -5

Where did you get -1 and 0 from? @sleek plank

[sleek plank]

instead of moving x over to the right side by adding, i subtracted 5 over to the right

giving me
-x+5=0 -> -x = -5

which when converted into row form was -1, 0, -5

[wise hill]

Where is there a 0 on the side of the constants?

Or -1

Im confused

Is there a better way you can show me?

[sleek plank]

-x = -5 -> -1x + 0y = -5

[wise hill]

I agree

[sleek plank]

the 0 in the row is just the constant for y

which is why it goes in the y column

[wise hill]

Aren't there two 4's on the side of the constants?

[sleek plank]

ok, and?

those rows dont affect this row when we're making our matrix

[wise hill]

Thank you!

That was correct

[sleek plank]

np!

[wise hill]

Why was mine wrong?

[sleek plank]

it probably was just being stingy about the way you solved it

technically yours isnt wrong

[safe radish]

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[mossy shuttle]

$\log_{x} (x - \frac{1}{x}) = \log_{\frac{1}{x}} (x + \frac{1}{x})$

[flat frigate]

Golden

[red delta]

Change of base on the right to base x

[hard crest]

or just change them both to base e and be done with it

[mossy shuttle]

it is base x

[lean otter]

lmao

[mossy shuttle]

do you mean the one on the right

[red delta]

I mean right

[gritty umbra]

i sent that 10 mins ago 😭

[mossy shuttle]

not sure how to do that we just started logarithms

[red delta]

Yes sorry

[mossy shuttle]

yeah i did that

[hard crest]

,tex .log rules

[flat frigate]

[red delta]

I have been switching left for right since today

😔

[mossy shuttle]

then what

[plucky elk]

Do this

[plucky elk]

Use the last row here

[mossy shuttle]

@plucky elk is this correct?

[marble mulch]

this is my solution

[mossy shuttle]

so is where im up to correct

[marble mulch]

yea

i think you already cleard the harder parts, everything after is just quadratics

[mossy shuttle]

ok cool thanks

.close

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[magic quiver]

Hello, I'm having trouble with the last question in this series of questions. Help with finding the answer would be much appriciated! Thanks!

[plucky elk]

Jump discontinuity means limit is finite but not equal at the point

[magic quiver]

im also confused on the notation

is it asking me for the (-1, 1)U(2, 3) type of notation or the -1<x<1 typr of notation?

[thin bridge]

the first type, interval notation

[magic quiver]

thank you

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[weary umbra]

I’m not sure how to do 23

Or 24

[safe radish]

@weary umbra Has your question been resolved?

[weary umbra]

<@&286206848099549185>

<@&286206848099549185>

[foggy ridge]

a. Determine the other x-intercept.
The other x-intercept is x=0.
b. Find the equation of the circle.
The standard form of the equation of a circle is:
(x — h)^2 + (y —h)^ 2 = r^2
where (h, k) is the center and 'r' is the radius.

1. The center is (3, 3) and the radius is 3.
2. Plugging in these values:
   (x - 3)^2 + (y - 3)^2 = 3^2
   (x - 3)^2 + (y - 3)^2 = 9
   The equation of the circle is(x - 3)^2 + (y - 3)^2 = 9

[weary umbra]

How did you find the other x intercepts

@foggy ridge

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[merry sphinx]

imma keep this channel for now i have to talk too much so

[merry sphinx]

okay

i have been trying to make smoothing

in simple terms

it just wants this :

1. get the distance between current rotation and max rotation

2. do stuff to either speed up the rotation the further away it is or slow down the more near it is

so me and my friend

figured out this formula (which i bet you 300 dollars wont work)

rot += Math.sqrt( 1 - 4 * ( ( 1 - 1 / gadget.maxRotationSmoothing ) * rot / gadget.maxRotation ) ** 2 ) / 3000

in visualization

here is how it looks like

https://www.desmos.com/calculator/gs8kyrqpg6

am i doomed or can someone help me achive a formula

that would do the job

imma ping helpers in 15 mins so i apologize before i even do so

lol

just to add a couple of information

rot means current rotation

max rotation smoothing is the value of smoothing

10 should smooth that it goes slow like extremely

and 1 should do some simple slowing

we need this for a game we have been working on lol

it lets people edit their stuff and its just the last part of the update imma push

(now gonna go finish max rot)

[umbral swan]

it's pretty unclear what exactly you desire, could you clarify the specifics

[merry sphinx]

ok so

there is this feature called smoothing

it gets the distance

between the current rotation (rot)

and the max rotation

[umbral swan]

You have a current rotation, max rotation and the desired behavior is that the rotation strictly approaches the max rotation, but with a decrease in its rotation change?

