help-0

[steel olive]

what is the formula of speed

in terms of distance and time

[alpine sable]

s = d/t?

[steel olive]

yes

so if x is total distance

speed of them both will be x/4.8 and x/8

u r given that x/4.8 = x/8 + 2

now just solve for x

[alpine sable]

24?

[lone heart]

@alpine sable Has your question been resolved?

[hot marsh]

@alpine sable

How to proceed further

[alpine sable]

what is the formula that i have to use?, do you guys have atleast the name of whjat this is called so i can search in google and yt and try to figure it out?

[potent garnet]

creating and solving equations for distance problems

the only formula needed is st=d were s=speed, t=time, d=distance

[alpine sable]

i understand now thanks!

.close

[lone heart]

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[misty notch]

If i have an isosceles triangle and i revolve it around it self, would the base become the circumference of the cone circle?

[echo socket]

Diameter*

[misty notch]

could you link me some sort of 3d demonstration of it?

I cant find the right words to Google what I'm looking for lol

[surreal mason]

https://youtu.be/5ODykPUKWGc?t=41 something like this?

[surreal mason]

diameter or radius? im probably missing smth lol

[echo socket]

The base is the diameter of the circle

[misty notch]

In this case one of that triangle's side will become the radius

but in an isosceles one I'm not sure

[surreal mason]

weird in the diagram above it looks like the radius. anyhow i dont know enough about this to be speaking anyways 😂

[misty notch]

It is the radius, because its a right triangle

[echo socket]

Oh you meant rotating it around one of the sides

I thought you were gonna do it around its height

[surreal mason]

oh i misread your question then my bad

[misty notch]

on my book it says rotate it around its base

would that make a difference?

[lone heart]

@misty notch Has your question been resolved?

[lone heart]

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[knotty oriole]

How does one derive such an expansion?

[mortal trellis]

well there is a formula for the taylor series

essentially just differentiate over and over again

[knotty oriole]

O

Differentiate with respect to what?

I want to give up ngl

[mortal trellis]

h

[hot marsh]

https://tenor.com/view/its-me-im-the-problem-taylor-swift-problem-taylor-im-the-problem-gif-26994473

[mortal trellis]

well wolfram alpha made the series with respect to h

[knotty oriole]

Oh i see

[mortal trellis]

you could also make the series with respect to a. then you would have to differentiate with respect to a instead

you should not use a taylor series to calculate a derivative

that's circular

[knotty oriole]

Yeah

Oh ok

[knotty oriole]

I see

Ok, not sure how to proceed

Is thre some identity i may not be aware of?

Ill open a new channel where the q is more clear from the get go

.close

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[lone heart]

@knotty oriole Has your question been resolved?

[pseudo ice]

Hmm, what are you "allowed" to use to show that? (e.g. can you take the limit $\lim_{h\to 0} \frac{e^{h} - 1}{h} = 1$ for granted, or the series expansion of $e^{x}$?)

[ocean seal]

chartbit

[knotty oriole]

i can use any legal means i suppose

its a recreational question

i've been suggested to try to use the inverse relation

[pseudo ice]

Ah, what's that?

[knotty oriole]

some theorem that says if f and g are inverse functions, then f(g(x) = x

i think, not sure

[pseudo ice]

Hmmm, I don't know, may or may not be what I was thinking of...

At least personally, the way I did it was to write $a^{h} = e^{h\cdot \ln(a)}$ and use the $e^{x}$ series expansion

[ocean seal]

chartbit

[pseudo ice]

There is an easier way to do it though, using the fact about that e limit, that I ended up finding 😂

[knotty oriole]

god dam

i am getting very frustrated. Now i feel a need to prove that $\dv{e^x}{x} = e^x$

[ocean seal]

madlor

[knotty oriole]

perhaps i should show it more generally first

[lone heart]

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[knotty oriole]

dumb bot

go die in a scrapyard

[pseudo ice]

.reopen

[lone heart]

✅

[pseudo ice]

There you go 😂

[knotty oriole]

well tbf i dont know how to progress

the inverse strategy is not nescesarily working out

[pseudo ice]

I know those feels 😂

[knotty oriole]

i think it would be beneficial to my general understanding of math to be able to prove it 😮

[pseudo ice]

There's a proof of the above on "planetmath" if you're feeling lazy and not wanting to do it all out

[knotty oriole]

so its surely worth trying

[pseudo ice]

Guessing do it via the $e^{x} = \sum_{k=0}^{\infty} \frac{x^k}{k!}$ representation?

[ocean seal]

chartbit

[pseudo ice]

There's probably another way, but that's what I thought of first

[knotty oriole]

that sum doesn't use differentiation so

i suppose thats nice

you did use some identity im a bit unfamiliar with

$a^h = e^{h\cdot \ln a}$ is new to me

[ocean seal]

madlor

[knotty oriole]

no its not

nvm lol

thats really clever

[pseudo ice]

Haha yea, it was one they stated in a formula booklet I had ages ago, I believe it's underrated honestly

[knotty oriole]

nice

i was finally able to to prove it 😄

thanks for your help, very grateful

$e^{x} = \sum_{k=0}^{\infty} \frac{x^k}{k!}$

this came in clutch too

[ocean seal]

madlor

[knotty oriole]

but that one is vaguely familiar

.close

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[knotty oriole]

😄

[pseudo ice]

Got'eem

[knotty oriole]

plugging in a=e reveals d/dx(e^x) = e^x too

[lone heart]

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[viscid pagoda]

How would I solve problem 4? I tried solving it, but I'm not even sure if my diagram is right.

