help-27

[flat raft]

i just need a hint

because i am stuck

[vital pasture]

I mean you are given two things. Could you use the definition of an even function?

[flat raft]

Yes

And implicit differentiation

Chain rule

Function is even if f(-x) = f(x)

[vital pasture]

Well is f(0)=0 odd nor even?

[flat raft]

f(0)=0 is for all odd functions

[vital pasture]

And for even?

[flat raft]

idk

[wise plank]

f’(x) is even

Therefore f’(-x) = f’(x)

Integrate both sides

You’ll get -f(-x) = f(x) + C
And you know that f(0) = 0
Find C and you should be done

[flat raft]

C=0

[wise plank]

Yep

so f(-x) = -f(x)

[flat raft]

I didnt think to integrate

[wise plank]

Aka it’s odd

[flat raft]

Yep

[wise plank]

[flat raft]

I can finally sleep

.close

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[vast violet]

hi

[vast violet]

Lets say i multiply the 3/x

by (x-3) (x+3)

X cancel out '

How would i do this

like

3x-9+3x+9?

or

[fading sundial]

note the difference of perfect squares formula

[lusty sapphire]

The x does not cancel out

[vast violet]

oh

so multiply by x^2-9?

[lusty sapphire]

Basically

[vast violet]

ohhh ok

so

the -12/x^2-9

never need to get multiiplied right

[lusty sapphire]

It will, yes

[vast violet]

o

by the x only?

[lusty sapphire]

Consider each fraction separately. How would you remove the 3/x fraction? Multiply everything by x.

[lusty sapphire]

I feel that you are confusing yourself by trying to remove every fraction at once. I urge you to work on this one step at a time.

Try removing the 3/x fraction first

[vast violet]

Ok i restart

ok i try

so

3x^2-27

ok

i get this equation

3x^2-27=2x^2-6x=-12x

ok

with that

x=3 x=9

oh wait i make the plug in check

.close

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[devout snow]

@quiet glade Has your question been resolved?

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[misty lantern]

i need help with a puzzle thing

[misty lantern]

like the questions are like square take b

or star times b

[alpine inlet]

wut

[small quartz]

Can you give an example for something that you know how to solve?

[misty lantern]

the questions were square times c

star add a

like what?

[alpine inlet]

?

square times c?

1?

[misty lantern]

i thought that but no

do u add all the numbers in the collumn

[alpine inlet]

this is not a well defined problem

so don't know

[devout snow]

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@misty lantern Has your question been resolved?

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[delicate forge]

guys

is this down

end result of that up

after all the math rearangement?

pls pls pls

i just dont know if end result would have the ^2

[supple knot]

Yes it would

[delicate forge]

yo

but howcome the ^2 in the end?

[supple knot]

x = √a implies x^2 = a

[delicate forge]

ž

hmmm

[supple knot]

Squaring cancels the square root

[delicate forge]

look

maybe i make mistak here?

in the process

[supple knot]

What is the starting equation

[delicate forge]

in the picture it is in the 3rd row

[supple knot]

Which

[delicate forge]

im confuse how in the finish

we divide all by K/N

[supple knot]

Does it include the ÷b looking thing

[delicate forge]

yes

its sigma

or somethjing

[supple knot]

Why are you only dividing one side by sigma

[delicate forge]

i think both sides were divided by sigma no?

because we remove sigma from right side

[supple knot]

And you didn't write it on the left side?

[delicate forge]

there is S/Sigma right below

after the operatio

[supple knot]

This is in agreement with your picture

I don't know what you're confused about

[delicate forge]

ok so

im confuse why in the almost last part

we divide all by K/N and it magically spawns ^2

in the S/Sigma in the finish

this was something i was solving few months ago

so im looking at it now wondering if it makes sense

[supple knot]

It doesn't "magically spawn"

[supple knot]

It's basically this

And a / √a = √a

[delicate forge]

very confuse

😦

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[craggy sequoia]

Not sure where to begin.

[stable storm]

the boat is moving northward at 3 m/s and the current is pushing it westward at 1.9 m/s

you just use vector addition here to find the resultant velocity

[craggy sequoia]

So just add 3 m/s + 1.9?

[stable storm]

you have to use pythagorean theorem

since the two vectors are perpendicular to one another

[craggy sequoia]

okay

[stable storm]

yeah looks right

[craggy sequoia]

sqrt12.61?

it's asking for the bearing though

would I do inverse tan to find the angle?

[stable storm]

yeah

[craggy sequoia]

so, hold on

sqrt12.61 is the resultant velocity?

Now we're finding the direction via bearing?