[merry sphinx]

the rotation speed

varies

if its close to max rotation

then it slows down

if its far away from max rotation

it speeds up

[umbral swan]

k, if the current rotation is 0 and max is 1, then it'll start swiftly and gradually get slower in rotation change as it approaches 1

so you want one-sided interpolation

[merry sphinx]

current rotation

has no limits

so it goes from negative 360

to postive 360

[umbral swan]

ok, I'll assume it's not an angle since -360 to 360 wouldn't make sense, does it have recursive behavior? such that if the rotation is 360 and it increases by 1, it become -360/-359?

[merry sphinx]

361

is just 1

waaaaaait

i forgot

lmfao

the angle is in radian i forgot that

the max is math.pi * 2

[umbral swan]

it's recursive by 360 but its interval is 720 long?

if it's meant to be an angle then 361 = 1 = -359

meaning having negative angles is redundant

[merry sphinx]

nah

ignore the 360 part

the max is math.pi * 2

and the lowest it can get is 0

[umbral swan]

k, just to get the variables clear, your boundaries are always 0 to 2𝜋, and your current rotation & desired rotation are within that interval right

[merry sphinx]

yep

[umbral swan]

not sure if a desired rotation exists, but it sounded like that when you phrased the problem

[merry sphinx]

current rotation gets fixed

by keeping it in range of 0 to pi * 2

[umbral swan]

ok and if, let me put it in angles, the current rotation is 1 and the desired rotation is 359, the rotation change shall be negative

[merry sphinx]

it would not crash the server

[umbral swan]

since it'd be the fastest way to reach the angle 359

[merry sphinx]

when it gets to 2 billion-ish~

[merry sphinx]

current rotation is 0

and because it increases every tick

it goes up til it hits pi * 2

then resets back to 0

desired rotation is max rotation

its where the rotation should start going slower

[umbral swan]

so it shall reach 2pi, decreasing in speed and after the value is reached it resets and repeats

[merry sphinx]

yeah it does.

[umbral swan]

ok, now you options for onesided interpolation are many, linear, quadratic, exponential etc

do you intend to have a formula for the rotation or rotation speed

[merry sphinx]

rotation speed is a fixed number

can be changed tho

[umbral swan]

well if the rotation is meant to "first quickly but then slowly" approach the max rotation, the rotation speed alters

[merry sphinx]

yeah

gadget.rotationspeed

is the rotation speed

if i want to alter it i can just do const speedchange and do gadget.rotationspeed = speedchange

or push the change instantly

by doing gadget.rotationspeed =

you can do anything with the gadget.rotationspeed

[umbral swan]

kk

your current interpolation would be this

constant rotation speed

=> linear rotation graph

[merry sphinx]

yep

its alright

[umbral swan]

with quadratic behavior you'll probably already get a visually pleasing result

[merry sphinx]

the problem with code is that quadratic behavior is painful.

[umbral swan]

why'd that be

from a coding perspective any other form of interpolation (except for hacky ones) are most cost-expensive

[merry sphinx]

no ignore it i can code it

[umbral swan]

you can dissect a function of course into linear segments, much more barebones will be difficult

you can achieve some interpolations with bit manipulations too, but I doubt that's what you intend to get

[merry sphinx]

i have done some quantum physics lately so that solved the issue 😭

anyway

so

[umbral swan]

solved the issue for cost-expensive interpolations? 🐛

[merry sphinx]

no i mean solved the issue of me not liking quadratic stuff

[umbral swan]

k but is this interpolation something you want? and what requirements does it have to meet?

[merry sphinx]

this is nice

[umbral swan]

kk

[merry sphinx]

can you give me the formula

(to see what i can try w it if the game likes it or not)

since what we figured out looked like this

https://cdn.discordapp.com/attachments/1255476986135183360/1280892568581701686/aXtqyVi.png?ex=66df01aa&is=66ddb02a&hm=18e83af9d7109e6199fabb1141996b6f2f560a84c9f334f379d02e8cab2d6681&

^^ these are multiple formulas we tried

[umbral swan]

sure, if you tell me within which timeframe it has to meet

[merry sphinx]

it

see

rotation

is in milliseconds

[umbral swan]

is there a fixed interval like 10ms for it to hit max?