[viscid pagoda]

here's the jpeg if you can't open the heic file:

[lusty cloak]

Can somebody help

[vague coral]

#❓how-to-get-help

[lone heart]

@viscid pagoda Has your question been resolved?

[lone heart]

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[mortal trellis]

multiply everything out, get everything on one side and you should hopefully recognize something familiar

[keen cloud]

i did but idk what to do next

[mortal trellis]

what did you get

[mortal trellis]

how did you get that

[keen cloud]

i put 1/2ab on the other side and did subtraction

[mortal trellis]

ok I don't see how that leads to that result but whatever

try doing what I suggested

[keen cloud]

okay

i dont really get it

[mortal trellis]

dont really get what

[keen cloud]

how i can do that

i cant multiply it out

[mortal trellis]

by multiply out, I mean multiply both sides by (a^2+b^2) and by (2ab)

to clear the denominators

[keen cloud]

ah

[keen cloud]

i did that and got this

[mortal trellis]

you earlier said that you got that by subtracting 1/2ab

what now

[keen cloud]

i think i did something wrong

[mortal trellis]

show your work

[keen cloud]

okay

[mortal trellis]

that third line is false

unless you wanted to put a minus before the brackets in the numerator there

[keen cloud]

yeah my bad

[mortal trellis]

but ok I guess

[keen cloud]

its in the last line though

[mortal trellis]

ok

now lets look at the numerator

does that look somewhat familar

[keen cloud]

yeah

-(a-b)^2

[mortal trellis]

ok great

lets also keep the denominator factored like in the third line

so we know have $-\frac{(a-b)^2}{2ab(a^2+b^2)} \leq 0$

[ocean seal]

Denascite

[keen cloud]

yeah

[mortal trellis]

so we want to know whether the LHS is positive or negative

what can we do

[keen cloud]

it is negative no?

[mortal trellis]

what are a and b?

do we know that from the exercise maybe?

is that given?

[keen cloud]

no

[mortal trellis]

ok then we need to go through the cases

what happens if a and b are positive

[keen cloud]

then the expression stays negative ?

[mortal trellis]

yes. what key fact are we using here

[keen cloud]

i don't know english isn't my first language sorry

[mortal trellis]

the important part that we use twice here is that squares are positive

(or rather non-negative but yada yada)

but ok

next case, a positive and b negative

[keen cloud]

then b becomes positive because its squared?

[mortal trellis]

no b is still negative

[keen cloud]

why

[mortal trellis]

well cause it's negative and that doesn't change. do you mean that b^2 is positive?

[keen cloud]

yeah

[mortal trellis]

ok yes

and what about the whole expression?

[keen cloud]

still negative?

[mortal trellis]

no

[keen cloud]

how

[mortal trellis]

https://i.imgur.com/yS1fiNT.png

[keen cloud]

but the numerator is still negative

[mortal trellis]

the numerator is negative and the denominator is negative

that cancels

[keen cloud]

so we have to put it on the right side?

[mortal trellis]

wdym

the expression on the left is positive

so the inequality is false

[keen cloud]

for it to be correct

[mortal trellis]

no then you had 0 <= (something) with the something being negative now

[keen cloud]

ahh okay

i get it now

thank you

.close

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[simple mulch]

identifying significant figures

[simple mulch]

does it change during addition and subtraction

example

6.210 + 0.00043

vs

6.210 - 0.00043

[limpid turret]

nope

[simple mulch]

so weird

cuz in my example test

6.210 x 0.0237

i put, sig fig is 4

but the answer was 3

so is it always the least amount of sig figs?

or do u look for the sig figs AFTER u do the equation

any ideas?

[lone heart]

@simple mulch Has your question been resolved?

[lone heart]

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[tacit arch]

are you looking for the arithmetic sequence formula?

https://www.cuemath.com/algebra/arithmetic-sequence/

[tacit arch]

your sequence is a1, a2, a3, ...

find d = a2-a1

7,11,15,19,23, ... = a1, a2, a3, a4, ....

identify a1 and a2 first

7 is the first term in your sequence. a1 is the first term in the sequence a1,a2,a3...

a1 = 7

what's a2?

this is d

d = a2 - a1 = 11 - 7 = 4

[tacit arch]

a1 is cumbersome. here, they set a=a1

The latter eqn

$a_N = a + (N-1) d$

[ocean seal]

riemann

[tacit arch]

it's your N

not everyone uses your class's notation

[tacit arch]

.

[tacit arch]

.

