help-26

[thorny flame]

bob420

bob420

[pastel salmon]

the graph does not intersect y -axis

since it is a real valued functions

to veirfy your knowldge )

[topaz sinew]

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[thorny flame]

Question mark

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[winged moth]

HGGH

[topaz sinew]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

@winged moth Has your question been resolved?

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[neon iron]

How to measure distance between any 2 stars?

[arctic heath]

use a ruler.

[shut belfry]

I would use law of cosines

[arctic heath]

wow, how

[shut belfry]

if i know distance from my eye to the star1

and star 2

[arctic heath]

how u know lol

use a ruler

hhaha

[shut belfry]

no

That's dumb

[arctic heath]

how you know then

[shut belfry]

https://en.wikipedia.org/wiki/Law_of_cosines

@neon iron

[arctic heath]

i mean, how you know the distance between ur eye and star 1

[shut belfry]

Parallax

[arctic heath]

wuu

genius!

gud job

[shut belfry]

But it's pain to wait for 6 months

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@neon iron Has your question been resolved?

[arctic heath]

: <

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[rocky jewel]

Is this wrong?

[rocky jewel]

Or is the idea that e^c is any constant so we might as well pull it down?

[abstract wadi]

Yes, but it's some other constant.

[rocky jewel]

and if so - should we just wait with adding the +c until the end? o_O

[ivory sorrel]

that's not wrong per say, that can be rewritten as e^ce^x^2/2

where e^c is a constant

[rocky jewel]

yeah that's what I was thinking

[ivory sorrel]

but the problem is now the constant can only be positive

as e^x's range is R+

[rocky jewel]

so I should just say D = e^c

but i mean if it only can be positive doesnt that mean i did smth wrong

urgh

Because for the second one the +C is inside of tan

it just feels weird that one time it's outside of a function and the next time it's inside ;P

[abstract wadi]

No, it's meant to be a constant.
It was going to have a fixed value anyway. It does matter if it's always > 0, it's still a real number.

[abstract wadi]

Could be anywhere.

[ivory sorrel]

if it's positive it won't reprsent the entire family of curves though, would it?

[rocky jewel]

so how come that they can say e^C = C in the first one?

[abstract wadi]

It would.

[abstract wadi]

They can't, should have used some other letter.

[rocky jewel]

ok so then it's "correct" to say e^c = D

[abstract wadi]

It is.

[rocky jewel]

y(x) = De^x^2/2 - 1

awesome

thank you a ton

have an amazing day

.close

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[hard hinge]

how do i do this

[hard hinge]

page 1

page 2

[vivid spire]

What-

Which one.

[hard hinge]

page 3

all of thenm

[vivid spire]

Which one?

[hard hinge]

all

[vivid spire]

"All"

[hard hinge]

eveyr problem

or just how to do 1 of each

[vivid spire]

Alright, in the first 10 questions you have to use the fundamental identities to simplify expressions

Do you know what they are?

[hard hinge]

i think were gonna get them

on the test

lemme pull it

up

ok

got em

[hard hinge]

now what

[neon iron]

now solve it

[hard hinge]

lol

[neon iron]

first question sin(u+v)

[hard hinge]

thats the equivalent of saying just win

[vivid spire]

snow's not wrong.

[hard hinge]

"just win the game"

[neon iron]

what would it be equal to

its not

[vivid spire]

Just look through the pythagorean identities

And simplify the fractions

[hard hinge]

aight so first one is 1/cot^2+1

[vivid spire]

For the first ten questions

[neon iron]

no

[neon iron]

you dont need that for the first one.

[vivid spire]

He sent some questions before this.

Read the help channel from message #1

[neon iron]

oh

[hard hinge]

ok sin^2

ist the first one

[neon iron]

okay my bad sorry

[hard hinge]

next is tan / 1-cos^2 which is sin. tan/sin

[vivid spire]

Just look at the identities

[hard hinge]

yeah i know the basics of how to do it but on the more complex ones i usually take the wrong path

[vivid spire]

1. $\frac1{\cot^2 x+1}$

[vivid spire]

So what would you do?

[hard hinge]

switch the cot^2+1 to a csc

and then flip to make it sin^2

[vivid spire]

Exactly

And then?

Yep!

[hard hinge]

AYYYY!!

[vivid spire]

Mhm

[hard hinge]

we should do a hard one

[vivid spire]

Sure

[hard hinge]

i usually choose the wrong thing

thats my problem with these oens

[vivid spire]

It's okay, practice will help

Its actually 1 AM here lemme fix my bed firs

lol

||this server has made me mess up my sleep sched||

[hard hinge]

$\frac\cos^2x{1-\sinx}$

[thorny flame]

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

[hard hinge]

dangit

[hard hinge]

ok well ima try #10

[vivid spire]

okay

[hard hinge]

hey if you gotta sleep tats fine

i dont want to make you fuck upp ur sleep

[vivid spire]

$\frac{\cos^2 x}{1-\sin x}$

[vivid spire]

Yeah cool...

