help-10

[obtuse pebble]

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[graceful marten]

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[obtuse pebble]

✅

[graceful marten]

Is there a specific reason why you cannot take it as

u = 3cosx + 1

Or did I just do it wrong

du/dx = -3sinx

dx= du / -3sinx

-> sinx (u)^1/2 x du / -3sinx

-1/3 x u^1/2 du

[zenith raft]

you can

[graceful marten]

Is the next step correct

-2/9 u ^3/2

[zenith raft]

don’t wanna think rn soz i’m out

[graceful marten]

nw nw nw

have a good relax

[silk trout]

That’s correct

[graceful marten]

Ok yea

I somehow got the Limmits wrong

On my first try

:/

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[obtuse pebble]

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[graceful marten]

ty

[sage dagger]

hello

[sage dagger]

yesssssss

[graceful marten]

.reopen

[obtuse pebble]

✅

[graceful marten]

BUT you can also do 1+ (x-1)^1/2

right?

[sage dagger]

what happens if you choose the whole denominator to be u

[sage dagger]

are you sure du/dx is correct?

[graceful marten]

No?

I guess I need to use the product rule

And you can’t do it like that

What I did

Yes it is correct 👍 @sage dagger

No it’s not

[sage dagger]

$\frac{du}{dx}=\frac{1}{2\sqrt{x-1}}$

[warm shale]

water beam

[graceful marten]

It’s (x-1)

Yeah

🦫

[sage dagger]

i dont think this is the same thing

[graceful marten]

yeah

(x-1)

and then it is hehe

[sage dagger]

blud

ok

$\int_{ }^{ }\frac{1}{u}\cdot du\cdot2\sqrt{x-1}$

[warm shale]

water beam

[sage dagger]

then you ge tthis

this doesnt look much better than what we started with

[graceful marten]

Yep

Hmmm

But then you have x-1 to get rid of

[sage dagger]

yes why would you want to use this sub

[graceful marten]

First like, last line

[graceful marten]

Bc I get asked in exam by sub

Figure this out

So I have to know it

Otherwise I wouldn’t be doing it frl frl frl

Also I’m doing the safe method

[sage dagger]

u were asked to let u = x-1

sqrt

x-1

not the whole denominator

[graceful marten]

Yeah but I don’t know when I can do what

If that makes sense

U = sub

,rotate

[graceful marten]

What did I do wrong?

Top left

Turned into 2(u-1) / u

Via u-1 = swrt (x-1)

And then I integrated it and got

2u -4u ^ 1/2

Where did I go wrong

did I go wrong?

.close

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[graceful marten]

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✅

[graceful marten]

Did i go wrong somewhere?

u = 1 + sqrt(x-1)

Oh i see

[crude coral]

what is the question?

nvm u got ur answer i think

[graceful marten]

Yea

-2/u is

-2 u^-1

not u^-1/2

Im confused

Q.1

-2 / u

How integrate

Q.2

Also is this possible to find the value of u

through

@crude coral

[crude coral]

always remember that
$$\int \frac{1}{x} = ln|x|$$

[warm shale]

JustToPro

[crude coral]

cuz if u make it into $x^{-1}$ u get something like this $\frac{x^{-1+1}}{-1+1}$ which is equal to $\frac{x^0}{0}$ which is undefined

[warm shale]

JustToPro

[graceful marten]

rightttt

ok!

will note that down

[crude coral]

so u have $\int \frac{-2}{u}$ which u can split into $-2\int \frac{1}{u}$ which ends up being $-2\ln{|u|}$

[warm shale]

JustToPro

[graceful marten]

right

Yeah

If

e^x = u^2 + 2

How e^3x = ??

Lol

cube?

Nvm yeah cubed

lol

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[north anchor]

How I can find asympotes to exponential equation?

[last pilot]

horizontal or vertical

[north anchor]

yea

[last pilot]

and also

!xy

[obtuse pebble]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[last pilot]

no like which

[north anchor]

i dont hve problem

[last pilot]

gimme an example and what u want to find

[north anchor]

e^|x+1|

[obtuse pebble]

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[fossil osprey]

I need help with some Bivariant data I think the topic is, I need to find a lower limit and an upper limit to check if there are any outliers for my datasets

the datasets are:
155, 160, 162, 166, 168, 172, 176, 176, 176

150, 150, 150, 151, 152, 154, 156, 170, 207

155, 157, 160, 161, 163, 164, 167, 167, 169

any help much appreciated im lost 🙏

[fossil osprey]

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[late flare]

can some1 help please

[grizzled shore]

what have you tried

[late flare]

i chose a

because i can see the graph decreasing from j to l

but answer key says that am wrong

[grizzled shore]

how can you tell what the speed of a particle is

[late flare]

isnt speed velocity?

and thats the graph of velocity

on the image

[grizzled shore]

can speed be negative?

[late flare]

hmm

i dont understand

[grizzled shore]

it's a yes no question

what's the definition of speed?

