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[sterile ibex]

I keep getting 29.4

Position change is 88.2 divided by 3 seconds

[light sonnet]

Do you know derivatives?

[sterile ibex]

This is the first lesson in them for me

I know velocity is change in position over change in time

[light sonnet]

In other words, derivative of position is velocity

[sterile ibex]

Yes

[light sonnet]

That means for that question, you take the derivative

[sterile ibex]

The lesson just said that a derivative of something is just its slope

And the worksheet problem that had a similar problem did the exact same thing I did, take the difference of change in position divided by the change in time

?

[sharp flame]

That gives you the average velocity

Not the instantaneous one

[sterile ibex]

What I did?

[sharp flame]

yes

As dldh said you need to take the derivative and plug in 3

[sterile ibex]

Isn’t it asking for the velocity after 3 seconds?

Yeah

Didn’t I do that?

[sharp flame]

This?

[sterile ibex]

9.8(3)^2

3-0 on bottom

[sharp flame]

no that's the position

no

[sterile ibex]

And then divide

[sharp flame]

Take the derivative

$\dv{t} at^n = nat^{n - 1}$

[glossy valve]

neonperseus

[sharp flame]

Surely you've seen this before

[sterile ibex]

Acceleration but not the power rule yet no

I’ve seen it but not from the lesson

[sharp flame]

no a is just a constant

huh you haven't learnt the power rule yet

That's weird

[sterile ibex]

Yeah

This is literally the first lesson post limits

[sharp flame]

oh bruh do they want you to use first principles

[sterile ibex]

My teacher said that a derivative is just a slope of a line tangent to a curve

[sharp flame]

[sterile ibex]

I’ll post the practice problem

But this one is asking for the average velocity after 3 seconds though

[sharp flame]

You can't do this problem without knowing derivatives

Yeah this one isn't average

It's instantaneous

[sterile ibex]

How

Where is that info

It says after 3 seconds

So I have to take my 29.4 and take another derivative?

I’m looking for acceleration then?

[sharp flame]

Yes but with nothing said you need to assume they mean at that instant

no no

You have a position function

Differentiate it once and plug in 3

That's it

[sterile ibex]

Yeah 9.8(3)^2

[sharp flame]

Bruh

DIFFERENTIATE IT FIRST

$\dv{t} 9.8t^2 = 2 \times 9.8 \times t$

Now plug in 3

[glossy valve]

neonperseus

[sterile ibex]

Can I just walk through this with you real quick

So the 9.8t^2 is the position right

We haven’t covered d yet so I’m assuming that’s derivative

That’s divided by time right

The 2, where is that coming from

?

Anybody?

<@&286206848099549185>

[torn jolt]

how can I help you ?

[sterile ibex]

Hi!

Just have a question on some material above

[torn jolt]

go ahead I'll try and help

[sterile ibex]

Apparently someone gave me the answer but I just want to know really why I’m plugging things in where they are

Okay so the question in the pins asks me to find the speed of an object dropped y = 9.8t^2 after 3 seconds

I incorrectly got the answer of 29.4 and I’m told to differentiate beforehand, but I don’t see the logic of how i get there

This is my first lesson in derivatives

My teacher hasn’t broken down d yet, and my understanding of derivatives was told to us is that derivatives is a slope of a line tangent

And is the rate of position change divided by the change in time, for velocity

But I’m assuming that both position and time are 0 so plugging everything in lands me 29.4

[torn jolt]

okay, d is a simple notation that means differentiate

[sterile ibex]

Gotcha okay

[torn jolt]

when ever you see dy/dx it means to differentiate the function y with respect to the variable x

[light sonnet]

As it was previously mentioned

That gives you the average velocity
Not the instantaneous one
You found the average vel, you want the instantaneous, which requires the derivative

[sterile ibex]

Gotcha okay keep going

[torn jolt]

differentiation is simply finding the change in a variable with respect to another variable

[light sonnet]

Do you know the definition of the derivative? Ie this

[sterile ibex]

Okay gotcha makes sense

[torn jolt]

in your problem the variable is y = 9.8*t^2

[sterile ibex]

Yeah

[light sonnet]

Because if you don't know the deriative shortcuts, you use this instead

[torn jolt]

to get the change in y you need to find two values like y1 and y2 then find the difference between them y2 - y1 and this will give you dy

and the same applies with the t that is t2 - t1 which will give you dt

[sterile ibex]

So the y1, if t = 0 that should all be 0 right?

Or is that already given and implied by the “y” for y1

That position is 9.8?

[torn jolt]

yes, but in calculus we want to get the change according to the behaviour of a function simply subtracting the values won't be exactly right for some functions

that's why we say with respect to another variable

[sterile ibex]

And so that’s why we use d?

[torn jolt]

exactly

[sterile ibex]

Right right right, so then if 0 is the starting position and time in seconds, we’re just subtracting the starting position from the new position in time?

[torn jolt]

now remeber that I said we need y2-y1 which is the change in position and t2-t1 which is the change in time ?

[sterile ibex]

Yeah

[torn jolt]

Isn't the chance in position mean the distance ?

[sterile ibex]

Yeah!

[torn jolt]

and the change of time gives me the time taken to cover that distance ,correct ?

[sharp flame]

I think you can just use the average velocity formula and apply the limit to it to get the instantaneous velocity

[sterile ibex]

Yes!