So the denominator looks scary right?

Dw abt it

[hard hinge]

yeah but i guess it would become cos

[vivid spire]

Lets look at what we can do with the numerator

Because that thing is squared

So what do u know abt cos^2 x

[hard hinge]

do we do the thing with the highest multiplicity first? why are we focusing on the top part of the fraction here rather than the denominator?

i just want to know because this is where i usually get tripped up

[vivid spire]

We're trying to simplify, right?

[hard hinge]

yea

[vivid spire]

So you could either try:

• write sin x in terms of cos x

• write cos x in terms of sin x

You have your three pythagorean identities with you...

Now tell me which way is simpler

[hard hinge]

i would normally do this

$\frac{\cos^2x}{\cos}$

[vivid spire]

Okay see...

[thorny flame]

river

[vivid spire]

$1-\sin^2{x}=\cos^2{x}$\\
$1-\sin x\neq\cos x$

[vivid spire]

You see...

[hard hinge]

oh

ok

yall are latex pros lol

[vivid spire]

Nahh its okay

I was more like you when I joined

I told ya, practice makes everything good

Mhm so what'd u do now

[hard hinge]

i think this one would be simpler

maybe i can change cos^2 into 1-sin^2

[vivid spire]

Yep!

You can

So...

$\frac{\cos^2 x}{1-\sin x}$\\
$=\frac{1-\sin^2x}{1-\sin x}$

[hard hinge]

yes ok cool now does one of the 1-sin cancel?

[vivid spire]

Hmmm... something doesn't feel right about it... We have a square on the sine above

But there's no square below...

So it won't cancel out

[hard hinge]

ok

[vivid spire]

Something you can think about... the numerator.

Maybe use that one identity you learn in previous classes

You can see a sine square being subtracted from a one (square?)

[hard hinge]

i dont see what you are getting at. are you saying that the 1 is squared somehow?

[vivid spire]

You could always think of it as

$(1)^2-\sin^2x$

[vivid spire]

It doesnt change anything.

Because 1^2 is just 1

[hard hinge]

yes which is why i thought that one of the 1-sin would cancel out

[vivid spire]

Mhm not so easily

So it'd be

[hard hinge]

$\frac{1^2-\sin^2x}{1-\sin x}$

[thorny flame]

river

river

[vivid spire]

$\frac{\cos^2 x}{1-\sin x}$\\\
$=\frac{1-\sin^2x}{1-\sin x}$\\\
$=\frac{(1)^2-\sin^2x}{1-\sin x}$

[vivid spire]

Yah see!

You got the latex right.

[hard hinge]

lol i copypasted yours and changed it slightly

[vivid spire]

Thats how u learn hahah

You might've heard of... a^2-b^2=...

[hard hinge]

nope

it makes me think of a^2+b^2=c^2

[vivid spire]

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

[vivid spire]

... rings a bell?

[hard hinge]

nah lol sorry

[vivid spire]

Ohh it's okay

It's just an algebraic identity

You can prove it by simplifying the rha

Rhs

Sorry I'm gonna type horrible now

Cause I'm no longer on pc

[hard hinge]

i seriously cant see how this doesnt work

oh maybe because theres a subtract sign on the top and bottom

i cant break it apart like that

ok i see now

[hard hinge]

so i cant do this

[hard hinge]

so what do i do next?

[hard hinge]

np man and if you need to sleep thats fine

.

.<@&286206848099549185> how do i do this

$\frac{\cos^2 x}{1-\sin x}$

[thorny flame]

river

[hard hinge]

i need to simplify with identities

[slender edge]

how can you rewrite cos^2(x)

in terms of another trig function

[hard hinge]

i can make it 1-sin^2

[vivid spire]

I'm sorry I don't get pings from the server

[hard hinge]

oh np

[slender edge]

how can you rewrite 1-sin^2(x)

[vivid spire]

Noo ...

You can't do this

[slender edge]

with difference of squares

[hard hinge]

how

[slender edge]

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

yes

so how would you do it with 1-sin^2(x)

[hard hinge]

i dont know how to map that onto 1-sin^2

[slender edge]

well here a would be 1 and b would be sin(x)

[hard hinge]

ok

[slender edge]

so you would get (1+sin(x))(1-sin(x))

[hard hinge]

ooooooh

[vivid spire]

Anyway vereity id appreciate if you could help him

I'm gonna go sleep it's 1 30 am

[hard hinge]

yes thank you for your help

[hard hinge]

yeah man you gotta sleep lol

[hard hinge]

ok so one of them cancels and im left with 1+sin

is that all i can do there?

[vivid spire]

Yep

[hard hinge]

ok col

ima clsose this and open another one for the next problem

is that what i sohuld do?