[stable storm]

yeah

and we can then use inverse tan

to find the angle it makes

[craggy sequoia]

kkk

-57.7 (rounded)

[stable storm]

you dont have to use negative there

[craggy sequoia]

It's the absolute value?

[stable storm]

because we're just trying to find the angle with the right triangle up there

yeah

[craggy sequoia]

okay

so 57.7

[stable storm]

and its opposite over adjacent

[craggy sequoia]

We're in the second quad. though

[stable storm]

so it should be 1.9/3

[craggy sequoia]

Isn't 3 the opposite though?

[stable storm]

oh wait you labeled the theta there

i recommend labeling it next to the 3m/s vector

since thats where we are starting from

[craggy sequoia]

Would it change the result?

[stable storm]

well it would be the complementary angle to the angle you got before

but usually for this type of problem

you label the theta there

[craggy sequoia]

ok

so

32.3?

[stable storm]

yep

[craggy sequoia]

But we're in the second quadrant.

so 180-32.3?

[stable storm]

for physics we dont really care about what quadrant its in

we can just label it 32.3 degrees northwest

or if you want to be more specific

32.3 west of north

[craggy sequoia]

This is for trigonometry.

But that's the way my teacher did it.

[stable storm]

huh

what would you label as the direction then

[craggy sequoia]

Wait, I messed up.

it would be 90 + theta or 180 - (90+theta)

so 90 +32.3 = 122.3

or 180 - 122.3

[stable storm]

thatll give you the angle you originally labeled

this way also works actually

[craggy sequoia]

oh okay

so that equals 57.7

[stable storm]

yeah

[craggy sequoia]

so the bearing would be N57.7W

[stable storm]

yeah that looks good

[craggy sequoia]

Now how would I do B?

[stable storm]

so what would be our velocity in the north south axis

[craggy sequoia]

what do you mean?

[stable storm]

like how fast are we moving vertically in the direction of the 68 m

[craggy sequoia]

3 m/s?

[stable storm]

yep

now you have displacement and velocity

[craggy sequoia]

How would I calculate that?

I was taught this in Trigonometry today, so forgive me if i'm slow on the uptake.

[stable storm]

do you remember what the velocity formula is

[craggy sequoia]

We didn't really go over any problems this in-depth.

[stable storm]

its alright

[craggy sequoia]

I don't think we went over it..

I don't know what the formula is.

[stable storm]

ah

so velocity

or average velocity

is displacement over time

[craggy sequoia]

v = d/1?

d/t*?

[stable storm]

yeah v=d/t

now we know v

and d

we can solve for t

[craggy sequoia]

what is v?

68?

[stable storm]

v is velocity

which you said was 3 m/s

[craggy sequoia]

and the displacement is 1.2m/s?

[stable storm]

so from the problem

it says we travel

[craggy sequoia]

1.9*

[stable storm]

68m northward

the d in this case would be 68m

and v would be 3m/s

[craggy sequoia]

So what is displacement? Like the definition

[stable storm]

its really just distance

with direction

or more formally

the vector sum of all distances

well its probably easier to understand it as final position minus initial position

but i dont think you would need to worry about that for now

[craggy sequoia]

okay

so 68m = 3/t?

[stable storm]

its v = d/t

so it would be 3 = 68/t

[craggy sequoia]

oops

I'm assuming we multiply both sides by t to undo the division?

so 3t=68

then divide both sides by 3?

[stable storm]

yeah

[craggy sequoia]

okay

What do I round to? and do I include a unit?

[stable storm]

well t is time

so it should be in seconds

[craggy sequoia]

ah

[stable storm]

you can round to the nearest hundredth or whatever your teacher prefers

[craggy sequoia]

23 seconds should be fine.

Now, part c.

[stable storm]

yeah thats fine

so how would approach this

we can list what we know so far

in the west direction

[craggy sequoia]

yeah

so.

we know the magnitude is sqrt12.61

We know the bearing

and we know the time it takes for the boat to cross the river

[stable storm]

thats good

[craggy sequoia]

so where does the boat reach the river?

[stable storm]

but we do not use the resultant velocity here

we want to use the velocity of the boat in the west direction

[craggy sequoia]

This part?

[stable storm]

yep

[craggy sequoia]

What does the problem mean by downstream? That's tripping me up.

[stable storm]

so as the boat moves across the 68 meters

the river pushes it downwards

with a velocity of 1.9 m/s

thats why when it goes across the river

it moves downstream

or westward

[craggy sequoia]

"downwards" as in to the left?

[stable storm]

yeah

[craggy sequoia]

So, how can we calculate that?

give me a hint.