[merry sphinx]

like performance.now()

gives you an answer in milliseconds

here is the code i had before

[umbral swan]

I meant do you know which interval it has to fulfill

or is it arbitrary

[merry sphinx]

arbitrary

it will go round and round til my brain dies

or my game dies

there is no fixed ms that it needs to hit max

@umbral swan this is the normal rotation formula

rot += Math.PI * 2 + ((performanceNow() * speedMultiplier) / 3000) * gadget.rotationSpeed;```

performance.now is the current time

and its in milliseconds

speed multi is 1.2 always

[umbral swan]

k, you'd have this for a fixed interval

if it were to hit max rotation in T = 1s for instance

and x is the current time

[merry sphinx]

ok

so x is rot

[umbral swan]

oops time, x = time

[merry sphinx]

t doesnt exist

as i cannot get the exact time its supposed to be hit in

[merry sphinx]

ok

then x means performance.now()

kk

make sure its in milliseconds tho

[umbral swan]

what confuses me is that you want time-independent smoothing

[merry sphinx]

see

the angle

gets constantly changed

there is no specific time

its supposed to hit max rot in

it just keeps rotating til its into max rotation

if it is

then it just stops

that behavior was coded

but smoothing

wants it so it slows down the more its near to max rot

til it hits max rot and it does not go to 0 rotation speed

[umbral swan]

sure, so from the start you wanted a function which doesn't take time, but only the current rotation and spits the next rotation?

[merry sphinx]

yeah

[umbral swan]

k, a sec

[umbral swan]

I'll just recommend using sigmoid as it's one of the best interpolations and you can control the gradient easily

[merry sphinx]

oh ok

[umbral swan]

only difference is that it approaches the desired value in infinity, but this can be corrected by rescaling

[merry sphinx]

oh just so you know

the current rotation goes thru this formula first

rot = rot % math.pi * 2

[umbral swan]

here the rescaled versions

[merry sphinx]

which just makes sure it doesn't go after math.pi * 2

or before it

[umbral swan]

that's clear

[umbral swan]

would this be the kind of smoothing you want?

[merry sphinx]

yeah

but if it goes over max rot

then what would it do?

normally this is not a thing i fear

because i made it so max rot has stuff to do

like if reached it either stops at it

or reverses

or goes and sets rot to negative the current rot

[umbral swan]

well it'd go to 2pi + 0.0001 for instance

and due to the mod 2pi operation

[merry sphinx]

but we have it so if the max rot is 0

[umbral swan]

it becomes 0.0001

[merry sphinx]

it just goes all way around

without stopping

reversing

or setting rot to negative

[merry sphinx]

hmm

[umbral swan]

if max rot is 0 then rot goes from 0 to 0

[merry sphinx]

ah

[umbral swan]

how shall that work

[merry sphinx]

if max rot is 0 then just ignore it completely

that is for our code

if its 1 or more

then it would be counted

as existing

and would do something

[umbral swan]

ok

and if max rot = -pi for instance

which sense would that make

nywys at least for positive angles, here are the formulas

NewRot yields the new rotation value

by inserting the current rotation x

[merry sphinx]

ok

sigmoid is not a provided function within the math. set so imma probably have to use sigmoid.js

but its all alright

[umbral swan]

actually one correction, it'll make it even better

this

[merry sphinx]

or i could use a simple function

const k = 2;
function sigmoid(z) {
  return 1 / (1 + Math.exp(-z/k));
}```

[merry sphinx]

hmm

what is x here

[umbral swan]

x is current rotation

[merry sphinx]

that is alright

what newrot(x) does tho

[umbral swan]

everything in the formulas are constants except for x

[umbral swan]

it gives you the new rotation

given the current rotation

[merry sphinx]

let me try to code dat

lmfao

1 sec

[umbral swan]

SmoothingConst lets you alter the smoothing behavior

[merry sphinx]

then its gadget.maxRotationSmoothing

[umbral swan]

for instance this would be set with MaxRot = 360° and SmoothingConst = 5:

[merry sphinx]

ok

let me try the formula

[umbral swan]

if you want a simpler formula I'll briefly make another one

[merry sphinx]

hmm

[merry sphinx]

no current thing should work

[merry sphinx]

Invalid left-hand side in assignment

..

ok

i might have done something that made it mad lmfao

[umbral swan]

well I can't fix your java errors

I primarily code in c,c#,py

[merry sphinx]

i use c c# and py too

but rn using js

1 sec

okay

@umbral swan the sigmoid function i used was this 1 / (1 + Math.exp(-z/k));

k is 2

is it not valid?

i could use (x) => 1 / (1 + Math.exp(-x));

yeah @umbral swan it did not work

[umbral swan]

k but as said I can't fix the java issues :/

[umbral swan]

looks generally right tho

I've made an easier one:

which uses two smoothing constants

[merry sphinx]

nvm nvm

nvm

it does

speed up

[umbral swan]

ok

[merry sphinx]

but it slows down

by literally

0.00000001

[merry sphinx]

the older one was more understandable.

😭

[umbral swan]

dym in the end?

it becomes too slow

[merry sphinx]

currently it shows speed up

[umbral swan]

or what is the problem

[merry sphinx]

but no slow down

[umbral swan]

k, well the function does mimic a slowdown

[umbral swan]

then try this function instead and attempt the former sigmoid later

bc I'll have to go in a sec

[merry sphinx]

what are perc and cutoff

[umbral swan]

And choose SmoothingPerc = 0.1 and SmoothingCutoff = 0.01 to start with

[umbral swan]

smoothing percentage is your smoothing parameter

how much you want to smooth

but as percentage

so 0% no smoothing

100% max smoothing

the cutoff tells when the infinite smoothing process should stop

in this case on a change of 0.01

[merry sphinx]

hmm

[umbral swan]

do you get the desired result?