[sharp flame]

$\lim_{t \to 3} \frac{9.8t^2 - 9.8(3)^2}{t - 3}$

[glossy valve]

neonperseus

[torn jolt]

so dy/dt means that we're just dividing distace by time right ?

[sterile ibex]

Yep yep!

[torn jolt]

isn't that the velocity of an object ?

[sterile ibex]

Yes!

[torn jolt]

does it now make sense to you the dy/dt gives the velocity ?

[torn jolt]

how did you get this formula ?

[sterile ibex]

Yes!

[torn jolt]

I hope now you know how to solve your question

[mossy gust]

Hello. Im new here. And i am not really used to how things work here. If I should direct my question somewhere else Ill gladly do so. Im trying to solve the integral 0 to π/2 sin^4 x dx. I know the answer is supposed to be 3π/16 bc calculators. But my work cant land me there. I have my work here.

[sterile ibex]

I keep following this concept but the answer I’m getting isn’t there : (

[torn jolt]

what is the answer you get ?

[sterile ibex]

29.4

[torn jolt]

did you differentiate ?

[sterile ibex]

Ugh I’m not sure if I am, to be completely honest

[torn jolt]

didn't we say that dy/dt is differentiating with respect to t?

[sterile ibex]

Yeah

[torn jolt]

thanks for your honesty

[torn jolt]

why didn't you 😅

[sterile ibex]

You’re the best teacher

So here’s where I’m at to just verbalize this

[torn jolt]

I'm still a student though 😅

[sterile ibex]

Patience + knowledge + step by step

I’m a teacher irl (the arts) and you have a great way

So lemme write this out

[torn jolt]

the problem is we are not sure that t1 = 0

[sterile ibex]

Wait really

That isn’t implied

[torn jolt]

it's possible that I'll tell you I throw the object at time 1 seconds and I want it's velocity after 3 seconds

[torn jolt]

it's a possiblity not a must you may start at time t1=0 but also you can start at any other time value

[sterile ibex]

Ohhhh okay okay

So how do approach from that now

Then it just becomes t -3? Or 3-t?

In the denom

[sharp flame]

It's just the definition of a derivative

OP said they're familiar with limits and average velocity

[torn jolt]

why (t-3)-->0?

[sharp flame]

Since the average velocity is given by the secant, this formula, which is the limiting case of a secant, gives us the tangent

[sharp flame]

$f'(a) = \lim_{x \to a} \frac{f(x) - f(a)}{x - a}$

[glossy valve]

neonperseus

[sharp flame]

It's just rise over run

[torn jolt]

I've never seen this before

[torn jolt]

I know this one

[sharp flame]

yeah that one is derived from this

x - a = h

[torn jolt]

the method I used was to show you how the rate of change of the position with respect to time gives you the velocity

[sterile ibex]

Yeah this is the way for me

[torn jolt]

okay that is new to me

[torn jolt]

thanks alot

[sterile ibex]

Okay let me ask this so I can make headway

The change of position

Is that 9.8-0?

Or is it 88.2

Or is it 88.2-9.8?

[torn jolt]

no because you don't have value for time t1 and t2 you only know that t2-t1 = 3

and this is not enough information to find the change in velocity

[sterile ibex]

Here’s the practice problem version of this same problem

See #6

#6

So following that right,

[torn jolt]

in this problem he gave you to starting time and the ending time as coordenate points so you do have t1 and t2 in this problem

[sterile ibex]

That’s it without the answer

It says from rest right, isn’t that 0?

[torn jolt]

this means the velocity was 0 not time

[sterile ibex]

But also time, no?

[torn jolt]

no

[sterile ibex]

So there could be time above 0 while the rock isn’t moving?

[torn jolt]

not a must that when an object start moving from rest that it starts from time 0

[sterile ibex]

But isn’t the question based around the notion of how fast an object is falling within a set amount of time?

[torn jolt]

time passes no matter what is the state of the object, and it may be graphed as a constant that is a line parallel to the time axis

[torn jolt]

yes, but you know the amount of time but don't when was the start

[sterile ibex]

Hmm

Time squared implies two seconds right

Two units of the time value passing?

So isn’t it 9.8 times 27 divided by 3

Nah that’s still 88.2

[torn jolt]

not two units no

[sterile ibex]

Yeah idk if it wasn’t implied that the start of the rock dropping starts the time of the rock falling I wouldn’t know

[torn jolt]

it's not in math problems you have to take the information form the problem and focus on the details

[sterile ibex]

It says a rock is dropped from rest (0) to fall freely toward the ground.

The distance the rock has fallen is modeled by y = 9.8t^2

Where does 9.8t^2 fit in

Is that the change in distance? 9.8?

Or is that y1 and we have to get y2

Because if that’s the change from 0 in position and time then t^2 has to be 9

[torn jolt]

no it's the function that discribes the distance covered by the rock at some time t

[sterile ibex]

Yeah so that’s the change in position in a set of time

So we aren’t starting out at 9.8

But even then

None of those potential answers are here

[torn jolt]

the is if t=1 the rock covered distance 9.8 if t = 2 the rock covered the distance 39.2 and so on

[sterile ibex]

OH

I SEE HOW YOU DID IT

you’re incrementing t by 1 for each second and then squaring

Not increasing the exponent just because

Wow wtf was I doing

But even then

3 seconds is 9

So after 39.2 it’s 88.2

[torn jolt]

but this won't help you find the velocity unless you get the rate of change of the distance, since the position can be described by the distance, the rate of change of the position and the rate of change of the distance are the same

[sterile ibex]

Yesssss

So isn’t 9.8 the change of distance and/or position?