[late flare]

velocity

lol

[grizzled shore]

no

speed cannot be negative

speed is the abs val of velocity

[late flare]

what about velocity?

[grizzled shore]

velocity can be negative

[late flare]

so speed is a scalar quanity?

why velocity is vector?

[grizzled shore]

thats... a very complicated question to answer fully

[late flare]

am just confused ngl

[grizzled shore]

but you can think of it as velocity has all the information

speed only has part of it

speed doesn't care in which direction you're going, just the magnitude

[late flare]

so basically i learn from that

whenever i see speed

i abs value the function

so nothing goes underneath the x-axis

[grizzled shore]

you absolute valute the velocity

[late flare]

ok i got it

thanks alot

can i ask another question please

this confues me alot

[grizzled shore]

this is a bit harder to explain

so first it's saying that f(0) is at -5

[late flare]

how do you approach it

like when i sent the question

how did you first tackle it

[grizzled shore]

and then it tells you that the derivative can't exceed 3

so im thinking

im fixed at 0

(0, -5) is on the graph

now from this point if i go towards the right (because 2 is on the right of 0)

i can't just jump up as much as i want

i can't just reach say 50

then there's 2 parts

there the first part that's just intuition

and the 2nd part is an actual proof for why the answer is what it is

[grizzled shore]

the intuition i have here is that if i can't have a gradient more than 3

then having 3 the entire time will let me "climb the highest"

[grizzled shore]

this one uses the mean value theorem

[late flare]

this part confused me

but can you complete, i may understand at the end

[grizzled shore]

suppose f(2) = 2

oh btw the answer is 2

but we kinda need it for the mean value theorem

suppose first that f(2) = 2

we also know that f(0) = -5

and that f is continuous on [0, -5] (f is differentiable everywhere)

and that f is differentiable on (0, -5) (f is differentiable everywhere)

by the mean value theorem

[late flare]

i know the mean value thoerm

i just dont understand how you're solving it

lol

[grizzled shore]

there exists a c ∈ (0, -5) such that f'(c) = (f(2) - f(0))/2 = 7/2 = 3.5

but f'(x) ≤ 3 for all x

so this c can't exist

so then f(2) cant be 2

[grizzled shore]

we know everything is true except this

[late flare]

so basically because (f(2) - f(0))/2 = 7/2 = 3.5 is greater than 3

its 2?

[grizzled shore]

it means that 2 can't be a possible value for f(2)

it doesn't tell you if the other ones also can't be

or can be

[late flare]

i mean is that how we approached our answer?

[grizzled shore]

well when i looked at the question

i first used intuition to think it probably cant be 2

then i tried to prove that statement

and the tool i used to prove it is the mean value theorem

[late flare]

how did your intuiton tell your that lol

[grizzled shore]

well we're limiting f'(x)

that's how fast my function is allowed to grow

so that means if there's an impossible value it must be too "high"

[late flare]

can you help me with this

i didnt understand how g(1) became = 0

[grizzled shore]

well the point (0, 1) is on the graph

that means f(0) = 1

applying the inverse of f to both sides

f^-1(f(0)) = f^-1(1)

0 = g(1)

[obtuse pebble]

@late flare Has your question been resolved?

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[worthy otter]

e

[worthy otter]

How does math work ? Let's say I am trying to calculate percent error of something which is (measured value - actual value) / actual value * 100 %
Now how does this yield me percentage of error ?

what does |error| / actual value yield me ?

[kind hawk]

well its called the relative error

it tells you how big the error is compared to the actual value. if the relative error is for example 1% then thats probably fine but if the relative error is 50% then thats pretty bad

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[high heath]

I have 3 questions I need help with

[shut rampart]

what are u need?

[high heath]

Here’s the first

[shut rampart]

shoot

[high heath]

I typed it on Desmos but couldn’t find it

Wait wrong one

Sorry

Here it is

?

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[cold rampart]

.close

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[high heath]

Thanks for the help man

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[fluid snow]

#1195800467880558672 message

[obtuse pebble]

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[past walrus]

Can someone explain to me how this is plugged in a calculator?

Cuz when I plug it in I get a different answer

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[fair pine]

I was solving the integral ∫((a+x)^3)dx and I expanded the cube into ∫(a^3 + 3 a^2 x + 3 a x^2 + x^3)dx then solved it as a^3 x + (3 a^2 x^2)/2 + a x^3 + x^4/4 however wolfram says that is wrong. Shouldn't it NOT matter whether I expand the cubed expression or not? What am I missing?

[willow wadi]

because it can also equal ((a+x)^4)/4

but when you expand it, it changes

uwu:3

[fair pine]

yeah but I'd expect it to stay consistent no matter the form as (a+x)^3 = a^3 + 3 a^2 x + 3 a x^2 + x^3

is there a reason why I can't just expand?

[willow wadi]

its because you end up with seperate terms

each term may require different method of integration depending on its form

and not just a simple deriavtive rule like the cubed one

[fair pine]

Hmm so are any of them "more" correct. Or just plain correct and the other one's wrong?