$a_N$ is the "Nth term"

[ocean seal]

riemann

[tacit arch]

$a_1$ is the "1st term"

[ocean seal]

riemann

[tacit arch]

i'm explaining your question

Nth term is the "general term"

[tacit arch]

.

the general term depends on N

you calculated d

and a

.close

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[gloomy citrus]

i need help

[gloomy citrus]

8 C

[last ether]

They're probably gonna tell you the same thing lol

[gloomy citrus]

i understand how do dialate and what not but once i get to the y/-2=2^x-1 -1

[gloomy citrus]

ye but i dont know how to simplify it

[last ether]

Multiply f(x) by -1/2

[gloomy citrus]

can i multiply an exponential like 2^x-1

[last ether]

$-0.5(2^{x-1} - 1)$ I'm pretty sure

[last ether]

-0.5 becomes a coefficient of 2^(x-1)

[ocean seal]

Umbraleviathan

[gloomy citrus]

would that be the final answer?

or should i expand?

$(-0.5 * 2^{x-1} +2)$

[ocean seal]

RMS

[gloomy citrus]

something like this?

[last ether]

Well -0.5 • -1 isn't 2

[gloomy citrus]

bruh

$(-0.5 * 2^{x-1} -0.5)$

[ocean seal]

RMS

[gloomy citrus]

so like this?

would this be the right answer?

[last ether]

-1 • -0.5 is not -0.5

[gloomy citrus]

gomd

$(-0.5 * 2^{x-1} +0.5)$

[ocean seal]

RMS

[gloomy citrus]

is this better

[last ether]

Yeah

[gloomy citrus]

so this is the right answer?

[last ether]

Im@highly sure yeah if the translations are in sequential order

[gloomy citrus]

the answer that was given was $(2-2^{x})$ tho

[ocean seal]

RMS

[formal fiber]

i can help

rms i can help

[gloomy citrus]

wouldnt mind it

please

[formal fiber]

are you having any trouble on an equation?

[gloomy citrus]

simplifying it

[gloomy citrus]

C

question 8C

[formal fiber]

simplifying what?

is there an image of it?

the full equation of it

[gloomy citrus]

its on this attachment

[formal fiber]

ok

[gloomy citrus]

question 8C

$y/-2=(2^{x-1} -1)$

[ocean seal]

RMS

[gloomy citrus]

this is what i got

[formal fiber]

oh ok

the bot gave what i was gonna say

[gloomy citrus]

repeat it if you like

[formal fiber]

no its fine

but i have a equation that i cant solve

can you help me?

[gloomy citrus]

sure

[formal fiber]

ok

sorry

i was in the bathroom

anyways

let me send image

[gloomy citrus]

ok wheres the problem

[formal fiber]

this is what i did for it

[gloomy citrus]

its not wrong

[formal fiber]

really?

[gloomy citrus]

missing a few decimals

but should be fine

[formal fiber]

oh ok

thank you

im a god at calculus

im very good at it

give me an equation of it

dont give me word problems i hate them

[gloomy citrus]

simplify this

${y/-2}=(2^{x-1} -1)$

[ocean seal]

RMS

[formal fiber]

ok

/let me get a paper

i dont understand it

the way you set the equation and input up is confusing

whats the answer?

[gloomy citrus]

@formal fiber this was the answer

$(2-2^{x})$

[ocean seal]

RMS

[gloomy citrus]

did u get that?

[lone heart]

@gloomy citrus Has your question been resolved?

[atomic osprey]

need help with conjuntion and disjuntion in geometry

[lone heart]

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[pearl robin]

I’m trying to find the ACF (autocovariance function) for this AR(2) process but I’m a bit confused because there’s no X(t-1) term. Ik it’s 0 but still confusing. Where do I go from here?

[lone heart]

@pearl robin Has your question been resolved?

[compact temple]

is this where i get help?

[outer lark]

#❓how-to-get-help

[lone heart]

@pearl robin Has your question been resolved?

[sacred swallow]

does anyone have the answer sheet to serge lang's basic mathematics book?

[compact temple]

i just read it but it says go here so here i am

[lone heart]

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[fallow grove]

Need transformation help:

here is the prompt
-a horizontal stretch by a factor of 1/6
-a vertical stretch by a factor of 4
-a reflection over the x-axis
-a vertical translation by 3 units up
-a horizonatal shift 6 units right

I got y = 4(-1/6(x-6)) + 3

[fallow grove]

$y = -4(\frac{1}{6}(x - 6)) + 3$

is what I got

[fallow grove]

.close

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[foggy onyx]

hi

[foggy onyx]

Example 1.5 Find the Future Value

1. Ana invested ₱30,000.00 in a bank having 8% interest rate of compounded annualy for 10 years. How much ana will gain in after the term of 10 years?

2. ₱51,000.00 at 8 1/2% compounded quarterly for 12 years.

Example 1.6 Find the present value

1. Rayven is planning to invest at a bank, and he is expecting to gain ₱43,000.00 for 5 years, expecting at a rate of 10% compounded annually. How much should he invest to gain the expected balance?

2. ₱80,000.00 at 7% compounded quarterly for 8 Years.

this is not a homework or exam

i have a presentation nextt week and i just wanted to make sure if i have a correct given values

[raw laurel]

$w²y³x⁻²/w²y⁻⁵x³

[foggy onyx]

Example 1.5
1.
P = ₱30,000
R = 8% ≈ 0.08
T = 10 years
N = 10

P = ₱51,000
R = 8 1/2% ≈ 0.085
T = 12years
N = 4

Example 1.6
1.
P = ₱43,000
T = 5 years
R = 10% ≈ 0.10%
N = 5

P = ₱80,000
R = 7% ≈ 0.07
T = 8 Years
N = 4

i just wanna make sure that my given isc orrect on the given problem.