[torn jolt]

no it's not

[sterile ibex]

Then what is it

[torn jolt]

to find the change 9.8*(t+c)^2 - 9.8*t^2

c is the change in time t2-t1

the rate of change have to be with respect to another varaible which is t that is the definition of the rate of change is

lim h--->0 (f(x + h) - f(x))/h

and h is the change in x that is x2 - x1

[sterile ibex]

And is that time, x yeah?

[torn jolt]

yes

and f(t) is the y that describes the distance

[sterile ibex]

Change in distance

?

[torn jolt]

nope just the distance the change in distance is f(t+h)-f(t)

[sterile ibex]

Yeah my teacher explained none of this

So basically I can’t do these problems yet

Is what we’re saying

[torn jolt]

was these problems a homework or something like that the teacher gave it to you or that you were trying self learning and practicing ?

[sterile ibex]

I’m going to school online, and this was the next lesson in my sequence. Everything else has connected beautifully, but the lessons come paired with a test, and the lesson about derivatives this one is attached to doesn’t go into d or anything related to those formulas. The next lesson is called “the derivative defined as a limit” and the lesson paired with this test is called “what is a derivative”

The lessons of this portion were from when my teacher was working at NASA and did it as an after thing, and then went back and redid a bunch of lessons, but this lesson hasn’t been

What I basically know about derivatives is that it’s the rate of change of a variable to another variable

And I assumed I had all the working parts to solve this problem, starting position, ending position, through deduction, being that everything should start at 0 and then they give me the end distance etc

Since that would be solvable given what the lesson was about

[torn jolt]

the next lesson will tell you everything we just did tell you about derivatives and rate of change and limit definition of the derivative just be patient

[sterile ibex]

Awesome. Yeah I’m excited honestly. Some times what I do when I run in to things like this is just watch a few lessons ahead, do the problems in the lesson, and then go backwards and that is usually good, but since I never went this far when I was in high school I didn’t want to take any chances

[torn jolt]

I've always been excited to math and calculus myself but found that things depend on one another so try to take it easy and step by step

[spiral vigil]

yeah with calculus it's best to take it one small step at a time

[sterile ibex]

I definitely will. I was afraid for a moment of a gap between jumping from the precalc class to calc 1 because of the trig identities which I don’t remember covering but I ended up with a 92 for the limits unit so I was feeling decent on that

[torn jolt]

fact specially calculus 😅

[spiral vigil]

and then you can look back and see how much ground you've covered from start to finish

(having said that i kind of ignored trig identities for the most part and just look them up when I need them)

[sterile ibex]

I’m super glad to hear that that wasn’t a major thing that I didn’t spend a crazy amount of time on then 🤣🙌

[torn jolt]

calculus depend on almost everything trig, algebra and sometime graphs so it's preferable if you take it step by step no jump aheads

[sterile ibex]

Yeah I definitely don’t jump ahead

[torn jolt]

In fact I always prefer to prove them myself 😅

[sterile ibex]

Outside of moving from the algebra 2/trig/precalc move they had a separate trig only class I didn’t take because we did a lot of trig in the course I did take

Everything else I feel solid on, 97 for all of algebra trig and precalc

92 for the limits portion, I just want to make sure I can buff this section up as I go along

But I really appreciate all the help, this place is seriously the absolute best no exaggeration

[torn jolt]

great job try working on them from time to time so that you don't forget lots of them and move slowly in calculus and don't leave a point you don't understand to pass by

[sterile ibex]

@torn jolt you’re a boss, hands down, I major majorly appreciate you and your effort, thank you so so much, and to everyone else who’s popped their head in

[torn jolt]

happy to be able to help

[sterile ibex]

Yeah I got you, I’ll continue to stay articulate and zero’d in on everything

Have a wonderful night everyone

[torn jolt]

you too

[sterile ibex]

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[fervent geyser]

i need help with my home work

[fervent geyser]

i din learn it yet

help

[thorn isle]

hello

i believe the answer is $720

[fervent geyser]

hey can u help me

i dont know how to show worl

work

[thorn isle]

is it okay if i type it out or would you like me to write it down for you?

[fervent geyser]

yes pls

[wise wyvern]

@thorn isle

[thorn isle]

yes?

[wise wyvern]

That's not how it works.

You don't give out answers.

You help the asker to reach the answer.

[thorn isle]

ah my bad

that sounds right, sorry

[fervent geyser]

im confused?

[wise wyvern]

It's alright. Have you done similar problems before?

Have you made any progress so far with this one?

[fervent geyser]

no

[thorn isle]

do you know how to make simultaneous equations out of word problems?

[fervent geyser]

my teacher didnt teach us this so i confused why she gaves us it 4 homework

idk even know where to start

[wise wyvern]

Do you know what the unknowns are?

In the problem.

[fervent geyser]

how much money the spent?

[wise wyvern]

That's one.

What else?

[fervent geyser]

there final costs?