[willow wadi]

to be honest, im not 100% well versed into this, im also assuming it has something to do with "a" being a variable. nto sure how much more i can help as my knowledge on this is pretty limited.

[fair pine]

awee should I ask this somewhere else then? what'd you recommend

[daring sorrel]

It should not matter

I think wolfram is trippin

[obtuse pebble]

@fair pine Has your question been resolved?

[fair pine]

but a^3 x + (3 a^2 x^2)/2 + a x^3 + x^4/4 != (a+x)^4/4 no?

[daring sorrel]

The RHS is not the correct result. You need to do usub; you cannot just apply the exponent rule.

(only need to do usub if u dont expand)

actually maybe im trippin

I think those are just the same thing

[fair pine]

rhs is the solution to ∫((a+x)^3)dx with usub and the lhs is expanding and taking the integral raw

[daring sorrel]

These seem to be the same

If you account for the +C you should add

[fair pine]

I havent hand checked it myself but the rhs should have a term with a^4 whereas the lhs doesn't have it no?

[daring sorrel]

yeah but a^4 is constant so it is only a constant difference (which the +C will handle)

[fair pine]

OHHHHHHHHHHHHHHHHHHHH

THAT MAKES SO MUCH SENSE NOW

HOOOOOOOOOOOOLY

THANK YOU NAMESAKE I THINK I GOT IT AND IT'S CLEARED NOW

because yes without a^4 they ARE the same

[obtuse pebble]

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[shut rampart]

.close

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[fleet hollow]

I need help witht this question I honestly dont even know where to start please somebody help

[queen briar]

note ACD as x

[fleet hollow]

ok

[queen briar]

then DCB is 2x

[fleet hollow]

yea

[queen briar]

2x+x + 75 + 51 = 180

the sum of all angles

[fleet hollow]

ohh

[queen briar]

and from here its pretty straightforward

[fleet hollow]

yeah i get it now thank you so much

.close

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[quiet rapids]

for what value of m(x) is this differentiate?

[quiet rapids]

I was thinking [0,3] and (3,5]

but isn’t that just all real values

[lapis charm]

Do you mean for what values of x is m differentiable?

[quiet rapids]

yea that’s what i mean

[left vault]

its not differentiable at 3

[lapis charm]

Can you try to visualize the tangent line at 3

It’s kind of a meaningless question because there are an infinite number of them

The derivative is undefined

[quiet rapids]

why is it not differentiale at 3

[fathom flicker]

Do you know the definition of the derivative?

[obtuse pebble]

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[spark spear]

Hi, this is a seemingly simple problem I've been trying to solve for half a day now.
(please see image)
Production cap = 0.5
Current production = 0.1
How many days will it take to reach the production cap?

So far I've managed to boil it down to:

You have a sequence of x numbers.
a(1)=0.1
a(x) is the only number >0.5
a(n+1)=0.001*{[a(x)]^2/a(n)}
Because I've plotted this sequence in Excel, I can see that the difference between the last 2 numbers is the last one that's > 0.0005
And if we changed the production cap from 0.5 to say 0.7 or 0.8, the difference between the last 2 numbers would be the last one that's > 0.0007 or >0.0008 respectively.
So if we plotted a curve over this sequence and another one over the differences between this sequence's numbers, the first one would cross 0.5 in the same place that the second one would cross 0.0005 so production cap / 1000.
Untouched on help-forum for over 15 mins, so <@&286206848099549185>

[obtuse pebble]

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[obtuse pebble]

@spark spear Has your question been resolved?

[obtuse pebble]

@spark spear Has your question been resolved?

[obtuse pebble]

@spark spear Has your question been resolved?

[obtuse pebble]

@spark spear Has your question been resolved?

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[pure nacelle]

Hi my exam is in like 10 hours could anyone explain how my teacher got this solution?

[pure nacelle]

mainly for A

I havent looked at b much yeet

because I am confused how he got A from just a rotation of pi/2 about the x axis

<@&286206848099549185>

is anyone still awake that could help

It’s ok I tried to look up matrix representation but I couldn’t find an example that contained this little information

[obtuse pebble]

@pure nacelle Has your question been resolved?

[pure nacelle]

If no one joins should I like like just wait a few hours I don’t wanna like spam ping helpers if they can’t do the prob or they are all sleeping

[obtuse pebble]

@pure nacelle Has your question been resolved?

[pure nacelle]

Ty haha

[zenith raft]

it's saying you can determine what T is just by where it sends e_1, e_2, e_3

if you picture the hint

where does e_1 get sent? where does e_2 get sent? where does e_3 get sent?

example: e_1 = (1,0,0) gets rotated 90 degrees and gets sent to to (0,1,0)

and e_2 = (0,1,0) gets sent to (-1,0,0)

(0,0,1) doesn't get changed

now if we write A as
[a b c]
[d e f]
[g h i]
then just by matrix multiplication we have A(0,0,1) = (c,f,i). but also A(0,0,1) = (0,0,1). so (c,f,i) = (0,0,1)

the other columns can be determined similarly by where A sends e_1 and e_2

[obtuse pebble]

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[obtuse pebble]

Please don't occupy multiple help channels.