Compound Interest

let
P be the principal/present value
R be the interest rate
T is the time period/term
N be times of compounded (annually, semi annually, quarterly, monthly, and daily).

can anyone answer?

[lone heart]

@foggy onyx Has your question been resolved?

[foggy onyx]

can anyone answerrrrr

[lone heart]

@foggy onyx Has your question been resolved?

[molten pivot]

$FV = PV(1+r)^n$

[ocean seal]

Mr. Gamer

[molten pivot]

There is nothing more to it

Keep in mind that n is the number of periods

And r should be the periodic rate

Which may or may not be equal to the annual rate

[harsh vigil]

Need help

Nvm I did it

[lone heart]

@foggy onyx Has your question been resolved?

[pliant cedar]

close the channel

[lone heart]

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[finite fern]

Hey guys

[finite fern]

Can anyone check up on how I did? Thanks!

[hot marsh]

@finite fern what?

I just see task.not what you've done

[hollow leaf]

U don't even need quadratic equations for most of these

Number 3 x is -3 or -4

[finite fern]

Oh wait

Hold on

I frogor 💀

Color coded too

[hot marsh]

@finite fern
2nd isn't good

[finite fern]

Uh oh

[hollow leaf]

When u move a term from one side of the equation to the other, what happens to the sign?

[finite fern]

It xhanges

[hollow leaf]

Yep it flips

So for number 2 check it again

[hot marsh]

Everything else is fine

[hollow leaf]

Yep

[finite fern]

Thankz!

Imma work on 6-10 later

[hot marsh]

@finite fern they ask of u to give them numbers tho

For example in 3)
A is 1
B is 7
C is 12

That's what task wants you to do

[finite fern]

Im too lazy so im color coding them

Red is a

Yellow is b

Green is c

[hollow leaf]

X shouldn't be highlighted then

Cuz it's asking for the values of a, b, and c

[finite fern]

Oh

Oope

Oops

Random question, why are if then statements part of math?

Conditional, converse, inverse, biconditional and such

And contrapostive

[prime badge]

your question is not a math question
it's like why do people say "do laundry" instead of "wash", like "I wash on sundays".
There must be some reason, but like, it's not very interesting to know why that happened.

[left juniper]

yo

sup

[lone heart]

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[dim crystal]

Can I get some help with my math homework?

I badly need it today

[alpine sable]

For the first question, probably start with completing the square of that equation to get the equation of a circle

you will find the focus of the parabola once you find the centre of the circle

[dim crystal]

I dunno how to solve it😭

[dim crystal]

can you help me? i still can't figure it out

[alpine sable]

You have
[
x^2 + y^2 -6x -6y + 17 = 0
]
Can you turn that to the equation of a circle?

[ocean seal]

♡LexQa♡

[dim crystal]

nope

[alpine sable]

Are you familiar with completing the square

[dim crystal]

no, sorry

[alpine sable]

Umm I think you should look it up

[lone heart]

@dim crystal Has your question been resolved?

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@dim crystal Has your question been resolved?

[lone heart]

@dim crystal Has your question been resolved?

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@dim crystal Has your question been resolved?

[lone heart]

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[radiant karma]

How do u do this?

[lone heart]

@radiant karma Has your question been resolved?

[radiant karma]

<@&286206848099549185>

[wild trail]

That looks like sum of alternating square

Separate the positive and negative and then try to use some formula

[radiant karma]

Which formula

[wild trail]

I mean it is sum of squares so ...

[radiant karma]

Yeh but here its positive and negative

[wild trail]

That's why I told to separate them

[alpine sable]

i dunno effecient way

[wild trail]

Looks fine to me

Instead of 2k -1 you could have taken 2k+1 to include 19

[alpine sable]

yes

[wild trail]

Although that would shift +1

[alpine sable]

🏃‍♂️

[wild trail]

[lone heart]

@radiant karma Has your question been resolved?

[daring lark]

Guys please help me in this question.

[pliant cedar]

u shud get ur own channel

btw u can do this with the midpoint theorem

[jaunty acorn]

guys what does 2ab mean? (a=2 b=4)

[lone heart]

@radiant karma Has your question been resolved?

[last path]

it means 2 times a times b , 2 * a * b = 2ab

[alpine sable]

Kind sir if your question has been resolved please close it. It been active for many day now and is taking away from kind users.

[lone heart]

@radiant karma Has your question been resolved?

[radiant karma]

Many days?

I made it a few hours ago

[tame shell]

pair it up as (1-4), (9-16), (25-36), (49-64), etc

this is a sum of an arithmetic sequence

[lone heart]

@radiant karma Has your question been resolved?