[wise wyvern]

That's the same thing.

There's something else that'd determine their final costs.

[fervent geyser]

the number of cds

[wise wyvern]

Exactly.

Let's say the number if CDs is "n" and the total cost is "c".

Is that fine?

[fervent geyser]

sure

[wise wyvern]

For the sake of simplicity.

Now c is the total cost for both of them.

[fervent geyser]

whats the formula?

[wise wyvern]

You'll get there.

[fervent geyser]

alr

[wise wyvern]

If a CD costs $2.75 how much do 3 cost?

[fervent geyser]

8.25

[wise wyvern]

How'd you do that?

[fervent geyser]

2.75(3)

nvm i giv up

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[grave elm]

Can 3b be reduced to determining whether ((P∧Q)→R) → ((P→R)∨(Q→R)) is a tautology?

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@grave elm Has your question been resolved?

[spiral vigil]

yes

[grave elm]

thx, I just wanted to make sure 👍

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[distant halo]

Can you use 4! * 4!

[tame bobcat]

are the ways they could be seated also to be considered ?

or just they number of ways they can be distributed to the taxis ?

[distant halo]

ans this

[distant halo]

I think this

<@&286206848099549185>

ping me

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@distant halo Has your question been resolved?

[distant halo]

.close

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[torn jolt]

Help on finish this sequence of numbers problems

[brisk imp]

No one can help you if you do not post the problem :3

[empty sapphire]

sounds like you're just not trying hard enough, Luna 😉

[brisk imp]

maybe try to identify the type of the sequence

either arithmetic or geometric

write its general term

and deduce the asked terms (substitute by integers n)

[torn jolt]

well

it doesnt seem to be either

it seems to be a sequence that is something like

[torn jolt]

$a_{n+1} = \alpha a_{n} + \beta$

[glossy valve]

matthewzz

[torn jolt]

but even that doesnt fit it

[brisk imp]

Ah, sequences defined by a recurrence relation

[torn jolt]

que numero is next

my guess is its /2 then to get to the next number you do 16*9^(n)

10 -> 26 = 10 x 16 x 9^(0)

26 -> 170 = 26 x 16 x 9 ^ (1)

but doesnt seem that simple

[brisk imp]

Yeah, it does not work for 6 -> 10 :(

[torn jolt]

ohhh right

[brisk imp]

i think you can find a 3nd degree polynomial

p[n=0]=6

p[n=1]=10

p[n=2]=26

p[n=3]=170

p[n]=a n^3 + b n² + cn + d

4 coefficents to be determined, 4 equations

[torn jolt]

this was a timed test with 30 q in 20 mins

LOL

[brisk imp]

😂

How would someone GUESS how to move from 6 to 10 to 26 to 170

in 20/30 min

Haha

[torn jolt]

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[brittle robin]

I don't understand why we're substituting in the values of x and y from the parametric curve into our gradient

that was the one step I didn't do and got 2xcos(t) + 2ysin(t)

[stiff musk]

i don't think it makes sense to mix x,y with t...

t is the parameter which controls the x and y coordinates, i.e. x(t) and y(t) are functions of t

that's what they're doing after the second = sign, plugging in the formulas for x(t) and y(t)

[brittle robin]

hm

but aren't these two separate curves? why do they share t

ohh okay

had to visualize it a bit

ty

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@lean sinew Has your question been resolved?

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[serene sage]

why isn't it simply 3:7?

[proper hawk]

because it's mot

not

when dealing with ratios treat them as fractions

a:b=c:d means a/b=c/d

[serene sage]

ahh

so q/r * r/s?

3/5 * 10/7

q/s = 6/7

thxx

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[green trail]

Hi

[full forum]

Please don't occupy multiple help channels.

[green trail]

I want to ask

Can someone show me how they would walk through simplifying the cube root of 500

Heres the problem

You have to find three nunbers in your factor tree

[pale dome]

you already have #help-16 dont open multiple channels

[green trail]

500
5 100
5 20
5 4

This is the solution

5 cubr 4

But what if I did

500
5 100
2 50

Is it possible to get to the solution?

[green trail]

Sorry I’ll go back after

[pale dome]

close this one and lets move to help-16. or close help-16 and stay at this one

[green trail]

Done

[pale dome]

k 👍

[pale dome]

yes it would still be possible to get to the solutions

[green trail]

How

Wist so they dont have to be right next to each other

Is that what ur saying

[pale dome]

well continue breaking down 50 and you'll see

[green trail]

500
5 100
2 50
5 10
5 2

?

But thats 5 cubr 2 not 4

[pale dome]

there are 2 2's

thus 2^2

[green trail]

Huh

But we need 3?

Oh

[pale dome]

that is why we keep it in the radical

[green trail]

So whats left in the radical is

The other prime

That we dont take out

Then we see the power of that prime

[pale dome]

by "other prime" do you mean 2*2?

[green trail]

2

Itself

It went down to the very bottom with 5

Ok now I have cubr 72 how do I do this

[pale dome]

count how many twos are in
500
5 100
2 50
5 10
5 2

[green trail]

…

72
9 8
2 4
2 2

So theres three 2’s?