[timid silo]

Integrating this

,

Isnt it just (x-2)^-1

oh isee what i didd wrong

.close

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[junior turtle]

I got there but idk, doesnt seem cool to solve, any other methods ?

X and Y are matrices (2,2)

[obtuse pebble]

@junior turtle Has your question been resolved?

[junior turtle]

Ehh Bot maybe ur my only friend

<@&286206848099549185>

[obtuse pebble]

@junior turtle Has your question been resolved?

[obtuse pebble]

@junior turtle Has your question been resolved?

[obtuse pebble]

@junior turtle Has your question been resolved?

[strong plinth]

@junior turtle i don't have much motivating to say, but eliminating a variable in this equation set essentially gives you a quadratic matrix equation $-X^2 + XA - B =0$ and this kind of stuff is really tough to solve in general afaik

[warm shale]

Lartomato

[strong plinth]

i'm not sure what this exercise is trying to do; is this for a specific class?

The explicit matrices in this problem are neither positive definite, nor symmetric, nor do they commute with one another, so I'm not sure if there's anything good to use about this scenario. Otherwise there would be clever things to do

[obtuse pebble]

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[meager palm]

in the context of equivalence relations, what is the difference in these 2 symbols

[brave bramble]

Neither symbol is standard. We'll need more context

[meager palm]

okay

ill show it

[brave bramble]

Maybe "these are exactly the same element when considering the relation n"
And
"These are related under the relation T"?

[brave bramble]

Symbol salad

[meager palm]

I thought 1 and 2 were saying "A is related to B considering n"

until I saw 4

and I was like, maybe im stupid

then i started confusing equivalence classes

I dont know im kinda lost now about what these symbols mean

Like are they all saying "A is related to B"

[brave bramble]

Using :(arrow) for "is defined as" oml

[meager palm]

Yeah

its a little, unconventional (based on what ever other practice I do on the internet)

but yeah do you u nderstand what im confused about (and ty for helping)

[brave bramble]

I'm left to assume 4 is a typo, and these are all regular relations

[meager palm]

There are multiple sumbols for relations right?

[brave bramble]

Even then, some of the relations have a number, some have a set, some have an operation

[meager palm]

also could I ask a quick q about 2

I was trying to do reflexivity, the cardinality of the symmetric diff of A and A (assuming A is some set that satisfies the conditions) is 0, how can we know it is a subset of T?

[brave bramble]

Well, you can use ANY symbol you want. So I see they're feeling free to do that.

Problem is the symbols they're using imply some structure, but there's not one

We typically just use R for "random relation"

[meager palm]

Yeah that makes more sense TBH

[meager palm]

Am I misinterpreting 2?

[brave bramble]

Indeed, I see no reason to assume T is a numeric set.

[meager palm]

can you hlep me break it down

[brave bramble]

This statement implies, to me, that you understand it

[meager palm]

is T a subset of S, or the Powerset of S

[brave bramble]

It's just trying to compare a number to a set

[meager palm]

yeah but why would it ask that q

[brave bramble]

Which is jibberish, yeah

[meager palm]

are you sure im not wrong

this is like practice for my midterm

so like

idk why they would

put something wrong

[meager palm]

also is 3 literally just they are related if A is a subset of B

[brave bramble]

I see lots of errors in books, it happens. Tbh this whole section isn't promising.

[brave bramble]

Yes

[meager palm]

thanks for helping i appreciate it

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[timid silo]

need help

[timid silo]

why is angle BGE half of 135

[obtuse pebble]

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[silk sparrow]

did my prof invert the order on this one:

[silk sparrow]

my notes: the first subscript denotes the distribution the 2nd denotes the category/outcome

then we did an example problem like this:

shouldnt i = the distributuion ie the machine number and j = outcome ie too thin (1), ok (2) , too thick (3) ?

I can swap these things but it seems like they should have inverted the summation order ie the first sum for Q should be j and the second sum for Q should be i if we are going to invert them...

I know its alot but if anyone has the time to help id appreciate it

<@&286206848099549185>

[obtuse pebble]

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@silk sparrow Has your question been resolved?

[junior turtle]

@strong plinth well thanks you tried. The best take probably was to solve the system of 8 equations with 8 variables but thats hard. There are solutions to it but i dont see any way to solve it.

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[lavish fractal]

does (-27)^1/2 equal 3^√-27
I'm just confused if the 27 has to stay negative when turned into the cubed root

[lavish fractal]

ok wait no it doesn't i just googled it

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[vagrant kite]

how do I graph something symmetrical to 0?

[obtuse pebble]

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[haughty creek]

What markov property is used in the first step in the second image?