[merry sphinx]

i choose to stick with the older one

[umbral swan]

sure you can pick the former one, I just wanted you to try the other to see whether it works

or if some context is missing

[merry sphinx]

actually i have to leave now thank you tho your formula helped alot

like a hell ton alot

[umbral swan]

kk np

[merry sphinx]

as we couldn't get speed up before

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[candid ocean]

How do you evaluate:

d) |10-12| - | 3 - | 2-5| |

[candid ocean]

ik its absolute function and yeah it comes out as always positive but im confusedby the double brackets

so like |-2| - | 3 - | -3 | |

what do i do now

[round mango]

Yeah the annoying thing with || notation is it's not always clear which the left and right is

[candid ocean]

ya for this one its the - | 3 - | 2-5| |

so | 10 - 12 | is seperate

[candid ocean]

but im just a little confused on what i do from here

[round mango]

It is |( 3 - |( 2-5 )|)|

If that makes it easier to read

[candid ocean]

ya but what do i do after

im confused abt after

like | 3 - | -3 | |

is it | 6 |

and then 2 - | 6 |
= -4

🥲

[round mango]

No.

[tight void]

well what is the |-3|

and you are doing okay dw

[round mango]

Ignore the outside brackets for a moment, look at 3 - | -3|

[candid ocean]

ohh so i gotta make the -3 positive right away?

[tight void]

mhm

exactly

[candid ocean]

soo the answer is just 2?

[tight void]

ye

[candid ocean]

ahh ok i see

[tight void]

congrats

[round mango]

Yes.

[candid ocean]

thank uuu lol

[tight void]

that was annoying

enjoy the rest of your day

[candid ocean]

[tight void]

".close" when ur done

[candid ocean]

.close

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[desert pasture]

so I subbed -2 into the numerator, and assumed it;s a root

so 3(4)-a+3=0

so a=15?

and the lim is -1/3

[magic junco]

Looks aight

[safe radish]

@desert pasture Has your question been resolved?

[safe radish]

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[lean otter]

Hello

[lean otter]

Just a quick question, my teacher was telling me i was wrong here

[magic junco]

Alr, show your question

[haughty coral]

Hello?

I need help

[lean otter]

so we got a basic problem which was to find the slope and intercept of
1/2x -3y + 1/3 = 0

so i just said okay i'll put it in y = mx + b form and then state m and c

so my final answer was y = -1/6x - 1/9

m = -1/6 and c being -1/9

[loud osprey]

Should be positive

Cause ur moving the 3y to the right

By adding

1/2x + 1/3 = 3y

[lean otter]

Oh i see the problem im stupid

i just randomly changed the signs of 1/2x and 1/3 to (-) then multiplied it by 3

mb

Thanks

.close

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[quartz bloom]

we have this function and we had to calculate f' and f'', i calculated them correctly but i left the >= sign in the f' but the correct answer (as shown below) has only the > sign why is that?

[quartz bloom]

f' has a solution at 0 thats why i dont understand why 0 gets omitted

[torn star]

it probably is a cusp

[quartz bloom]

so

f'(0)=0

[torn star]

although f(0) is defined there, f'(0) would not be defined

[quartz bloom]

and how should i know thats the case

[torn star]

like how on y=|x|, dy/dx at zero is undefined

[torn star]

plug in zero for both of the piecewise functions at the discontinuity

oh its a jump mb

but its the same idea

[quartz bloom]

wait isnt it still =0

for both sides

0+ and 0-

[torn star]

wait it is

what does "si note che f e derivabile in zero e f'(0)=0" translate to

[quartz bloom]

he underneath wrote (note that f is differentiable at 0 and f'(0)=0)

ye tahts it

"f is derivable at 0" is this english

it means like that a solution exist

f''(0) doesnt exist thats why he put only x>0 there

but shouldnt be the case for f'(x)

waht do you think

[median vigil]

as a note, the usual english word is "differentiable"

[quartz bloom]

oh ye thx

[torn star]

yeah i dont understand why they wouldnt include the equals sign bc the functions are equivalent and their slopes are the same at that point

[quartz bloom]

ok great thx

he must have made a mistake or soemthing

or he just decided to do it this way

[torn star]

if they say f is differentiable at zero then that is the case

[quartz bloom]

maths is an opinion to him as i saw on other exercises

[quartz bloom]

ye exactly

alr thx

i have another question tho

then they ask to establish if f ∈ C^n(R) for n = 0, 1, 2

im not sure how should i do that

im not even sure what that is

[torn star]

do you have a sc of the original?