Is it 2 cubr 9

[pale dome]

yep

[green trail]

Great

What about exponents

In sqr we look for pairs

X* x * x you take out x^2

In cubr would you take out x^3

[pale dome]

mhmhh

[green trail]

Does this seem difficult

Do-able 2 hours

[pale dome]

that is an subjective question so i couldnt rlly tell you

[green trail]

In comparison to factoring tho?

That shit is difficult

And takes long

[pale dome]

once again thats still pretty subjective. to me, these are pretty easy. to you, maybe not

[green trail]

Radical 18

3 6
2 3

[pale dome]

?

[green trail]

The three here is not a pair

But can I still take it out??

I thought u could only take it out if its like
9
3 3

[pale dome]

when you ask questions like this i cant help because of the lack of context. try to be specific with your wording and provide an image in relation to your question

[green trail]

What?

Sorry but if u dont know what am saying thats not my fault

[green trail]

I been putting my factor tree like this

[green trail]

Then I said radical 18 and put its factor tree

[green trail]

This is not hard to understand once you know am talking about simplifying radical

[dusty scaffold]

well there's two of it

is there some condition on what "a pair" is other than it consists of two things?

[green trail]

I thought they had to be right next to each other in the factor tree

I guess a perfect square?

2 * 2, 4 * 4, etc

[dusty scaffold]

their positions in the factor tree are entirely about how you made the tree, they don't tell you anything about the number

for any arrangement of the factors of a number you can make a factor tree that has the factors in that order

so no they don't have to be next to each other

[green trail]

Gotcha

Anyone here

Sorry nevermind

Lmfooo

Ima just close

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[green trail]

I’m back

[proper hawk]

question?

[green trail]

I wrote it down so I can send it but I just solved it while doing that

[empty sapphire]

a true mathemetician

[dusty scaffold]

programmers call this "rubber duck debugging"

you explain the problem to a rubber duck

[empty sapphire]

it's true. I have a rubber duck on my desk

[green trail]

Math is hella fun

At least when you understand it

Been on it 5 hours straight

Foiling radicals 😭

Weirdest looking shit

[onyx pond]

at least you won't learn how to factor 5+2sqrt(6)

[green trail]

Lol you can factor that

6 certainly can’t, and you can’t add the five to the 2

[onyx pond]

(sqrt3 + sqrt2)^2

not so useful tho

[green trail]

Didnt the outer and inner cancel out in conjugates https://mathsolver.microsoft.com/en/solve-problem/@1fzt6iom7?ref=r

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[untold wolf]

i know its (0,-1)

but how can u find that without graphinf it

[sleek apex]

plug 0 in for x

you cant graph this

[untold wolf]

ok well what then

[sleek apex]

i told you

[untold wolf]

i sis

did

[sleek apex]

y intercept always occurs when x is 0

[untold wolf]

i got y=-2

[sleek apex]

and vice versa

brother

anything to the power of 0 is 1

[untold wolf]

oh bruh

ok

well

what about this

how do u find this

is it y=0?

[sleek apex]

no

have to find what it approaches on the left

plug in a very small value for x

,w compute 2*(4^-9999)

[glossy valve]

Results provided by WolframAlpha

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

Requested by Arctic#1647

[sleek apex]

oh

,w compute 2*(4^-99)

[glossy valve]

Results provided by WolframAlpha

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

Requested by Arctic#1647

[sleek apex]

idk why wolfram doesnt approximate

maybe cause i used compute

but yeah essentially 0

[untold wolf]

why tho

[sleek apex]

1/a very big number is 0

4^99 is very small

[untold wolf]

uhm

no

4^99

is a huge number

[untold wolf]

what is 1/a

[sleek apex]

1/(a very big number)

[untold wolf]

howdoes any oif this correlate to y=2*4^x

[sleek apex]

i plugged in a very small number for x

or

a very negative number

[untold wolf]

ok

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[jovial star]

I completed part A but I am having trouble with part B mainly because i don’t think i am visualizing it properly

[onyx glen]

you cut a paper cone along its directrix and unroll the resulting surface onto a table

[jovial star]

oh ok

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[whole escarp]

Is number 1 right?
And how to do no 2?

Do i just switch the 1-x to be -x+1?

[onyx glen]

why'd you write × for x there

[whole escarp]

Oops

[onyx glen]

but yes if it helps you then by all means go for it

[whole escarp]

Im also kinda confuse like do i
1:6x^4 or -x:6x^4?

[onyx glen]

??

[whole escarp]

For the first step?

[onyx glen]

well what's the leading term in -x+1

[whole escarp]

-x

But like if its 1-x

Is it like I always go for the X or..what?

[onyx glen]

what makes a leading term leading is its degree, not where it happens to be written...

of course it's -x

even if you write your divisor as 1 - x

[whole escarp]

Is it kinda like the same thing as if it's -19+13x+6x^4 and you always fo the 6x^4 first?

[spiral vigil]

yeah

generally you want to write your polynomials in decreasing power order

not always, but generally

[whole escarp]

I feel like im doing something wrong

Its not done yet

[sharp nebula]

6x^3 (-x) = ?

[whole escarp]

Ah

Is it suppose to be like this..?

[sharp nebula]

Noh

This is true
However
U hv to rmb it's like division
U hv to minus the line u got

So - (-) = +

Which will not remove the 6x^4

[whole escarp]

Hm..so 6x^3 becomes 6x^4 instead?