[remote dagger]

It’s not Markov property

It’s just a fact about independent events

[haughty creek]

What events are independent here

And how do i show that they are independent

[remote dagger]

not reaching j in d steps and (k-1)d steps

[haughty creek]

How do i show that not reaching j in the first (k-1)d and X_m =/= j from (k-1)d + 1, ..., kd are independent

It doesnt necessarily seem too intuitive for me, since letting X_m = j in the first (k-1)d events could result in a way bigger chance of hitting j again in the next kd events. Let the row of the transition matrix corresponding to the state j be smth like eps for everythign other than j and then 1-eps for j

unless im mistaken somehow @remote dagger

[obtuse pebble]

@haughty creek Has your question been resolved?

[haughty creek]

<@&286206848099549185>

[haughty creek]

<@&286206848099549185>

[mental galleon]

stop with these notifications

[haughty creek]

alright dude

[mental galleon]

its annoying ngl

[haughty creek]

okay?

[mental galleon]

I am doing 8 year math

[haughty creek]

Good to know

do you know how to help me?

[obtuse pebble]

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@haughty creek Has your question been resolved?

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[obtuse pebble]

@viscid otter Has your question been resolved?

[viscid otter]

<@&286206848099549185>

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<@&286206848099549185>

<@&286206848099549185>

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[thin pawn]

The position P of a boat going in a straight line after t seconds can be expressed as $\frac{2t^2}{5(12+t)}$. What‘s the boat‘s speed after 12 seconds?

[warm shale]

ℑμΤ𝛄𝛗θ

[wary badger]

absolute value of velocity

[thin pawn]

I tried it and got 1/60 km/s (P is in km btw), but I wasn‘t sure if what I did was right?

[stone radish]

differentiate the position wrt time

[wary badger]

you differentiated?

,w differentiate (2x^2)/(5(12+x))

[thin pawn]

I knew that speed = distance/time, and distance here is P(12)

[warm shale]

Results provided by WolframAlpha

Click here to refine your query online
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Requested by c.knief

[wary badger]

nono

[stone radish]

you need velocity not distance

[wary badger]

this is a position function

it’s direction may be changing and its velocity may not be constant

so you can’t just use distance/time

that’s average speed

[thin pawn]

Ohh

[wary badger]

only works if no acceleration

meaning the second derivative would be zero

[thin pawn]

I see

Welp

Flunked that one

[wary badger]

just plug in 12 to the derivative

and if it’s negative then make it positive

[thin pawn]

Fair. I guess it would have helped if I took a physics class first hm

[wary badger]

because speed is a scalar

[wary badger]

yes definitely

[thin pawn]

Well I‘m gonna go get some physics basics down before I flunk other problems like this one. Thanks for your insight :)

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[outer otter]

Forget the graph though

It will help for an explanation cuz in struggling in calculus

[wary badger]

we can’t see the function

is all that’s given initial velocity and acceleration?

[outer otter]

Wait

[wary badger]

waiting

[outer otter]

I fegot

[wary badger]

damn

[outer otter]

This i think

[wary badger]

ok so the standard kinematic equation

so which part

[outer otter]

Everything other than graph

I have the values already

[wary badger]

so you did part b

[outer otter]

C d and e

Yes

[wary badger]

ok

so

do you know how to differentiate using power rule

with respect to t

[outer otter]

No I was absent for my lessons

[wary badger]

oof

ok

[outer otter]

And I'm behind

[wary badger]

well

do you know how to take the derivative of anything?

do you know what it means

[outer otter]

Dy / DX something

[wary badger]

yes that’s the way we write the derivative

if it’s a function of the form y=f(x)

[mellow quest]

[unreal musk]

[do you know how to differentiate x^n, have you seen that before?]

[outer otter]

Yes

[wary badger]

what is it

[outer otter]

X square 2x

Or something

[mellow quest]

tf

[wary badger]

uhh do you mean the derivative of x^2 is 2x

[wary badger]

?

[outer otter]

Yes

[mellow quest]

its cool

emoji

[wary badger]

yea so in general the derivative of x^n is nx^(n-1)

meaning multiply by the power then subtract one from the power

or exponent

[outer otter]

Yes I'm aware

[wary badger]

so what’s the derivative of (1/2)at^2

if t is the variable

[outer otter]

But i can't diffintiate anything complex

[wary badger]

and a is a constant

[outer otter]

Ok

At?

[wary badger]

yes

now what’s the derivative of ut

with respect to t

[mellow quest]

just send him a video of basic

defferentiation

[wary badger]

go ahead

[outer otter]

Can I just get help with getting the answer

[mellow quest]

idk any

i leant from book

learnt*

[outer otter]

Step by step tutorial how to basic 🙏

[wary badger]

i’m asking you questions that are from your question

[outer otter]

Ik

[wary badger]

what’s the derivative of ut

[outer otter]

U

?