[quartz bloom]

this is the entire thiing

im asking about (ii) now

[torn star]

ok yeah that's beyond my understanding of calc and theoretical notation, i would ask someone else

[quartz bloom]

uhh ok yeah thanks for your help

i will wait for someone else to join in

[safe radish]

@quartz bloom Has your question been resolved?

[safe radish]

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[upbeat ridge]

Hello

[upbeat ridge]

Not sure how to start

[soft prism]

What do you know about compositions

[safe radish]

@upbeat ridge Has your question been resolved?

[upbeat ridge]

I'm confused about part b)

[terse lichen]

definition of even function?

[upbeat ridge]

f(x) = f(-x)

[terse lichen]

cool

so g is even

so g(x) = g(-x)

[soft prism]

Take 2 sample values of x and try it out on h

[terse lichen]

now h(x) = f(g(x))

if you plug x and -x what do u get

[upbeat ridge]

f(g(x)) & f(g(-x))

[terse lichen]

and since g(x) = g(-x) they're the same thing correct

what does this tell you about h

[upbeat ridge]

They are even?

[terse lichen]

because?

[upbeat ridge]

^

No?

[terse lichen]

ik

[upbeat ridge]

Also, what if f is odd

[terse lichen]

wanted you to say h(x) = h(-x) but whatever

[upbeat ridge]

@terse lichen

[terse lichen]

lemme think

[terse lichen]

well that will depend on the value of g(x)

[upbeat ridge]

f(x) is dependent on g(x)?

[terse lichen]

if f is odd then f(-x) = -f(x)

[terse lichen]

actually are you asking if f is odd then what will happen to h?

[upbeat ridge]

Yes

[terse lichen]

well if you're assuming g stays even

then h is still even

[upbeat ridge]

Okay

Thanks

.close

[safe radish]

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[minor notch]

@Helpe

[minor notch]

<@&286206848099549185>

need help w this one

[random cobalt]

Alr

[random cobalt]

Do u know the dst triangle

[minor notch]

no

what’s that

[random cobalt]

So

Here

D
ST

[minor notch]

distance = speed + time

[random cobalt]

Worst possible illustration for it

Not +

But yeah

[minor notch]

x

[random cobalt]

So

The best way to do these

Is

What do we know

Vs what do we not know

We know the times for both

[minor notch]

f1 + f2 is 3124 miles

[random cobalt]

Yeah

So we know the timings for each and we also know

That the Boston one is 48 slower

So

[minor notch]

yes

[random cobalt]

If we can get both distances

And equal it to 3124

Then we good

So

What is distance equal to

[minor notch]

3124

[random cobalt]

No I meant in general

[minor notch]

=

[random cobalt]

Speed times time remember

[minor notch]

speed x time

[random cobalt]

Yeah good

So

If we use X

For speed

To

Seattle

[minor notch]

3124= x+2.6h

[random cobalt]

And use X-48 for speed to Boston

[random cobalt]

Well we wanna use 1 variable

[minor notch]

yes

[random cobalt]

2.6x + 2(X-48) = ?

Do u know what the ? would be

[minor notch]

3124

[random cobalt]

Yea

So we have

[minor notch]

why are u multiplicating 2.6 by x

[random cobalt]

2.6x + 2(X-48) = 3124

[random cobalt]

Because X = speed to Seattle

And 2.6 was the time to get there

So u multiply to get distance

Likewise

X-48 is the speed to Boston

And 2 hours was the time it took to get there

[minor notch]

ohh

got it

[random cobalt]

So u get distance to Seattle + distance to Boston = 3124(total distance)

[random cobalt]

Great

Do u think you can do the rest on your own

Or do u want some help with the rest of it

[minor notch]

i think

wait

[random cobalt]

Alr ping when u need me

[minor notch]

i did it

thx

[random cobalt]

Np

Congrats

Anyways be sure to close the channel

[minor notch]

thx but there’s another problem i’ll ping u if i need

hold on

[random cobalt]

Oh ok

Can u send the problem so I have an idea of what it will be like

[minor notch]

is this looking good

@random cobalt

[random cobalt]

U have the right idea

I like the way u approached it it

One thing

[minor notch]

yes

[random cobalt]

I think a better way to approach it

Is to have 1 big formula

Rather than like 2 smaller individual ones to manage

I encourage you to limit the # of variable

And have one equation mapping the whole system

Kinda like before where we have a sum of 2 speed times time

[minor notch]

i did that

[random cobalt]

Oh Alr

Nvm

Remember btw

The sum of those two should equal the total interest

[minor notch]

it’s not working

[random cobalt]

Not the total principals

And also

[minor notch]

how do i get total principals

[random cobalt]

4000

It’s given

It’s just X+Y

[minor notch]

but for each lone

[random cobalt]

Which is another thing

[minor notch]

loan

[random cobalt]

U put X for both

But they are diff

So u need to use a system

Use the equation u made

To have

110 = everything else

And use X and Y

Not just X

[minor notch]

huh

instead of 4000 i do 110

[random cobalt]

110 = x(0.03)(1) + y(0.025)(1)

4000 = x + y

Solve the system

Maybe ur teacher lets u have a graphing calc

So u could just graph both lines

[random cobalt]

^you know how I got these rt?