[sharp nebula]

No

6x^3 is correct
But it's missing sth

I suggest u switch the position of -x so u can see clearer

[whole escarp]

Oh

Ohh

-6x^4+6x^3?

[sharp nebula]

Where r u putting this

[whole escarp]

?

[sharp nebula]

U want to eliminate (6x^4), not make it bigger

Close tho

[whole escarp]

Hm

?

[sharp nebula]

Ye

[whole escarp]

Then can i just do 13x-(-6x^3)?

[sharp nebula]

I would write 6x^3 first, then bring 13x down

For arrangement sake

[whole escarp]

Bring 13x down?

[sharp nebula]

U hvn't yet used these 2

[whole escarp]

So like

Do i just

6x^3+13x-19?

[sharp nebula]

Yes

[sharp nebula]

Basically switch positions of 13x-(-6x^3) haha sry

[whole escarp]

Is this right?

[sharp nebula]

Mmm
Yes

[sharp nebula]

Quotient is correct

Remainder?

[whole escarp]

Ah

0

[sharp nebula]

Mmm

[whole escarp]

Nice

[sharp nebula]

Ye ur good

[whole escarp]

Thanks a lot

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[west elk]

kindly help me

[full forum]

Please don't occupy multiple help channels.

[west elk]

previous one was not replying

[rugged aspen]

@west elk whats the problem?

[west elk]

let's consider a triangle ΔABC, and a line l parallel to one of its sides, say side BC, intersecting the other two sides at points P and Q, If line l intersects side AB at point P and side AC at point Q, then:
AP/PB = AQ/QC

If line l intersects side AB at point P and side BC at point Q, then:
BP/PQ = BA/AC

If line l intersects side AC at point P and side BC at point Q, then:
CQ/QB = CA/AB

explain last 2 statements

bye i have some work so i have to leave

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[magic rover]

Does anyone know how to draw a circle through three points (the circum circle) of a triangle in tikz

[magic rover]

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[jolly marsh]

Hey there, I did come across a game yesterday and I couldnt solve it.
The rules are as followed:

• Start with 3 dots.
• the players are taking turns drawing a line doesnt need to be straight) between two dots and creating another dot on that line.
• dots can only be connected to 3 lines
• lines cant cross
• the player who cant draw a line looses.

I think it can be solved using graph theory but I'm not versed in that.
I think I have 'solved' the maximum numbers of dots, but not the minimum and if you start you can always win (like tictactoe).

Max number of dots:
any dot has 3 degrees of freedom. At the start the system has 9 degrees of freedom. Every turn 2 dots are connected (system loosing 2 degrees of freedom) and one dot is created on that line (system gaining one degree of freedom).
So you can have a maximum of 8 turns ending with 9 dots and one degree of freedom.

How could one determine the minimum and the perfect strategy?

[pulsar widget]

https://youtu.be/XKsTGdN-4_M

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[normal thicket]

My answer 0

[onyx glen]

both you and the answer key are wrong. the two-sided limit of floor(x+1) at -1 just doesn't exist.

[void nova]

That's not the floor

The integer part, if I'm not wrong rounds to the nearest integer, so [-0.1] = 0, whereas floor(-0.1) = -1

So the answer in green is correct

[onyx glen]

[x] is "the greatest integer in x"

that to me reads like it means floor?

[grave elm]

Even if it worked like that, the answer would be 0

[onyx glen]

from the left it approaches -1 but from the right it approaches 0

[normal thicket]

[-0.1]=-1

[void nova]

Ah sorry I don't know why I thought 0 was in green 😅

[simple ridge]

yes and since the answer key says -1 then they probably meant to ask for the limit from the left

but they didnt do that so they are wrong

[void nova]

Yes 0 is the right answer, which is not marked as correct, very strange

Anyhow, that question is wrong yep

[onyx glen]

it is CATEGORICALLY not our job to speculate what the authors meant!

[normal thicket]

Why the delhi teacher board has lots of mistakes in previous papers

Can't they copy-paste some questions from math exchange 😂

[simple ridge]

ik thats why i reacted with the skull face XD

[normal thicket]

Lim -1-h of [x+1] would be -1 right

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[raw light]

Hello, I am a civil engineer trainee and been given a deadline on a test when i work 13 hours per day 6 days a week. I was wondering if someone could help me out with a test its been causing me a lot of stress and I really need some help.

[stiff summit]

What kind of help?

[raw light]

its a calculus test and I am literally clueless on how to do any of it. I got given 2 weeks to do 3 tests, trig, algebra and calcus. I had no idea what calculus was prior

[fair oracle]

post your question

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[fiery karma]

can anyone help me solve this torque problem?

[stiff summit]

What is the problem statement?

[fiery karma]

you have to balance the weights given their masses with the indicated numbers on them

so that you have a stable scale

i tried doing some algebra but didnt seem to work

oh and also you have to put the weights in the places to the diamond shaped attachment points

[fiery karma]

this is important because you are restricted to only one solution

[stiff summit]

what did you get

[fiery karma]

only that the second place from the bottom should be an even number

2,4 or 6

i can probably solve it with some bifurcation, but i would like to know the logical solution

[stiff summit]

The logical solution would be to make equations to get a few constraints on the weights' positions

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[sacred shale]

can someone explain to me how/why this works?
ive just copied the solution off photomaths for now and i cant reverse engineer it
if anyone has a cheat sheet with the related identities that'd be awesome too

[sacred shale]

or is it just wrong overall

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@sacred shale Has your question been resolved?