[stable storm]

we know what the velocity westward is right

its 1.9 m/s

and we also know the time

how can we relate these two things to get displacement

[craggy sequoia]

Eureka!

v = d/t

[stable storm]

yep you got it

[craggy sequoia]

we know the time and velocity

so just multipy?

multiply*

v = 1.9

t = 23 seconds

[stable storm]

yeah

[craggy sequoia]

so not multiply

1.9 = d/23

well yeah, multiply

[stable storm]

yep

[craggy sequoia]

23 * 1.9 = d

okkk

43.7

[stable storm]

that seems right

[craggy sequoia]

Thank you so much for your help, y0shi.

Have a good night.

[stable storm]

your welcome

you too

[craggy sequoia]

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[glacial vigil]

how do i go about solving this?

[glacial vigil]

do you add the other cos x term over and make it equal to each other then square root? then what

[supple knot]

Factor the left side

[glacial vigil]

cos (x) (cos (x-1))

[supple knot]

Use ab=0 implies a = 0 or b=0

[glacial vigil]

huh? so you're saying to substitute the x's with a's and b's

[supple knot]

No

[supple knot]

This is a product of two terms

[supple knot]

And so is this

[glacial vigil]

yeah

[wicked turtle]

careful with the parentheses, this isn't right as written...

[glacial vigil]

oh

cos (x) (cos (x) -1))?

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[jovial fractal]

my caculators answer is basically multiplying a negative somewhere, where did i go wrong 😭

[tame palm]

How did you go from u * sqrt(5-u) to 5u^(1/2) - u^(3/2)?

[devout snow]

@jovial fractal Has your question been resolved?

[jovial fractal]

ya im a little braindead 💀 i just saw it on the calculator and thought i couild do that but then i realized that it uses 2-x as u instead of x+3

tysm

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[tame palm]

There's nothing wrong with what you did. You did another change of variables, but didn't change the variable nor did you change du.

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[jaunty abyss]

Hello. I am factoring grouping polynomials. How can I make the numbers in the parenthesis the same? I know I should factor out a negative but I’m not sure how to do that and where to put those negatives…

[devout snow]

@jaunty abyss Has your question been resolved?

[jaunty abyss]

Never mind

I forgot to put a negative for the 7

BYE YALL

thanks for nothing 😂

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[next nymph]

Quick question:
Why in the derivative of x^a i have Domain Restrictions while in the derivative of [f(x)]^a no?

[next nymph]

For example :
Does the derivate of this function exists?
f(x) = -2x^(3/2)
I would say that it exists and it's f'(x) = -3x^(1/2) but do i have to say that x>0?

Or does the Domain Restrictions say that in case a is Real number, such as pi, i have to say that x>0?

Wait, let's make is simpler :
Does the derivative of this function exists?
f(x) = (-7)^x

Since a = -7 -> a<0 then the derivative of f(x) doesn't exists because ln(-7) is not defined, am i right?

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[honest ether]

This is supposed to be the answer key for this problem, but aren’t you supposed to multiply by pi to find the area of the base of the cone?

[wooden wraith]

yes

If that's supposed to represent the volume of the cube, minus the cone, then they forgot the factor of pi, you're right

[honest ether]

alr thanks just making sure I wasn’t missing anything

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[civic hazel]

English question : can one say "to bound a function" ? As in, "to find a bound for a function"

[near trout]

that seems reasonable

like

'to bound a function like sin(x), we can consider inequalities such as sin(x) < |x|'

would be a valid sentence

[civic hazel]

Thanks a lot !

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[hard knot]

So I started off with
there is a least + rational #

So
n = a/b

and then I added -1 and -2 to it

And that proves its smaller than n

BUT It can also mean its a negative number so idk what to do

Oh,
I guess its

A/2b

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[hard knot]

I got it

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[obsidian basalt]

Is this correct notation

[obsidian basalt]

$\frac{\partial f}{\partial x \partial y}[f(x, y)]$

[woven radish]

_Ω_

[acoustic leaf]

writing the f twice is a bit redundant

if it's a second derivative, the top curly d should also have a 2

[obsidian basalt]

okay thanks

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[torn coyote]

Are these the actual forces or the reactions of them ?

[coral crescent]

The reaction should be at the pin, no?

[torn coyote]

It only has horizontal at the pins

And I'm asking about those arrows. What are they ?

[coral crescent]

Should be actual forces

[torn coyote]

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[marsh turtle]

I am suppose to group them together.. how?

[marsh turtle]

I know I can group 0011 and 0110

And 0111 and 1011

But what do i do about 0101 and 1101

[devout snow]

@marsh turtle Has your question been resolved?

[marsh turtle]

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[normal wadi]

I think the problem is that you are providing insuficient information about the problem statement. like qhat kind of operation does U represents

[marsh turtle]

I am suppose to make a prime detector

Where U =f(X3,X2,X1,X0)

<@&286206848099549185>

[short iron]

What're you having trouble with? They tell you the steps you need to take, what step are you stuck on?