[lone heart]

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[celest cosmos]

Hello

[celest cosmos]

So i need help with my performance task if thats okay?, like just a bit explanation

so

[woven plaza]

Hlo

[celest cosmos]

Hello

.close

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[frigid owl]

How can I prove that sin^4x - cos^4x + 2cos^2x = 1

[frigid owl]

I managed to simplify it to this
2-cos^4x+sin^4x-2sin^2x=1

[upper estuary]

Uh I don't think that simplifies anything

Apply difference of squares to sin^4x - cos^4 x and work from there

[frigid owl]

I just changed it to this

differences of squares?

[upper estuary]

a^2 - b^2 = (a+b)(a-b)

you can expand it to see how it works

[frigid owl]

2 - (cos^2x - sin^2x) - 2sin^2x = 1

[upper estuary]

uh not quite

in the above example, a^2 - b^2 = (a+b) (a-b), a=sin^2x and b=cos^2x

[woven plaza]

(sin²x-cos²x)(sin²x+cos²x) + 2cos²x

[tiny coral]

but sin^2x + cos^2x = 1

[woven plaza]

Yea

[frigid owl]

wait hold on

how do you do cos^2 like that

[woven plaza]

Google keyboard on phone 🙂

[frigid owl]

o

[woven plaza]

Just longpress the 2 button

[frigid owl]

(sin²x-cos²x)(sin²x+cos²x) + 2cos²x

would it just become

(sin²x-cos²x) + 2cos²x

[woven plaza]

Yes

Now that again becomes sin²+cos²

Which is 1, rhs

[frigid owl]

what

[trail ginkgo]

Take away the parentheses and combine like terms

[earnest oar]

any easy way to memorize multiplication tabla

table*

[long axle]

@earnest oar #❓how-to-get-help

[frigid owl]

.close

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[ornate heath]

Have I proven that the limit of a product is the product of the limits (ie part b) of the theorem)?

[ornate heath]

(Ignore a), sorry about that)

[ocean seal]

person2709505

[lone heart]

@ornate heath Has your question been resolved?

[ornate heath]

<@&286206848099549185>

[wild trail]

The bounds are more or less calculated in hindsight. There is no need to remember them.

It's just algebraic manipulation at work

[ornate heath]

So basically whatever bounds happen to pop out of your scratchwork are as good as any?

Or do you mean those bounds in particular can easily be rederived?

[wild trail]

Yess, kind of. What happens is that you want to bound everything by epsilon ultimately and you use cheap tricks to do that

In fact, there are more than one ways to do this, you can go easier to understand but weird bounds

[ornate heath]

Actually, is there a way to do this that uses the "largest possible" delta?

Since I guess that would be the opposite of a cheap trick

[wild trail]

Here is another way to do this

[wild trail]

Sadly no, choosing the delta is part of the trick, in fact the most important part

The whole point of doing this is that you only want constants on the right side cause that could be easily manipulated

[ornate heath]

Oh what this is awesome

[ornate heath]

Does that mean it's not possible to know the largest delta-neighbourhood whose image through the function is in the epi-neighbourhood of the limit?

At least for a general product of functions like we had here

[wild trail]

More like, we don't bother about that cause we just want some delta not the most optimum delta

[ornate heath]

Ok, I see

[wild trail]

If it works it works kinda stuff

At the end of the day all you want to do is finish the proof

The beauty of the proof comes much later, as a student you shouldn't care about it much

[ornate heath]

The beauty of this proof in particular?

[wild trail]

I mean wouldn't you agree that the bound looks ugly in the first proof

vs here, you have a much cleaner no nonsense proof

[ornate heath]

Oh wait, you're referring to the ugly bound here

Or sorry, were you referring to the one that was different for f(x)-l and g(x)-m?

Either way yes, the proof you sent was much more elegant looking

Where was that from btw?

[wild trail]

The one I sent is from Principles of Mathematical Analysis, Rudin

[ornate heath]

Ah that book

[wild trail]

yeah, it's a good book for supplement

Not great for a textbook

It's famous for slick proofs

[ornate heath]

Hmm, maybe I'll have to look through that to see if there are any results we proved in class that could be made slicker

[wild trail]

Sure, so are you good with it?

[ornate heath]

Yes, thanks!

[wild trail]

[ornate heath]

.close

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[ember badge]

im so lost

[ember badge]

how am I messing this up

cause I think the assignment is just broken

for b I got 87.01235064

[dawn void]

i am stuck in a question

[lone heart]

@ember badge Has your question been resolved?

[hollow leaf]

@ember badge I just wanted to point out that the value u got when rounded to the nearest hundredth is 87.01 not 87.02 which is what u put

[ember badge]

@hollow leaf yeah ik

I was messing around with the decimals

to see if that was it

[hollow leaf]

Alr

[ember badge]

but I tried 87.01

still didnt work

[hollow leaf]

I actually don't know this topic well

So I can't rly help u

[ember badge]

no worries

thanks for trying tho 🙂

[hollow leaf]

I got 57.95..?

Is there a formula for determining temperature after a time period when the environment is a specific temperature

[rose sigil]

newton's law of cooling?