[wary badger]

mhm

so

we have ds/dt=u+at

does this make sense

[outer otter]

Yes

[wary badger]

and ds/dt is just velocity

now we differentiate this equation to find the acceleration

because a=dv/dt

[wary badger]

differentiate this

what do you get

[outer otter]

So just a?

My wifi

[wary badger]

yes

because the derivative of a constant is zero

so then for d just plug in 2 and 6 to the velocity equation

ds/dt

=u+at

[outer otter]

Was that the answer for c?

I and ii

U+ A6 and u+A2?

[wary badger]

no part c wants the equations

part d wants you to use those values of t

[outer otter]

So I change t to 2 or 6

[outer otter]

This?

[wary badger]

part c just wants

ds/dt=u+at

d^2s/dt^2=a

part d wants

v(2)=10+(5)(2)

v(6)=10+(5)(6)

a(2)=5

a(6)=5

[outer otter]

Okay

So 20 and 40?

[wary badger]

yes

[outer otter]

And to compare I say this is underestimate or overestimate

Or what

[wary badger]

you can just say one is greater than the other

[outer otter]

Comparing to what I got from gradient on graoh

[wary badger]

obviously the derivative is more accurate

because it’s the instantaneous value

how did you estimate the slope

[outer otter]

Draw triangle

From curve

[wary badger]

you just did (s(6)-s(2))/4

[outer otter]

I got 20 and 40 for the gradients of the graph aswell

[wary badger]

so you should have 150-30/4

120/4=30

[outer otter]

For what is this

[wary badger]

or wait

did video by 4

[outer otter]

Yeah

Isk

[wary badger]

you should’ve gotten 30

for the average velocity

[outer otter]

Oh I was doing the gradient for each

[wary badger]

how did you find the slope of a quadratic

[outer otter]

Not the average

[wary badger]

without doing derivatives

[outer otter]

Draw from the graph

[wary badger]

can i see

[outer otter]

I'll have a look

[wary badger]

did you just draw a tangent line

i’m not sure what they wanted you to do

maybe they did want the tangent line

that’s strange though

[outer otter]

I don't have the paper or a photo of it but the gradient is easy to calculate u draw a tangent form the curve

[wary badger]

why would they ask you to do the derivative after

ok yea sorry

we don’t do that in america

[outer otter]

My calculus teacher writes the questions I think

[mellow quest]

u still here

[wary badger]

what’s wrong with you?

[outer otter]

Can u confirm one of my answers for another question

[wary badger]

sure

[outer otter]

I got somewhere around 31000

Wait

Did it send

[wary badger]

yes

so did you set the perimeter equal to 750

then do A=LW

2L+2W=750

L+W=375

W=375-L

[outer otter]

Yes

[wary badger]

A=375L-L^2

differentiating and setting equal to zero

375-2L=0

L=375/2

W=375/2

[outer otter]

Then squared it

[wary badger]

yea

[outer otter]

What's the answer?

[wary badger]

idk 375^2 /4

[outer otter]

35156

I think I got that answer

[wary badger]

i got yea

[outer otter]

I'll have to check later

That's all I had to ask

Thanks for the help

[wary badger]

you’re welcome

.close

[obtuse pebble]

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[lament atlas]

what does this 15 choose 2 mean in this answer

i understand 20C4 are all the possibilities

[lapis charm]

How many ways are there to choose 2 that have been tagged

And how many to choose 2 that haven’t been

15 choose 2 and 5 choose 2 right

[lament atlas]

als shouldnt that 5C2 be 4C2

[lament atlas]

5C2

[lament atlas]

18c2

[lapis charm]

No cause 15 haven’t been tagged

So 15c2

[lament atlas]

yes sorry

[lapis charm]

Do you agree with the answer now

[lament atlas]

bu the question i s propability that HAVE been tagged

you said not tagged

[lapis charm]

Well if 2 of the four have been tagged

Then of course the other two haven’t

[lament atlas]

i don't get it

[lapis charm]

The numerator is saying “how many ways are there to get 2 that have been tagged and 2 that haven’t been tagged”

[lament atlas]

i mean i get that 2+2=4

i still don't understand why you insisnt on haven't

instead of have been tagged

[lapis charm]

I mean

Imagine if instead of asking about 2 tagged

They said 2 that haven’t been tagged

Exactly the same question right

[lament atlas]

why the same

[lapis charm]

Because they are asking for 2 and 2

Lemme try to put it a different way

[lament atlas]

ok but why not thinkt about those that have been tagged

in an exam i would never think in the opposite way

[lapis charm]

You need to think of both

[lapis charm]

No I didn’t mean this I realized I phrased it in a bad way

You need to think of both

Like

Let’s say you have all of the deer separated into the two groups right in front of you

You need to pick four of them

The result that we want is if you pick 2 from the left group and 2 from the right group

So how many ways are there to do that? Well 5c2 times 15c2

How many ways are there to pick any 4? 20c4

[lament atlas]

2 groups are equal why 15 and5

[lapis charm]

I meant the two groups to be separated by tag

Those who have and haven’t

Make sense?