[marsh turtle]

the minimize the expression

[short iron]

Use a kmap!

Do you know how to use the Karnaugh map?

[marsh turtle]

.

But how do I group them?

[short iron]

You wanna group in the biggest groups in exponents of two's that you can (2,4,8,16...)

So group the biggest group of 1's that are next to each other first

It looks like you're gonna have a couple of single groups as well

[marsh turtle]

Oh so can have 1 cells as well?

[short iron]

Yes

[marsh turtle]

The I thought it had to be atleast 2

[short iron]

One groups would be equivalent to a four term literal

Does that help?

[marsh turtle]

i think Ill try and come back in a sec

[short iron]

It might also be worth reviewing k-maps in general, they are very handy for this kind of stuff

Idk if your course has a text, if not (I can't send links in here so you'll have to look it up yourself), if you look up "Intro to logic design marcovitz UoITC" you should easily find a pdf copy of the book, chapter 3 goes really in depth about k-maps with lots of examples and worked problems

Good luck!

[marsh turtle]

Something like this??

[short iron]

I can't double check at the moment, but I think you'd have 2 4 term and 3 2 term literals

[marsh turtle]

I assume not... XD

[marsh turtle]

Yeah so I am wrong lol

[short iron]

Just make sure you're groups any 1's that are 2 groups

Even if they overlap, I see three groups of 2 1's in the top right of your kmap

[marsh turtle]

ok ill take the advice

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[gentle wagon]

vertical shift is 1

idk how to find the phase shift

if its the distance from the origin i found the midpoint of pi/2 and pi which is 3pi/4

[lucid smelt]

are those sine and cosine functions ?

[gentle wagon]

its a secant function

i think the period is pi/2

i found the midpoint of -3pi/2 and -pi and subtracted it from the other midpoint which is 3pi/4

so the b value is 4?

i dont think there's a reflection

[lucid smelt]

i thought the same

i honestly can't help

sorry

[gentle wagon]

damn

[devout snow]

@gentle wagon Has your question been resolved?

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[halcyon rivet]

If every whole number is a factor of 0,
0 will also be a factor of 0

So if you divide 0 by 0, will you get a whole number?🤔

[bleak tide]

It depends what you call division

[crisp trench]

No. I wouldnt really call it every number is factor of 0 more like every number divides 0

[halcyon rivet]

What do you mean?

[limber atlas]

heres an example, find a way to give 10 apples to 0 people

[bleak tide]

You're asking what happens when you divide 0 by 0

what is "divide" here?

[halcyon rivet]

Im not asking about 10/0
Im asking about 0/0

[limber atlas]

understand first one, to understand second

[halcyon rivet]

Dividing a number by its factor should give another factor, right?

[halcyon rivet]

Nvm I answered myself

[bleak tide]

when you talk about factors, usually that can be rewritten as ab = c, and you say a,b are factors of c

Indeed, 0x = 0 for any x

so 0 is a factor of 0

[halcyon rivet]

The last line is wrong I think

Instead of getting a whole number, it should be getting another factor, and since it was already established 0 is a factor, everything is ok

[bleak tide]

however the idea of cancelling 0 from each side of that equation does not work, you end up with contradictions

[halcyon rivet]

I understood what was wrong

Thank you

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[halcyon rivet]

.reopen

[devout snow]

✅

[halcyon rivet]

Wait

[halcyon rivet]

Im not talking about cancellation

What I'm trying to say is

Nvm I understood again

Sorry

💀

I realized that transposition of multiplication is the same thing as dividing from both sides

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[desert fulcrum]

it basically means you have to generalize a formula for the sum of n terms

you know the sum of n terms is n/2(2a + (n-1)d)

you had 1/6 and 3/8 inside. they took the least common multiple (LCM) as 24

so you get 4/24 + 9/24(n-1) inside

and then you take the 24 outside which gets multiplied by 1/2

what do you get if you take 1/24 common out of 4/24 + 9(n-1)/24

[desert fulcrum]

if you take 1/2 common from 3/2 + 5/2, what do you get?

its 1/24

okay, have you seen anything in this form:
x(a+b)

what is this in an expanded form?

correct

in 1 way, yes

right

so 1/24 from 4/24 + 9(n-1)/24 gives..?

correct

so what is your new equation? n/2(1/24(4+9(n-1)))

correct

so you get n/48 there

it says kn

and kn is given as n/48

so what could n be?

kn means k*n, n/48 means (1/48)*n

🤷‍♂️

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[muted blaze]

Would this be 4/5?