[hollow leaf]

If it's linear then since it dropped 44 degrees in half an hour, then it would drop 85 degrees in 57.95 minutes

I'm just wondering is the decrease linear

[rose sigil]

also that says it's not linear 😶

[hollow leaf]

Oof ok ignore everything I just said

[ivory igloo]

apparently we have to convert the temperatures to fahrenheit?

oh nvm

its in fahrenheit

[ember badge]

I don't know whats going on cause I got the first part right

so I don't know why that wouldn't work for the second considering the part before was righjt

and its just a matter of setting the equation equal to 100

[ivory igloo]

hmm

so k = -2ln(0.6) rt?

100 = 75 + 110*e^(-kt)

25/110 = e^(2ln(0.6) * t)
ln(5/22) = 2ln(0.6) * t
t = ln(5/22)/2ln(0.6)

= 0.5 * ln(5/22)/ln(0.6)

almost 1.45020578

so almost in one and a half hours?

@ember badge

87 hrs sound weird for some reason-

[ember badge]

@ivory igloo OHHHH
THAT WAS IT

I got one more question

[ivory igloo]

whoa

[ember badge]

can you walk me through this question

I've been following along a video guide

but my answer is always wrong

[ivory igloo]

hmm

[pliant cedar]

rate of sales growth is prop to (70,000 - current sales) ?

[ember badge]

dy/dt = k(70-y)

[pliant cedar]

yeah

[ember badge]

y(0)=0

y(5)=22

[ivory igloo]

im suspecting that it involves e

[ember badge]

thats what I know

@ivory igloo it does

[ivory igloo]

oh.

[pliant cedar]

u must find y(12)

right

[ember badge]

yea

[pliant cedar]

why is ur answer wrong

[ember badge]

idk

I think either my constant is wrong

or my formula is wrong

[ivory igloo]

u got the formula for sales?

[ember badge]

dy/dt = k(70-y)
given:
y(0)=0
y(5)=22

let me find my

formula

then I g et

y=e^(-kt)+70

is that right?

[pliant cedar]

i guess u r missing a constant

[ivory igloo]

Things that grow or decay proportionally to itself, with no limits, is known as "uninhibited" growth/decay

i found this

and this

[pliant cedar]

oh so u thot the rate of growth is also prop to the current sales

[ivory igloo]

oh wait

[pliant cedar]

in addition to being prop to the difference?

[ivory igloo]

shoot

i didnt see that part 🤦‍♂️

[ember badge]

im missing a constant

but isnt k the constant?

[pliant cedar]

yes

[pliant cedar]

theres another one

when u integrate

[ember badge]

wat

[pliant cedar]

the constant of integration

[ember badge]

OH

C

I FORGOT

[pliant cedar]

yah lol

[ember badge]

y=e^(-kt-c)+70

[pliant cedar]

yeah

[ivory igloo]

ykw idk anymore

[ember badge]

so

how would I solve for both the constants now

[pliant cedar]

substitute the initial conditions given

y(0) = 0

y(5) = 22

[ember badge]

ok

so using y(0)=0

I got -ln(70)

for c

[pliant cedar]

yeah

[ember badge]

so now I would use

the y(5)=22 to get k?

[pliant cedar]

yeah

[ivory igloo]

ln(3360)/5 = k?

[pliant cedar]

whoa

idts

thats not what i got at least

[ember badge]

ok

for k I got

-(ln(35/24))/5

[pliant cedar]

btw it might help to write e^(-kt-c) = e^(-kt) * e^(-c), and just treat e^(-c) itself as a constant

[ember badge]

in decimal form k = -0.07545884

[pliant cedar]

yeah thats what i also got

[ember badge]

ok

so now I solve for 12

[pliant cedar]

yeah

[ember badge]

41.7

I got it

LETS GOOOOOO

[pliant cedar]

👍

[ember badge]

ok ok

I lied

im looking back

I have ONE more question

[pliant cedar]

lol

ok

[ember badge]

ok so I solved this yesterday

but got stuck on the last part

idk what a eulers method is

[pliant cedar]

oh idk that too

[ember badge]

damn

[pliant cedar]

thats a numerical method of solving differential equations but idk exactly how its done

[ember badge]

I'll figure it out

[pliant cedar]

i guess with eulers method rate of cooling is approximated as (temp after one min - temp right now) / 1 min approximately equals rate of cooling

[ember badge]

ic

[pliant cedar]

so (temp after 1 min - 95) = -0.025*( 95 - 20 )

so temp after 1 min = 93.125

then again

(temp after 2 min - temp after 1 min) = -0.025( temp after 1 min - 20 )
(temp after 2 min - 93.125) = -0.025( 93.125 - 20 )

and u keep doing that

till u get temp after 5 min

[lone heart]

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[ember badge]

@pliant cedar thanks!

I got it

[lone heart]

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[fringe cove]

hello, i have a question again about boolean algebra? can someone check if my solution is correct.

this is the given function -> F = XYZ + XY′Z + XYZ′
solution:
XYZ + X (Y' . Y) + (Z' . Z)
XYZ + X
XYZ

[delicate glen]

how did you get to the first part of the solution

since that would just be equal to X.Y.Z + X.Y'.Y + Z'.Z

instead, I would find the common factor in each of them

so X.(Y.Z + Y'.Z + Y.Z')

[fringe cove]

what i did is i bring down xyz and bring together not y and y and not z and z to cancel them since they're going to be equal to 1 and then i just bring down the rest which is the xyz + x but since x is equal to 0 that's why i got xyz as the answer

im really confused in this lesson so i don't know if im doing it right

[delicate glen]

think of 2 letters like XY as a multiplication

like X × Y

so if you want to factorise something

do it the same way as you'd do in any other maths class

I.e. xy + xz = x(y + z)

[fringe cove]

oh since from the original equation there are 3 X that are common in every term it means that i can factor them out

[delicate glen]

yes

[fringe cove]

can i still simplify or this is the final answer?