[lament atlas]

this ok

ok but i know i am repeating this but why do we care about those who are untaged

ah ok

so out of this 4 2 should be tagged and 2 untagged

an we multipy the combinations of each of them

.close

[obtuse pebble]

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[viral blade]

It seems right to me

Yeah

[obtuse pebble]

@vestal plume Has your question been resolved?

[obtuse pebble]

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[brisk crystal]

im not sure what this is

[alpine verge]

well rolle's theorem states that there exists a number c between a and b such that f'(c) = 0

so it should just be 0

[brisk crystal]

oh yeah ty

I was thinking of the x value that makes it 0

[dense imp]

i'm a bit confused by this problem since $f(-1)\neq0$

[warm shale]

Soosh

[alpine verge]

right it doesnt

[dense imp]

so their claim that this function satisfies premise of rolle's on that interval is wrong lol

[alpine verge]

so rolles shouldnt work

[brisk crystal]

so putting 0 didn't work

[alpine verge]

maybe use the mean value theorem instead

so we'd have $f'(c)=\frac{f(b)-f(a)}{b-a}$

[warm shale]

y0shi

[alpine verge]

since like the function doesnt satisfy RT

[obtuse pebble]

@brisk crystal Has your question been resolved?

[brisk crystal]

ok ty

[obtuse pebble]

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[viral tree]

.20 is the number of the question

I'm trying to find the value of x

[trail cliff]

find a common denominator

[viral tree]

I'll show you my process

I know that it's wrong , I don't know how to find the common denominator here

maybe if I multiply all the denominators I'll find it that way

so it will be 24x^2

I solved it.

.close

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[timid silo]

Slightly confused here

because he says

ar^n-2 * -r = -ar^n-1

[merry peak]

You messed up the exponents by 1 but yeah thats true

[timid silo]

not quite understanding how that calculates, been a long day, sorry if I'm being a little dense.

[merry peak]

Whats a *-r

[timid silo]

the pointer here he says the term immedietly before that is -ar^n-2

https://youtu.be/Cf0-6ngH2gs

[timid silo]

multipled by negative r

[merry peak]

The first term is n=1 and it’s r term is 0

So its ar^n-1

[merry peak]

So -ar

Whats ar*-r

[merry peak]

He didnt finish writing the second sequence

The second sequence has another term in it

[timid silo]

sorry give me a sec just trying to understand it from what you've said so far

trying to 'see' it.

[merry peak]

Whats a*-r

Its -ar

[timid silo]

yeah that makes sense

[merry peak]

whats ar*-r

-ar^2

Continue for all terms in the first sequence

You get -ar^n

[timid silo]

you mean -ar^n-1 sorry?

[merry peak]

-ar^n

[timid silo]

hm

[merry peak]

Its ar^n-1*-r

He didnt finish writing the sequence im prtty surr

Since it has a last term

[timid silo]

this makes it a lot clearer

actually yeah thanks I can work it out from here

thank you!

🙏

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[viscid gull]

no

@real lynx what's your reasoning

[knotty thorn]

it might be 11pm but is it me or are there no actual angles in this image

ive been staring at it for a few minutes now

[viscid gull]

There's arc measures

[knotty thorn]

oh, that's the one

never seen them just be ' x degree '

[obtuse pebble]

@real lynx Has your question been resolved?

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[silent acorn]

Six people are to be seated in a row. Calculate the number of ways this can be done so that two particular people, A and B, always have exactly one person between them.

[silent acorn]

can someone help me with this question

i dont understand how to go about it

[dense imp]

calculate the number of ways you can seat 6 people,
then think of the arrangements in which A and B are seated next to each other and subtract those from the total

[silent acorn]

but the questions asks for exactly one person in between them

would that not also include scenarios where there is 2 or 3

[dense imp]

oh right, my bad dunno why i read that as at least

i guess you could think about putting A in each seat 1 by 1:
if A is in seat 1, then B is forced to be in seat 3 and now you have 4! ways to arrange the remaining 4 persons in the 4 leftover seats

if A is in seat 2, then B is forced to seat 4 etc.

[silent acorn]

so would i just do 4! multiple times?

[dense imp]

if A is in seat 3 then B is forced to either seat 1 or 5, each of those would be another 4! arrangements so for seat 3 it'll be 2 * 4!

i think the other side will be symmetric so i expect it will be (4! + 4! + 2(4!)) * 2 ?

double check that i didnt do anything stupid because i do that a lot

[silent acorn]

i got the right answer ty

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[olive jungle]

Can someone please check if these findings about the graphs are correct

I feel like I got the cluster bit wrong

[cyan oxide]

what a cool problem

have you solved it?

[olive jungle]

Can u help me

Please

[cyan oxide]

what is the question?

[olive jungle]

Are my answers based on the graphs correct

As in its symmerty, clusters outlier ect

[cyan oxide]

oh then no lol sorry

[olive jungle]

Why

[cyan oxide]

uhm

because i dont understand

[olive jungle]

Oh ok

[cyan oxide]

oh i got it lol

[olive jungle]

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[gusty lava]

is this possible?