I believe four is the opposite and 5 is hypotenuse

and sin is opp/hyp if im right

[pale bolt]

yes

ping @muted blaze

[muted blaze]

thanks

@pale bolt

also if ur stilll ther

im thinking this is

17.5

[pale bolt]

,calc 385/22

[woven radish]

Result:

17.5

[pale bolt]

yep

[muted blaze]

but what does it mean

by the significant digits

[pale bolt]

oh good point i didnt read that

uhh lemme look up sigfig rules one sec

When multiplying/dividing, the answer should have the same number of significant figures as the limiting term.

so since 22 has 2 sigfigs, the answer should as well

so you need to round it to 2 sigfigs

[muted blaze]

okay so 18

thanks

how long

are you available for

[pale bolt]

im not going to commit to answering all your questions, if thats what you are asking, but if you keep posting I can answer while I am here most likely

[muted blaze]

of course not, I'm just starting mathematical physics and I think most questions I can answer myself but just looking for second eyes if u are still here

For this one I've solved

34.56 meters

[wheat pawn]

that's not 34.56

[lusty sapphire]

How'd you get 0.4226

[muted blaze]

ik that

82m * sin 25 degrees

[wheat pawn]

^this is correct, but your product isnt

[muted blaze]

oh

i see

34.654

[wheat pawn]

and you have to round to what

[muted blaze]

It doesn't say

I think it may wamt the entire number

34.6546975

it doesn't say to round to anything

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[muted blaze]

Constant velocity?

[muted blaze]

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[slim sequoia]

hello, i need help with this question

[slim sequoia]

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[past horizon]

Please do not close your channel and reopen a new one with the same question for no reason

[devout snow]

@stable fiber Has your question been resolved?

[stable fiber]

Ok

Plz help

<@&286206848099549185>

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@stable fiber Has your question been resolved?

[stable fiber]

I give up

Shit server

.closr

.clise

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@sudden grail Has your question been resolved?

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@sudden grail Has your question been resolved?

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@sudden grail Has your question been resolved?

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@sudden grail Has your question been resolved?

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@sudden grail Has your question been resolved?

[stray ledge]

good luck 💀

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[pallid perch]

A lot contains 1400 items., what is the probability of its acceptance?A sample of 200 items is taken and the lot accepted if no more than 2 defective items appear in the sample. If the lot actually contains 28 defectives
B
A sample of 20 independent pieces is taken from a production line and none of the pieces is defective.
a. What can be said about the percentage defective in the process?
b. If the actual percentage defective in the process is p= 2%, what is the probability of the above event? c. What is the probability if p = 4%? I need some help like do I use binomial here? <@&286206848099549185>

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[tender coral]

anyone free to help me out on this one :3 i’ve made it as far as understanding and do like -1< x-2 < 1 and (x-2)(2x+1) but i don’t know what to do with the 2x+1

[inland seal]

Factor 2x^2 - 3x - 2

Oh you did that

[magic thicket]

he already has

[inland seal]

Now use |x - 2| < 1 to find a bound on 2x + 1

[magic thicket]

|(x-2)(2x+1)| = |x-2| |2x+1|
Try to find an upper bound for each term

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[frank wigeon]

is this right so far?

[upper schooner]

[this assumes that L is nonzero, but of course if it were zero, wouldn't be much of a differential equation ]

[frank wigeon]

and this last part before solving for y?

This makes me sad

@upper schooner

[upper schooner]

Yep that's fine (assuming that R is nonzero as well!)

[frank wigeon]

@upper schooner

[upper schooner]

[upper schooner]

Better use that one

[frank wigeon]

Gross 🤮

Thank you @upper schooner 🙂

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[tender coral]

like by solving for x?

[magic thicket]

no

well not exactly

1 < x < 3
Use that to bound the second factor

[tender coral]

so like

[tender coral]

3< 2x+1 <7? am i doing that right

[magic thicket]

why does that hold ?

[tender coral]

wdym

[magic thicket]

what allows you to say that

can I always ?
I can for f(x) = 2x+1
But if 0 < x < pi, I can't claim 0 < sin(x) < 0, that'd be silly

[tender coral]

ngl i can’t think of how id otherwise go about doing it

[magic thicket]

that's the way

[magic thicket]

it's just that you need to find a way to justify that claim

[magic thicket]

because it doesn't always hold

[tender coral]

ah

hmm

so standard algebra won’t hold?😭 like i can’t take 1<x<3 and show like multiplying the inequality by 2 and adding 1?

[magic thicket]

you can

because x -> 2x and x -> x+1 are both increasing functions

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[tender coral]

so my proof holds up till 3< 2x+1 <7 then?