[delicate glen]

you can

Y.Z + Y'.Z + Y.Z' is the same as another much simpler operation

draw the truth table for that, and see if it looks the same as another operation

[fringe cove]

can i simplify them as what i did from the first? like this part Y.Z + Y'.Z + Y.Z will transform to y' . y and z'.z and since they're both equal to 1 i will only have x which is equivalent to 0

[delicate glen]

no

you can find another common factor in 2 of the terms

[fringe cove]

which is the z right?

[delicate glen]

either y or z

doesn't matter, there's a few different ways of doing this

[fringe cove]

z( y' . y)

[delicate glen]

and y.y' isn't 1, it's 0

since if y is 1, then y' has to be 0

0.1 = 0

[fringe cove]

oh really because our prof told us it's 1

[delicate glen]

your Prof might have meant y + y'

which is 1

[fringe cove]

oh okayy thank you

[delicate glen]

no problem

have you gone over how to simplify x + x.y?

[fringe cove]

nope still stuck in Y.Z + Y'.Z + Y.Z

[delicate glen]

I'll go over the process and you just let me know of there's something you don't get

y.z + y.z' has a common factor of y, so we can make thay y.(z + z')

so now we have y.(z + z') + y'.z

and z + z' will always be equal to 1, since they can't possibly both be 0

and that gives us y.1 + y'.z

and y.1 is just y

giving us y + y'.z

and we don't even need the y'

since if y = 1, the statement is already true

and if y = 0, then y' is always 1,

so the y' is redundant

and so cancelling out the y' gives us y + z

and thats out answer

and remember to add that x back in from the beginning to give us x.(y+z)

that all make sense?

[pliant cedar]

or u can use de morgans theorem i guess to arrive at the same answer but in a kind of uglier way

[fringe cove]

why cant we cancel y and y' also like z and z' ?

[delicate glen]

because the y' is attached to a z

(y+y').z = y.z + y'.z

[fringe cove]

its in different ttermterterterm right?

oh sorry

[delicate glen]

easiest way of doing it would just be to realise y.z + y.z' + y'.z is essentially just a complicated way of saying y + z

[fringe cove]

u use redundancy law for the last part right?

[delicate glen]

honestly I don't remember the names of the laws

[fringe cove]

like u removed the y'

[delicate glen]

yeah

[fringe cove]

okayyy got it thathanthanthanthanks

.close

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[pliant cedar]

yeah

[lone heart]

@pliant cedar Has your question been resolved?

[lone heart]

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[echo socket]

$L=\lim_{n\to{\infty}}\sqrt[n]{\frac{1}{3n-1}} = \lim_{n\to{\infty}}(3n-1)^{-\frac{1}{n}} \$
$\ln{L}=\lim_{n\to{\infty}}\frac{-\ln{(3n-1)}}{n} \$
Apply L'hopital's rule

[ocean seal]

A Lonely Bean

[fervent narwhal]

cool thanks

.close

[lone heart]

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[half belfry]

1+1=？

[keen pasture]

10 (in binary)

[pliant cedar]

😑

[half belfry]

Bin dir sehr dankbar

[keen pasture]

Please stop trolling. Asking what 1+1 isn't very creative either. Dozens of people have already done it

[rose sigil]

.close

[lone heart]

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[viral pagoda]

Omg

You're a mod

How do u become one

[rose sigil]

i'm not haha

[pliant cedar]

can anyone type .close and close?

[rose sigil]

idts

[viral pagoda]

So like... U have some odder position in this server?

[alpine sable]

Whaaat????

[viral pagoda]

Ye

[alpine sable]

How is this possible???

[viral pagoda]

Yea like HOW

[pliant cedar]

btw how are u assigned roles here

[viral pagoda]

Good Qn

[alpine sable]

Ooh, i have a good question

[viral pagoda]

Lolz

[alpine sable]

Why isn't any number from one interger that's divided by zero, isn't ±1?

[keen pasture]

Then please open a new channel 🙂

[alpine sable]

And they put "undefinde?

HAHAHAHAH you know, I'm not trying to get help about that question, HAHAHA

[lone heart]

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[alpine sable]

Ohhhhh, sheesh

[alpine sable]

Close

[keen pasture]

.close

[lone heart]

Channel closed

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[alpine sable]

How???