[minor notch]

got what

how do i find them seper’ate

if they’re in the same equation

@random cobalt

[random cobalt]

The equations

[minor notch]

yes

i do

[random cobalt]

Use the system of equations

[minor notch]

i just don’t know how to get x and y seperate

[random cobalt]

And get x and y

[minor notch]

wdym

[random cobalt]

Those r ur answers

[random cobalt]

So

Do u know how to solve a linear system of equations

For example

If I gave u

2x+4y=8
3x+2y=5

Smth like that

Do you know how to get x and t

Y*

[minor notch]

no

how

[random cobalt]

It’s kinda difficult to explain bc this is like an entire chapter ur teacher forgot to teach lmao

But

Can I recommend a short video to watch?

[lusty forum]

i will solve

on one condition

[minor notch]

yea

[random cobalt]

Alr

Here

[lusty forum]

through a math question u need help with

[random cobalt]

https://youtu.be/oKqtgz2eo-Y?feature=shared

U don’t have to watch all of it

Bc it shows diff ways to solve

The part u need is like about 3-5 mins

[minor notch]

@random cobalt i don’t have equations so i can’t cancel out

[random cobalt]

Yeah u can

I gave them to u

[random cobalt]

This

[random cobalt]

And this

[minor notch]

so do i also do 4000-110

[random cobalt]

No bc that won’t cancel out a variable

U should watch the rest bc that will teach u how to solve it faster and simpler

[minor notch]

u gotta do it on both sides

[random cobalt]

Does ur teacher let u use a graphing calc

[minor notch]

so what do i do with the 4000

?

[random cobalt]

^

[minor notch]

idk

class just started

[random cobalt]

What math class is this

[safe radish]

@minor notch Has your question been resolved?

[minor notch]

math-1414

[random cobalt]

Ok

So my advice would be to research how to solve systems of linear equations

And use it to solve this problem

Bc u need it

There are tons of tutorials online on yt and khan that can explain it better than I can

But once u do that

Try to apply it to this system

And u can ping me if you need help with that step

[safe radish]

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[cobalt sorrel]

Won’t this keep turning into an indeterminate form/

[safe radish]

Please don't occupy multiple help channels.

[cobalt sorrel]

<@&286206848099549185>

[plucky elk]

Nope

Use algebra to simplify the last expression

[safe radish]

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[delicate axle]

Is there a better way to say that if all of the coefficients are either constants or independent or dependent variables, it is said to be linear

[delicate axle]

Dependent on at most 1 variable? Ordinary?

Found a better way to put it

but I've tried re-wording this a few times so still, how would you put this in simpler terms?

[safe radish]

@delicate axle Has your question been resolved?

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[distant monolith]

Let I be sqrt(-1)

Will i^(4n+1 ) + i^(4n+3)=0 always?

[frozen marlin]

work it out for yourself and see

try expanding the exponents

[distant monolith]

As far as I did it is

[frozen marlin]

okay good lol

why were u doubting yourself

[distant monolith]

Using polar form?

[frozen marlin]

it's correct

[frozen marlin]

no, just... laws of exponents

[distant monolith]

No one mentioned this anywhere

[frozen marlin]

that is assuming n is an integer

[lean otter]

a^(n+m) = a^ n * a^ m

[safe radish]

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[frail stag]

can someone please help me how to figure out to calculate antilog of a negative number

and don't tell me to use a calculator for the love of god

tell me how to solve it

[safe radish]

@frail stag Has your question been resolved?

[versed wave]

judging by your tone i assume this is not the first time you have asked this and every single person who replied just tells you to use a calculator

and i am going to agree with them, use a calculator

orrr, you can manually calculate it

is the antilog here base 10 or e?

[frail stag]

this was the original question

i made an error it should be -1.565 instead of -1.2435

[frail stag]

yeah im so sorry if it came off as rude, its been bugging me for a day almost

[safe radish]

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[frail stag]

Dawg im asian, if shit like this gets asked, im so cooked, cause we arent allowed to use calculators in exams

.reopen

[safe radish]

✅

[versed wave]

my condolences if you are required to numerically compute log

[frail stag]

😭 YOU GUYS HAVE IT SO EASY

[versed wave]

well?