[tender coral]

and if we know x-2 is <1, even if we added it to the previous inequality, it wouldn’t surpass 7

[magic thicket]

it's all correct
I'm just asking that you justify something and watching you fail, that's all

[tender coral]

so would that complete it?

[tender coral]

oh

gimme a sec maybe

[magic thicket]

I expected you to answer that easily

[magic thicket]

but visibly you did not understand the nature of my question

[magic thicket]

which came because you did not sound confident

[tender coral]

yeah i didn’t

[magic thicket]

so I asked you to justify, so you could convince yourself
And you failed to do that

[magic thicket]

it was to justify that 1 < x < 3 implies 3 < 2x+1 < 7

[tender coral]

how else do you justfy it besides algebra? would you plug in the bounded x values to see that it holds or something?

[magic thicket]

.

so x -> 2x+1 is increasing

[tender coral]

how does that prove it tho

[magic thicket]

prove it

you're in undergrad
Take that as an exercise

[tender coral]

prove that it’s true or prove how that statement justifies the implication

[magic thicket]

that if f : [a, b] -> R is increasing, then min(f) = f(a), max(f) = f(b)
i.e., that a <= x <= b implies f(a) <= f(x) <= f(b) (the strict version is basically identical)

[magic thicket]

this may be taken for granted because the goal is not to prove elementary things about real numbers

[devout snow]

@tender coral Has your question been resolved?

[tender coral]

isn’t it simply because the bounds of x prove that it’s of a positive value

so naturally 2x and 2x+1 are positive and therefore increasing as well

[magic thicket]

[tender coral]

https://tenor.com/view/byuntear-sad-sad-cat-cat-meme-gif-25617057

[magic thicket]

I just don't know what to say

Just convince yourself at this point

[tender coral]

i don’t get it man😭is my logic at least adequate in terms of the proof? i’ve kinda lost the point by now

[magic thicket]

I've noticed

[magic thicket]

My goal was to get you to say it's because it's increasing

[tender coral]

i didn’t really get that from the example provided😭

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[devout snow]

@tender coral Has your question been resolved?

[torn coyote]

Need help in help-0

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[restive river]

I'm trying to solve this problem and it feels like it should be easy but I'm definitely missing something "^^

An object is dropped from rest, and its position is measured at times $0,\Delta,2\Delta,$, . . . , etc. Show that the ratio of the distances it travels in any two successive intervals is the ratio of successive odd integers.

So I got the position vector r at time t to be $\vec{r}(t) = \frac{1}{2}gt^2$, and so therefore for some $\Delta$, $\frac{\vec{r}(n\Delta)}{\vec{r}((n+1)\Delta)} = \frac{n^2}{(n+1)^2}$.

And then going from the opposite way, for consecutive odd numbers $2n+1$, $2n+3$, I get $\frac{2n+1}{2n+3}$, but these two ratios aren't equal? I'm definitely missing some steps because that feels too easy anyway, but I don't know what I'm forgetting to do or missing

[woven radish]

cinnabasil

[inland seal]

You are measuring r(t) from the start of the fall

You need the distance it travelled between nDelta and (n+1)Delta

Also for the next interval, so between (n+1)Delta and (n+2)Delta

[restive river]

Ohh, it's the ratio of dr/dt, not r

$\frac{\vec{r}((n+1)\Delta) - \vec{r}(n\Delta)}{\vec{r}((n+2)\Delta) - \vec{r}((n+1)\Delta)} = \frac{(n+1)^2 - n^2}{(n+2)^2 - (n+1)^2} = \frac{2n+1}{2n + 3}$

[woven radish]

cinnabasil

[restive river]

Yeah, that makes sense

Thanks! <3

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[dusty robin]

I'm not quite sure like what exactly I'm supposed to do with the table here

[dusty robin]

Nvm I figured it out

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[distant creek]

Hello

I did that and i wanna check it <@&286206848099549185>

[crisp trench]

Can you translate

[distant creek]

Its say to find domain for x and (idk the name in English) for y

Like the domain of x and y

@crisp trench

[crisp trench]

Domain and codomain/range

And what did you get?

[distant creek]

a) domain=> [-infinity , +infinity]
Range=> [2.8, -inifnity]

b) domain=>[-infinity, 0.9]
Range=>[-infinity, 2]

[crisp trench]

When we talk about infinity its always $\left<-\infty , + \infty \right>$

[woven radish]

casework

[crisp trench]

I forgot if its called closed or open

I guess closed

[wooden veldt]

open

[crisp trench]

Range is $\left<-\infty , 2.8 \right]$

[distant creek]

c) domain=>[-infinity, +infinity]
Range=>[-0.5, 0.5]

[woven radish]

casework

[crisp trench]

Yoz always go from smaller to bigger

[distant creek]

Yeah true i forgot that

Thanks

[crisp trench]

Thanks.