.close

[keen pasture]

Hacks

[alpine sable]

Thankss

[lone heart]

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[alpine sable]

hey im having trouble getting the slant height of a truncated cone in terms of the height of said cone

[alpine sable]

i found this but something seems odd, why is he writing R2 - R1 when R2 is supposedly the smaller radius

this is what i got

[mortal trellis]

Who says that R2 has to be the smaller one

[alpine sable]

thats what im saying

oh i mean

unless youre syaing

he used R2 as the bigger radius

[mortal trellis]

Yes

[alpine sable]

ah

so yeah what i wrote down is correct right?

cause i doubted myself for a second their

there*

[mortal trellis]

Yes is correct

It's always important to check what different people mean by their notation

[alpine sable]

bet

thanks dude

.close

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[swift spire]

can someone explain what 1:n means or n:1 in simple terms

[ember badge]

show the problem

[swift spire]

2:3

i aligned 1:n under it

and i figured you divide n (which is 3 here) from each side

[viral pagoda]

Wdym

[swift spire]

so 2/3 : 3/3

[swift spire]

like:

2:3
1:n

i watched a video this is how it is

as far as i know

[viral pagoda]

Ok

[viral pagoda]

1 part by n parts?

[swift spire]

does it also work for n:1?

[swift spire]

is that it?

[viral pagoda]

Divide by two ig

[swift spire]

i dont get it

the video link is https://www.youtube.com/watch?v=DMpHO2ehvMU if you wanna understand the technique

does 1:n/n:1 just explains that whatever happens to one side it must happen to the other side aswell

like

2:3

say we multiplied 2 by 4, so 3 must also be multiplied by 4, giving us:

4:12

i just answered myself

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[grave kiln]

hello, why is that correct if (x+2)(x+2)^2 is not equal to (x+2)^2 so that it is canceled?

[remote heron]

it looks like a partial fraction decomposition

[grave kiln]

yes, but for the denominator (x+2)^2 to vanish, multiplying (x+2)(x+2)^2 does not vanish

[vague coral]

didnt you see that they multiplied both sides by (x+2)^2

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[wheat isle]

How do i find the x and y intercepts of a function?

[wheat isle]

e.g y = 3x - 2

[mortal trellis]

x-intercept means the point is on the x-axis, so the y-value is 0

y-intercept means the point is on the y-axis, so the x-value is 0

so you can either plug x=0 or y=0 in the equation and then solve for the other one

[wheat isle]

so for this it would be

0, -2?

o

ok

[mortal trellis]

the y-intercept is at (0, -2), yes

[wheat isle]

and for the x intercept it would be

1?

(1, 0)?

[mortal trellis]

if x=1, then y = 3*1-2 = 1

so no

you want y=0

so 0=3x-2

[wheat isle]

but how do i find the x intercept of that

[mortal trellis]

can you solve the equation 0=3x-2 for x?

[wheat isle]

hold on

2/3

[mortal trellis]

yes

so the x-intercept is at (2/3, 0)

[wheat isle]

ahh okay

does this method only work for linear functions

[alpine sable]

no

[tribal haven]

works for any function

[wheat isle]

okay cool

[alpine sable]

for example

the x intercept of

like x^2 - 1

is when y = 0

so

the x intercept of x^2 - 1 is just plus minus 1

,0

[wheat isle]

that makes sense

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[native temple]

How to solve this? #help-6 message

[random gull]

writing x/$x2+$4x$4

[ocean seal]

𝐁ɴゞtereno_z_
Compile Error! Click the reaction for more information.
(You may edit your message to recompile.)

[pseudo ice]

for context

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@rapid onyx Has your question been resolved?

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[real tulip]

5tanx-3=1
0°<=x<=360°

[real tulip]

I know 1 point on the graph but how to i find the other one?

.close

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[fervent narwhal]

can you prove this using limit definition?

[jagged cobalt]

should be able to yeah

i believe you end up with 1/N<epsilon

[fervent narwhal]

I know but we have n=2k and n=2k+1

So it's like we have two different sequences

[pseudo ice]

The limit definition (for real number sequences) is that for all $\varepsilon>0$, you can find an $n_{\varepsilon} \in \mathbb{N}$ such that for all $n\geq n_{\varepsilon}$, you have $|a_{n} - l| < \varepsilon$

[ocean seal]

chartbit

[jagged cobalt]

youll have the absolute value of the sequence - so the top will just be 1

[pseudo ice]

For $a_{n}$ being the sequence and $l$ being your limit

[ocean seal]

chartbit

[pseudo ice]

(some definitions may make some of the equalities strict or non-strict, but they're all equivalent)

[fervent narwhal]

.close

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[alpine sable]

I thought the higher n, the more exact but i was wrong apparently, i tried with n=5 on this problem and got like 90 million but the actual answer is -653 because i have to choose n=3, i thought the higher n the better value but thats not the case, how do i pick n?

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Please don't occupy multiple help channels.

[mortal trellis]

iirc quadrature rules for high n are numerically unstable

maybe that's the issue

[alpine sable]

I used n=5 here

(The numbers from that table under n=5)

[alpine sable]

How can i choose what n then? In the solution that say "because the polynomial is of 6, we use 4-node..." but why

Whats the reason behind it

[mortal trellis]

well cause that's enough

[alpine sable]

Why not 3 then?

[mortal trellis]

3 node is only accurate for degree 5 iirc

[alpine sable]

Whats iirc

[mortal trellis]

if I remember correctly

k nodes -> accurate up to degree 2k-1

[alpine sable]

Ohhhhhh shit