[frail stag]

the good ol' log book

[frail stag]

base 10

my b didnt see that

[frail stag]

yes this is correct, but im yet to know how to calculate antilog of a negative number on paper

[versed wave]

antilog x base 10 is just $10^x$

[versed wave]

can you clarify for me that what $\overline1.2435$ means

[versed wave]

in + and - please

[frail stag]

@versed wave

input -1.565

instead of -1.2435

[versed wave]

-1.1565, not -1.565

honestly i dont know enough about log table, so i cant really help you with this

[frail stag]

wait im restarted yeah its -1.1565

[frail stag]

alright man, thanks anyways

thanks for atleast trying :> 🦑

[mossy lotus]

Arent you the same guy from yesterday? You saw the -2 + 0.8435 calculations

[mossy lotus]

You take the greatest integer function on the number and take the log of the leftover number

[frail stag]

WAIT

LETS FUCKING GO

I GOT IT

OUAHSDOUASHDOUAHSDOUAHSDOUASHDWA

EUREKA MOMENT

I GOT IT MAN

.close

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[broken solstice]

https://tenor.com/view/soldier-boy-aborddelimpala-the-boys-words-up-gif-26118496

[safe radish]

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[limber grove]

Help

ABC is an equilateral triangle
EF cuts halves (not sure how to translate it)
Prove that: BF is perpendicular to ED
And that FCD is an equilateral triangle

Apologies if any of my translations are wrong

[safe radish]

@limber grove Has your question been resolved?

[safe radish]

@limber grove Has your question been resolved?

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[dim nimbus]

integrate sqrt(v/(v-1)) with respect to v

[stable flint]

you mean this, just to confirm

just substitiute v-1 = t^2

[safe radish]

@dim nimbus Has your question been resolved?

[safe radish]

@dim nimbus Has your question been resolved?

[dim nimbus]

wait but then i can't integrate it either

[stable flint]

you can remember it if u want

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@dim nimbus Has your question been resolved?

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[full hazel]

Did i get these answers right?

[safe radish]

@full hazel Has your question been resolved?

[full hazel]

<@&286206848099549185>

[plucky elk]

1c is wrong

if the individual terms converges to a nonzero constant, then it diverges by the divergence test

[full hazel]

Oh right

Shouldve been obvious to me

.close

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[umbral solar]

guys why when solving integrals

put like this 40 behind the integral sign

I find it like useless action

because it end up the same?

is there hardcore reason to do so?

[median vigil]

not particularly, it just lets you focus on the function being integrated rather than the constants

[umbral solar]

but i can focus if i put 40*t^(-21)

[brave wolf]

If you can integrate it without factoring out the 40, then you can do it without it

[safe radish]

@umbral solar Has your question been resolved?

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[lean otter]

height wrt which base?

[cedar copper]

mb

wait

2sec

[lean otter]

okie

[cedar copper]

AB

height relative tO AB

[lean otter]

so 1/2 AB * height = area?

[cedar copper]

yes

[lean otter]

calculate the area and the distance between A and B then use this relation to find the perpendicular distance of the line segment AB from C.

Which is the height.

[cedar copper]

okay bro, thank you !

🫶

i keep getting the 14 sqrt 17/17

but the answer actually is 53/15

idk waht im doing wRong

.close

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[idle bobcat]

for the bottom one: how ddo i make a paralellogram with only the dots

i dont get the top one at all

[fickle monolith]

,rotate

[fickle monolith]

,rotate

dammit

[idle bobcat]

sorry

[hot crane]

Is this mathematics for highschool and/or college? Or basic math studies also for pre teens like middle schoolers accelerated?

[idle bobcat]

9th grade geometry

[hot crane]

Okay

[idle bobcat]

how do I do the first conjecture thing? I just need an example then I think I can do it for the rest

[daring crescent]

,rotate

[daring crescent]

Does there appear to be a correlation between studying and passing the quiz?

[idle bobcat]

yes ofc i just wasnt sure if i had to use math or js logic

[daring crescent]

I wouldn't assume so?

[idle bobcat]

yeah i was js checking thanks

dumb question sorry

[daring crescent]

The line going from top right to bottom left, cuts the square in half, then the other line appears to be cutting that line around a quarter mark

[daring crescent]

There is no such thing as a dumb question

[idle bobcat]

🤨

[daring crescent]

Do you have to use all the dots?

[idle bobcat]

no

[daring crescent]

Little hint, the outside corner dots, you won't need to use, but the dots on the outside lines you will (there are only two there, find the other two, you should be thinking how can you create two parallel equal length lines using those two out dots (they may or may not connect to eachother))

[daring crescent]

yep

[idle bobcat]

thanks

[daring crescent]

For this one, try and find a way the lines divide up the square, which line should you use to divide the square first? (once figuring out how the first line divides the square write the fractional area of the square on each side of that line)

[idle bobcat]

1/2?

or the other line

[daring crescent]

yep, do you mind sending a photo of just the square again?