[fossil river]

So u-substitution is being used. Do you have specfic question?

[sacred shale]

honestly, that was 50 minutes ago and i dont remember what qualms i had with it

shit that was over an hour ago

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[pale dome]

!status

[full forum]

What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above

[untold wolf]

1

[pale dome]

Do you know log rules?

[untold wolf]

i mean yeah

[pale dome]

There are 2 rules you can apply in this problem

[untold wolf]

well

which oens are they

[pale dome]

Which ones do you think? Hint: the inside of the log is being raised to the power 2, and being multiplied by 4

[untold wolf]

oh wait

is it

C?

[pale dome]

Can you show your work?

[untold wolf]

well

i know that if i use the

power property

[untold wolf]

i did it in my head

[untold wolf]

then i can seperate it into two

[pale dome]

Just a tip: don't do math exclusively in your head

[untold wolf]

well i dont but if i can

[pale dome]

Unless it's rlly simple math like adding

[untold wolf]

this is simple

its c right?

thats what i go

[pale dome]

What if you make a mistake in your reasoning? You can identify that mistake if you write down the steps.

[untold wolf]

i guess

[pale dome]

But yes, it is c

[untold wolf]

ok

i have anotha

questipn

so is the first step to make this exponential

like

216=1/6^x

and solve for x

<@&286206848099549185>

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[astral junco]

Two circles with different radii have chords
AB and CD
, such that AB
is congruent to
CD. Are the arcs intersected by these chords also congruent?

[astral junco]

I am having trouble visualizing the problem

[round gust]

Just draw it

[hot herald]

start by drawing 2 concentric circles

[astral junco]

ok

then i draw the chords

ok i'm pretty sure that the intercepted arcs have the same measure

is that correct?

Wait no

i think they done

dont*

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[astral junco]

.close

whys it not closoing

.reopen

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✅

[astral junco]

.close

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[rough tundra]

it is closing, it just takes a while :)

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[torn jolt]

I wrote all of this to solve the above problem $$h =49-4.9t^2 $$
$$h' = -9.8t $$
$$y_a = -4.9t^2 $$
$$x_a = 10 $$
$$y_b = 49-4.9t^2 $$
$$x_b= x_a + y_b \frac{1}{y_a}$$
$$\frac{dx_b}{dt} = -9.8t \frac{dy}{dt}\frac{1}{y_a}{} + 4.9t^2 \frac{1}{y_a^2} $$
$$\frac{dx_b}{dt} = -9.8 \frac{dy}{dt}\frac{1}{y_a}{} + 9.8 \frac{dy_b}{dt} $$

[torn jolt]

How insane am i?

[glossy valve]

brandon_hu

[torn jolt]

It's so wrong isn't it

😭

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[whole escarp]

Im kinda confused abt the 5x^2

[whole escarp]

So like is it like 5x^2÷2x = 5x/2

[pale dome]

No

Oh you edited it nvm

Yes

[whole escarp]

Its not like 5x^3/2 right?

[pale dome]

Not at all

[whole escarp]

Im kinda confuse on why its like that here

[pale dome]

What is x^2*x?

We're gonna ignore the 5/2

[whole escarp]

X^3?

[pale dome]

Yep

Now we bring back In the 5/2

[whole escarp]

Ohh

So it did that there

[pale dome]

Yep

[whole escarp]

I was confuse on why it added a *

[pale dome]

Yeah, also think of it as such:
(5/2)x^2*x
(5/2)(x^2x)
(5/2)(x^3)

[whole escarp]

But that's not right, right? With polynomial?

[pale dome]

Wdym?

[whole escarp]

Like with the question im working on

[pale dome]

Well with what your working on the next step should be to divide

Wait hold on

[pale dome]

Is this a calculator?

[whole escarp]

Yeah

Its photomath

[pale dome]

Ohhhh that explains everything

Photomath had an input error

It interpreted (5x^2)÷(2x) as 5x^2÷2*x

It divided 2 first then multiplied x. Which was wrong

[whole escarp]

So its an app error?

[pale dome]

Well it's an input error. Next time if you plan on using a calculator, use parenthesis

[whole escarp]

Hmm

How about symbolab?

[pale dome]

It was an input error on your part

[gilded current]

can i ask a question?

[pale dome]

Changing calculators wouldn't do a thing

[pale dome]

This channel is occupied atm. Create your own, see #❓how-to-get-help for directions

[whole escarp]

I wrote like 5x^2:2x

[gilded current]

oh ok sorry

[pale dome]

Np

[whole escarp]

And it added a * by itself

[pale dome]

That, you shouldn't do. Just write (2x)

[whole escarp]

Ohh

[pale dome]

Parenthesis are very important when it comes to calculators as they can't rlly think to see human error

[whole escarp]

I'll keep that in mind

Thank you

[pale dome]

Np :D

[whole escarp]

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[crude jackal]

um... anyone good enough in linear algebra here?

[crude jackal]

I have two similar math problems

that either give to the matrix or the eigen values

then they give you a combination of that matrix (Lets say A)

Now the question is, how to find the eigen values of the matrix which is combination of A?