So basically whenever you have infinity its always closed interval on that end

[distant creek]

So if i have 2, ♾️

Its [2, ♾️)

?

[crisp trench]

Yes

Infinity isnt a number

[distant creek]

Okay thanks

[crisp trench]

You cant include infinity

[distant creek]

Yup

Can u check c?

d) dom=> (-♾️,♾️)

Range=>[0, 2,5]

[crisp trench]

You write (-infty , + infty) otherwise ok

[distant creek]

Okay thanks

And d?

In English what are the two types of max and min

[crisp trench]

Idk what you did here

It should be all reals aka from -infty to + infty for both

[crisp trench]

Local and global

Id thats what you mean

[crisp trench]

It doesnt include 0

[distant creek]

When its 0 alway Open?

[crisp trench]

I mean shouldnt if its a bell curve

[distant creek]

Because i saw in the pic that it doesnt go up

[crisp trench]

Not always but in d case i dont think it includes 0

[distant creek]

Okay

[crisp trench]

I mean it does go from - infinity to + infinity

[distant creek]

Okay

Thanks man

The max and min in Spanish there is the most and the itehr

What are called?

[crisp trench]

Global and local?

[distant creek]

Global is the most up or down one?

And local the others?

[crisp trench]

Yeah

[distant creek]

Thanks really apreciate ur help

Il need u in a bit to check them

@crisp trench when its +♾️ its coun as global?

[crisp trench]

When its +infinity i dont think it has a max

I dont think infinity can be max/min

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[distant creek]

.reopen

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✅

[distant creek]

@crisp trench im back

For b

Max global is [1.2, 1.1]
Min global is [0.2, 1.1]
There isnt min or max local

<@&286206848099549185>

[alpine inlet]

can you post the whole task again?

[distant creek]

@alpine inlet

[alpine inlet]

por favor translatcion

que es el dominio

[distant creek]

Domain

[alpine inlet]

y el recorrido del cada

[distant creek]

But that is already did

I wanna check max and min (global and local) of b)

[distant creek]

This is my answer

[alpine inlet]

maximum global point of the curve in b)?

is the curve stopping where it's drawn or does it go to infinity?

[distant creek]

Go to ♾️

[alpine inlet]

then a global maximum would not exist right?

same for global minimum

[crisp trench]

Ye it doesnt there is no max

[alpine inlet]

and only you can see a local maximum and local minimum

[distant creek]

So bot are local?

Both*

Thanks

I have math exam tmrw and i wanna have a good mark

[alpine inlet]

I mean, also depends on how your textbook exactly defined these terms

[distant creek]

What we call x²-4?

$x^2-4$

[alpine inlet]

numerator ?

[distant creek]

$2x-1/x^2-4$

[woven radish]

1MG_CR

[distant creek]

The one that is up is numerator or the one that is down?

[alpine inlet]

no the down one is numerator

the upper one is denonminator

no

wait

i got that wrong

you're right

up is numerator

denominator

is the below

[distant creek]

Okay so in that pictor

[winter patrol]

d for down

[distant creek]

What value of x make the dominator =0

I wrote 2, -2

[alpine inlet]

yes

x^2-4 = 0 is equivalent to x^2 = 4

[distant creek]

How do i get the domain of that

[alpine inlet]

of f(x)?

[distant creek]

Someone already explained it, but still dont get ut

Yup

[alpine inlet]

domain is where f is defined

so the possible x values

in this case, I'd say there's no restrictions - could be any real number

[distant creek]

And here?

[alpine inlet]

because there's no quotient or something that divides by 0

[distant creek]

When its fraction?

[alpine inlet]

ye you need to avoid dividing by 0 with fractions

that's basically it

so set denominator to 0 and solve it for x. those x are not in the domain

[distant creek]

So for example in d its all real number, and not -2

[alpine inlet]

in d) we have 3x +6 as denominator

so 3x+6=0 means x = -2 needs to be avoided yea

[distant creek]

Okay thanks

And when its isnt a fraction it all real numbers no?