[daring crescent]

I would highly recommend doing that line first

[daring crescent]

,rotate ccw

[daring crescent]

You can see this much is true, right?

[idle bobcat]

yes

then divide the 1/2 by 1/3?

[daring crescent]

That would give 3/2 which cannot be true, your numbers are correct but your operation is not

(well relatively correct, is it 1/3 of the 1/2 triangle that is shaded or 2/3?)

[idle bobcat]

whoops thanks

so 1/3 total of the square is shaded?

[daring crescent]

I believe so

[idle bobcat]

thanks

so to answer the prompt i would write "the shaded area represents 1/3 of a square" and what else

then just the procedure?

[daring crescent]

The process we just did

[idle bobcat]

alr thanks

.close

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[idle bobcat]

.reopen

[safe radish]

✅

[idle bobcat]

bye have a good day

.close

[safe radish]

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[daring crescent]

There is a brief intermittent before it resets, you as well, no problem

[idle bobcat]

ty

[safe radish]

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[wispy flint]

why does y=vx for homogenous differential equations i'm having trouble understanding

[wispy flint]

so u divide out the 2xy then u use substitution but i dont understand how to do/understand the substitution part at all

[patent flame]

yes, first divide out the 2xy, then we get y' = (x^2+2y^2)/2xy = x^2/2xy + 2y^2/2xy, which simplifies to y' = x/2y + y/x. Maybe carry on from here?

[wispy flint]

I have that I just don't understand how to carry on

[patent flame]

remember to use the product rule on the LHS to find an expression for y'

[wispy flint]

but the left hand side is just dy/dx?

[patent flame]

yes, but after the substitution dy/dx = d(vx)/dx, which motivates the product rule

right now its y' = 1/(2v) + v, but we cant solve it yet, we need to change our LHS expression in terms of v and x

[wispy flint]

so does it just go vx = integral (x/2v +v) dx ?

[patent flame]

no, first we have to use the product rule on the LHS, as it doesnt just cancel out. also on the RHS its 1/(2v) + v. once you find the correct expression for the LHS you will notice certain cancellations, and the diff eq will become separable. in essence that is the point of the substitution

[wispy flint]

so LHS goes to v'*x + (v)x'?

or v'x + v?

[patent flame]

yes, we should get y' = dy/dx = x dv/dx + v

[wispy flint]

alright

then can u subtract v and get x dv/dx = 1/2v?

then div out x to get dv/dx = 1/(2vx)

[patent flame]

yes, now just separate and integrate - remember to include the integration constant, and then substitute back v as y/x as a last step

[wispy flint]

i'm getting stuck integrating i dont think im doing it right

[patent flame]

dv/dx = 1/(2vx), separate to get 2v dv = 1/x dx, and now integrate both sides

what would the LHS give us

[wispy flint]

v^2 = ln|x| + C

so y^2/x^2 = ln|x| + C

y^2=x^2ln|x| + C

thank u for helping me understand how to solve these kind of problems i finally get it now

.close

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[balmy forge]

could anyone show how to prove by mathematical induction ?

[safe radish]

Please don't occupy multiple help channels.

[obsidian oracle]

well induction has two parts:
Base case and recursion

For example if you want to show an <= 14 for all n

You start with the base case, n=1

(Here It's obvious that a1 <= 14)

Then recursion : suppose an <= 14 for some n

You now have to prove a(n+1) <= 14

You know a(n+1) = sqrt(2+an)

Which is smaller than sqrt(2+14) by induction hypothesis

So a(n+1) <= 4 <= 14

Which proves recursion

Thus induction has been proved and the statement is true for all n

[balmy forge]

ohh i see, yea i understand it now, thank @obsidian oracle

.close

[safe radish]

Channel closed

Closed by @balmy forge

Use .reopen if this was a mistake.

[safe radish]

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[fiery junco]

Help

[fiery junco]

I’ve tried this equation times and for some reason it’s like not mathing?? Like I keep doing one thing wrong each time which makes no sense because it seems easy enough

[median vigil]

what did you try?

[fiery junco]

well to find x i tried finding the derivative then setting it equal to 0

is that wrong?

[median vigil]

but it asks for "slope 2", not slope 0

[fiery junco]

ohhh

i have to set it equal to the slope then

[median vigil]

the derivative is the slope of the tangent line

[fiery junco]

yeah

so

i should do 4x-2=2?

or

idk

right

[fiery junco]

ya this makes more sense to me now lmao

[median vigil]

yes

[fiery junco]

so x=1

then i can plug that into the original equation and get my y value

[median vigil]

yes