BD = DC ; AB = sqrt3 ; AD = 3

do i use rule of cosine? but this practice shouldnt be done with a calculator tho

[surreal forge]

as stated there is not enough information

the length of BD is allowed to vary and thus so is the angle ADB

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[vagrant kite]

is x + 6 not a factor because if you insert 6 into the equation, it equals 0?

[thick torrent]

try factoring this equation first

[thick torrent]

you can already see an x to extract

[thick torrent]

wrong channel

[mortal birch]

??

[civic socket]

!occupied

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[vagrant kite]

so I factor the original equation?

[thick torrent]

that would be much easier than testing each choice to see if it evals to 0 yes

[vagrant kite]

ohh ok

x(x^2 - 9x + 18)

[thick torrent]

there's still more factoring you can do

[vagrant kite]

(x-3)(x-6)

x(x-3)(x-6)

ohh so then you just know that it's x+3

because all the other options are in there

ok thanks for the help i appreciate it

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[neat mist]

Please help with 2c
I think for a quadratic equation I have to use -b/2a to find the maximum
but I keep getting 105.8398 mph
but based on the numbers it would have to be 45-50 mph
here is my work so far:
#b.
#Compute the sums
sum_x2 <- sum(speed^2)
sum_x <- sum(speed)
sum_x3 <- sum(speed^3)
sum_x4 <- sum(speed^4)
sum_y <- sum(mileage)
sum_x2y <- sum(speed^2 * mileage)
sum_xy <- sum(speed * mileage)
n <- length(speed)

#Make a system of equations matrix
A <- matrix(c(sum_x4, sum_x3, sum_x2,
sum_x3, sum_x2, sum_x,
sum_x2, sum_x, n), nrow = 3, byrow = TRUE)
b <- c(sum_x2y, sum_xy, sum_y)

#Solving the system
solution <- solve(A, b)

#Find coefficients a, b, and c
a <- solution[1]
b <- solution[2]
c <- solution[3]

cat("Coefficients:\na =", a, "\nb =", b, "\nc =", c, "\n")

#c.
#Calculate the speed for maximum mileage
max_speed <- -b / (2 * a)

cat("The speed at which the mileage reaches a maximum is:", max_speed, "mph")

#105.8398

[coral hollow]

no need

he can just test for roots

[thick torrent]

it's much faster to factor this

i would not test it with each choice personally

[coral hollow]

sure

[neat mist]

So spoilers it is a quadratic with a negative a value. So does the root test of -b/2a still hold?

Oh should I do something else?

[thick torrent]

this is just the x coordinate of the vertex no

[neat mist]

Yes, why does it give me 105. Is my predicted quadratic formula wrong, like are my a, b, c values wrong?

[obtuse pebble]

@neat mist Has your question been resolved?

[neat mist]

How do I do that?

[coral hollow]

if you want to see if x - 3 is a factor

plug in 3 in the equation and see if you get a zero

[neat mist]

I do not want a factor I want a maximum, also 3 is not the maximum or a zero

[coral hollow]

wait

what's your problem

[neat mist]

Based on the numbers above

Fit them to a quadratic equation and find a maximum of said equation

[coral hollow]

you should already have the polynomial

just find the maximum

wait

you do have it right?

[neat mist]

i am not sure if it is correct

this is my process

#Compute the sums
sum_x2 <- sum(speed^2)
sum_x <- sum(speed)
sum_x3 <- sum(speed^3)
sum_x4 <- sum(speed^4)
sum_y <- sum(mileage)
sum_x2y <- sum(speed^2 * mileage)
sum_xy <- sum(speed * mileage)
n <- length(speed)

#Make a system of equations matrix
A <- matrix(c(sum_x4, sum_x3, sum_x2,
sum_x3, sum_x2, sum_x,
sum_x2, sum_x, n), nrow = 3, byrow = TRUE)
b <- c(sum_x2y, sum_xy, sum_y)

#Solving the system
solution <- solve(A, b)

#Find coefficients a, b, and c
a <- solution[1]
b <- solution[2]
c <- solution[3]

cat("Coefficients:\na =", a, "\nb =", b, "\nc =", c, "\n")

[coral hollow]

i forgor statistics

[neat mist]

a = -0.00827972
b = 1.752647
c = 13.27982

[coral hollow]

you can try and confirm with desmos maybe

[neat mist]

yeah is there an algebra way to solve this?

oh that is it

i made the graph wrong

this is not even close to the values in the table

darn

how to get the quadratic of these values?

[coral hollow]

yeah

least squares

[coral hollow]

make a table first

your values are correct

but b is off by 1

maybe you made a mistake there

[neat mist]

oh cool

so how do i get the max computationally

i need to show work I do not think I allowed to say "i plugged this into desmos"

[coral hollow]

set derivative to zero?