<@&286206848099549185>

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@crude jackal Has your question been resolved?

[crude jackal]

no

[crude jackal]

<@&286206848099549185>

hm...

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[royal sedge]

cant getanything after 4th line

[royal sedge]

hloooo

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[median halo]

is this correct?

[torn jolt]

19C2

That's 19*9

[median halo]

thats what i did

[torn jolt]

Then it's correct

[median halo]

wait

[torn jolt]

19*9 is not 342

[median halo]

isnt it permutations

[torn jolt]

What

Yeahhh

[median halo]

lmao

[torn jolt]

Forgot sorry

[median halo]

np

so 342 good?

[torn jolt]

Wait

Nahhh

19C2 into 2 right

That's 19*18

☠️

Wth

[median halo]

but its one row

[torn jolt]

Yeah still

Selecting 2 places for them to sit, and then multiply by 2! Fir arrangement

For

[median halo]

so we use combinations?

[torn jolt]

Yep

[median halo]

171?

[torn jolt]

Wait man Lemme just think

[median halo]

sure

[torn jolt]

1 min

Yeah

342

Arrangement

Necessary

[median halo]

bet thanks

[torn jolt]

Permutation

[torn jolt]

Thank you

[median halo]

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[leaden dirge]

i dont understand what I have done wrong here since i did the question the first time it said i only got 0.75/1 on the problem

[ivory cairn]

my guess is that you weren't supposed to consider the outliers in the max question.

[leaden dirge]

so its just 265

[ivory cairn]

i believe that's the answer they want, yes.

[leaden dirge]

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[timid heart]

unsure where to begin part b

[timid heart]

not sure how to proceed

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[timid heart]

oops, reopening

[spiral vigil]

you'll need to evaluate g at your starting point

the idea here is that you figure the (negative) gradient is the most efficient direction to go to decrease g
so if you draw a straight line from your starting point in that direction, you can easy calculate when points on that line equal g

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[timid heart]

oh thank you!!

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[paper kelp]

can someone help me with this one pls

[sharp flame]

$a + b + c = 100$

[glossy valve]

NEON

[sharp flame]

Have you seen this formula before $^{n - r - 1}C_{r - 1}$

[glossy valve]

NEON

[paper kelp]

no

[sharp flame]

Have you solved these types of problems before

[paper kelp]

no

is this combinatorics it looks similar

[sharp flame]

yes it is

[paper kelp]

how to use it here though

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[paper kelp]

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[distant halo]

There is no argument i the log 3 so how should I solve it

[unreal seal]

,rccw

[nimble crane]

I assume the argument is log5(N/2) then

should have parentheses to make it clear though

[distant halo]

There are no brackets around it

[nimble crane]

yeah I'm guessing its poor notation

but don't take my word for it

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[plush gull]

I didn't get that why this function is not undefined at 3 point. Okay i do understand it can be cancelled etc. but if we plug 3 into the expression it will be 0/0 which is undefined already. Don't i know about definition of functions or something? Or is it just a putative maybe?

[fast peak]

it is undefined at 3

[woeful hatch]

It's just that the limit as x tends to three is defined

[fast peak]

but you can continuously extend it to another function g(x) which satisfies f(x)=g(x) at all points x != 3 and such that g(3) is defined

[woeful hatch]

which crucially isn't yhe same thing

[fast peak]

and because f(x) and g(x) are essentially everywhere equal, you often dont make a distinction between them

[plush gull]

The idea i didn't understand that when it is a limit question which approaches to 3. We say hey let's see if they cancel each other and it is x+3 which will be 3+3=6 my teacher solve questions like this or maybe i remember wrong idk and it confused me so much

[fast peak]

for limits, you dont care about the point itself

you only care about the surrounding points

and for all the surrounding points you can cancel the x-3 because it is not 0

[plush gull]

does this expression has nonlinear graph? Like (x^2-9)/(x-4) do

[fast peak]

the graph looks like x+3

except at the point x=3

where it is undefined

[plush gull]

Websites like geogebra says it is still defined for 3 point

[empty sapphire]

they're wrong then. Try in desmos. If you hover over x = 3 on the line, it'll say "undefined" for the output

[plush gull]

if function itself turn out "x+3" wouldn't it be weird to say three is still undefined

[plush gull]

Oh wait my bad it is showing 3 is undefined too

[empty sapphire]

No not at all. What you're seeing here is the domain. The domain for your original equation was "All real numbers except for x = 3". It simplifies to a linear line by elimination, BUT since the original problem was a rational equation with a point that's undefined, then the linear line inherits the domain as well

[plush gull]

So is that about how functions was defined at first moment?

[empty sapphire]

as far as this question goes:
It can't be simplified any further than that (unless you wanted to do a difference of squares, but nothing is eliminated).

In that case you need to see the Left hand limit and Right hand limit behavior at x = 4. If they approach the same point or the same direction of an asymptotic line, then the limit exists. Other wise, for example, if the left hand limit approach infinity and the right hand limit approached negative infinity, then the left hand and right hand limits exists, but not the limit itself

[empty sapphire]

yeah pretty much. WE can simplify it as a linear line, but technically we'd still want to use the domain of the non-simplified function since we're, in reality, actually plugging into that equation. Hence why we can't plug in x = 3

[plush gull]

Okay i guess my confusion is disappeared thanks for your help