[alpine inlet]

I think yes

except for weird functions like tan()

[distant creek]

Okay i still in 4th grade in highschool

[alpine inlet]

but with polynomials, only fraction can be a problem

[distant creek]

So thats far

[distant creek]

So fs thats gonna be in the exam

[alpine inlet]

you'll ace it 😄

[distant creek]

Can u solve me them

Just to check if i have them rigt

[alpine inlet]

a) All real numbers

b also

c) x=2

I meant, all except x=2

d) all except x = -2
e) all except x = 1 or x = -1

f) all except x^2 -2x = 0 which I think is x = 2

I mean for f) you need to solve quadratic equation

apply the standard procedure (I forgot the formula)

[distant creek]

Thanks, i got them all right

[alpine inlet]

nice

[distant creek]

How do i calculate the poit where the funtion cut in line x

Without drawing it

[alpine inlet]

in line x?

you mean x axis?

f(x) = 0

if y is 0, it's on the x axis

so solve f(x) = 0

[distant creek]

I have a formula idk if its works

-b±√b²-4ac/2a$

@alpine inlet

[alpine inlet]

yea

(but division by 2a at the end of all that

that formula solve quadratic equations of type 0 = ax^2 +bx + c

[distant creek]

In a normal one like

Y=4x+6

How we do it?

[alpine inlet]

I mean, you could also say a = 0 and use the quadratic equation formula

but that is overkill

if you have 0 = 4x +6

then just move 6 to other side

and divide by 4

[distant creek]

Oh thanks

Thats easier

[devout snow]

@distant creek Has your question been resolved?

[devout snow]

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[lament raven]

When I derive, i get

$\frac{dV}{dt} = \frac{1}{3}\pi (2r\frac{dR}{dt}h + r^2\frac{dH}{dt})$

[woven radish]

lxve

[lament raven]

i plug in -12 for dV/dt, 5 for r, and 15 for h, but how do I get dR/dt so I can solve for dH/dt?

[near trout]

R is a function of H

the closer to the base of the cone, the wider the radius

[lament raven]

i was thinking of replacing 1/3h for R

[stable storm]

h won’t be 15 here since h also decreases as the volume decreases

[lament raven]

can you explain more

[stable storm]

as liquid is spilling out of the tank

the height of the liquid is also decreasing

just as how the leakage of a water bottle would work

the height of the liquid would decrease

[lament raven]

yes i know i need to find rate of the decrease of the height

i am stumpted after deriving the V= formula

[near trout]

the radius is a function of the height

[stable storm]

so if we look at the right triangle created by the height and the radius

as height decreases radius also decreases

but the ratio of the height and radius remains the same

because they are similar triangles by AA

[lament raven]

oh the ratio lol

yea idk why i forgot

yea i got

r = 1/3 h

as before

so i replace the r in v = 1/3 pi * r^2 * h with 1/3 h correct?

[near trout]

no

wait yes

diameter, radius, yes

[lament raven]

so $\frac{d}{dt}[\frac{1}{3}\pi(\frac{1}{3}h)^2h]$

[woven radish]

lxve

[lament raven]

like that?

[stable storm]

yep

[lament raven]

yea i still cant do it for some reason

am i deriving wrong?

i get $\frac{dV}{dt} = \frac{1}{3}\pi 3h^2 \frac{dH}{dt} * 9$

[woven radish]

lxve

[stable storm]

$\frac{d}{dt}[\frac{1}{27}\pi(h)^3]$

[woven radish]

y0shi

[stable storm]

that should be what you get after simplifying

and differentiating this should give you

$\frac{dV}{dt} = \frac{1}{27}\pi 3h^2 \frac{dh}{dt}$

[woven radish]

y0shi

[lament raven]

oh i see the mistake

[stable storm]

and now you can plug in h and dv dt

[lament raven]

after plugging in

i multiply both sides by 27

then divide -324 (-12 * 27) by pi * 3(15)^2

i get -0.1527

[stable storm]

if you plug in everything it should be $-12 = \frac{1}{27}\pi 3(9)^2 \frac{dh}{dt}$

[woven radish]

y0shi

[stable storm]

and then we can simplify the right side a bit to $-12 = 9\pi\frac{dh}{dt}$

[woven radish]

y0shi

[stable storm]

so $\frac{dh}{dt}=\frac{-12}{9\pi}$

[woven radish]

y0shi

[stable storm]

which is around -0.4244

[lament raven]

h is 15?

"The diameter of the cone is 10 feet, and the height is 15 feet"

[stable storm]

yeah but thats when the tank was full

when the volume is 27pi, h=9

[lament raven]

oh i see

[stable storm]

we are observing at when the volume is 27 pi as stated in the problem

[lament raven]

i missed that part completely

[stable storm]

yeah its fine

common mistakes

[lament raven]

to find h it would've been

$27\pi = \frac{1}{3}\pi r^2 h$?

[woven radish]

lxve

[stable storm]

yeah and r would be h/3 here

[lament raven]

i see

so right side would be $\frac{1}{27} \pi h^3$

[woven radish]

lxve

[stable storm]

yep

[lament raven]

i got 9.21.... for h

[stable storm]

the $\pi$ cancel and $h^3 = 729$