[vivid spire]

You can just continue here

[hard hinge]

ok

[thorny flame]

river

river

river

river

[hard hinge]

<@&286206848099549185> can anyone tell me where to go from here or what i did wrong? im trying to simplify using trig identities

[opaque crow]

What are you simplifying?

[hard hinge]

this

[opaque crow]

What are you trying to get to?

[hard hinge]

the most simplified version?

idk

it just says simplify using trig identitiers

[hard hinge]

burh whered u go

[topaz sinew]

@hard hinge Has your question been resolved?

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@hard hinge Has your question been resolved?

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[elder glacier]

can someone help me with this

i dont know where to start

[minor palm]

hi, what are you particularly struggling with?

[topaz sinew]

@elder glacier Has your question been resolved?

[elder glacier]

Where to start

I don’t know how to do the task

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@elder glacier Has your question been resolved?

[elder glacier]

.close

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[elder glacier]

can someone help me with these tasks

ive tried to use traingular numbers to solve it

but i cant do it

[topaz sinew]

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[simple orchid]

Hello

[simple orchid]

I'm not sure why f(0, π) = [2, 0, 0]^T

[tawny spoke]

substitute t=0 and s = pi into the vector

they put the values that the trig functions take at these values under

[simple orchid]

For the second line

0 - 1 = -1

Not 0

[tawny spoke]

0 + 0 = 0

[simple orchid]

Oh

My brain

mb

Thanks

.close

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[lyric mountain]

Hello,

I'm in a discrete math class. I tried doing the proof for theorem 1.7 and wanted to see if I could argue the point that 1.7 is true by using theorem 1.6 and 1.5.
If we let b be 2, then r is bounded by 0 and 2. r must be either 0 or 1. r can't be 1 and 0.

[topaz sinew]

@lyric mountain Has your question been resolved?

[topaz sinew]

@lyric mountain Has your question been resolved?

[rigid ivy]

The proof how you wrote it now is insufficient

Actually, it's mostly right, you just need one more detail

If we assume $n$ is both even and odd, then $a=2q_1+1$ and $a=2q_2+2$. Where's the contradiction?

[thorny flame]

SWR

[lyric mountain]

Well isn't that just redefining a?

Wait that's not the important part is it.

Let me think

Cause i know P and not P is a contradiction l.

[lyric mountain]

.close

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[wooden osprey]

so i learned theres something called euler substitution, which can be used for rational function with square roots in the dem

can it be used in this case, and how do i apply it?

[simple orchid]

Just curious, why is there two dx?

[wooden osprey]

probably typo, dont mind it

the fact that i didnt spot the error is concerning

[topaz sinew]

@wooden osprey Has your question been resolved?

[pastel salmon]

$\int_{}^{}\frac{dx}{\left( x+1 \right)\sqrt{x}+x\sqrt{x+1}}=\int_{}^{}\frac{\left( x+1 \right)\sqrt{x}-x\sqrt{x+1}}{x\left( x+1 \right)^{2}-x^{2}\left( x+1 \right)}=\\=\int_{}^{}\frac{\left( x+1 \right)\sqrt{x}-x\sqrt{x+1}}{x^{2}+x}\text{ }dx=\\=\int_{}^{}\frac{\sqrt{x}}{x}\text{ }dx-\int_{}^{}\frac{\sqrt{x+1}}{x+1}\text{ }dx=_{\cdots }etc$

[thorny flame]

Joanna Angel

[golden zodiac]

this looks so terrifying

writing this seems like it hurts

[pastel salmon]

smiles, but that only looks terrifying, but it is short way

[topaz sinew]

@wooden osprey Has your question been resolved?

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[lyric mountain]

My hint is that I need to use only two hypotheses. I thought I understood the proof but now I do't think I do

[lyric mountain]

#help-26 message

Here is what I was thinking at first and someone said I was partially correct

[drifting swift]

SWR made a slight notational misstep i think

what he was going for is

suppose $n$ is both even and odd at the same time, then we have $n = 2m_1$ and $n = 2m_2 + 1$ for some integers $m_1, m_2$. derive a contradiction from this.

[thorny flame]

Ann

[lyric mountain]

that makes more sense

[lyric mountain]

Am I going to far if I thought of n being a statement? Cause I know P and not P for example is a contradiction.

[dense rain]

I think your approach to use the division algorithm works, you were just a little too informal with your phrasing, and it's not the first thing one would think to try.

[lyric mountain]

what would be the first thing to try?

nothing else stood out to me

[dense rain]

The suggestion you were already given to you

[lyric mountain]

To use proof by contradiction ?

[dense rain]

both approaches are a proof by contradiction imo

If your remainder can be 0 and 1, it contradicts the uniqueness of r

[lyric mountain]

oh that's a good point

I was reminded in the book to pay special attention to the words used

[dense rain]

The natural exploratory step should be, the book told me two things cannot happen at the same time, (even and odd). Well, if that is true, what happens, so you set the two definitions to be equal and examine the equation you get.

You seem to have instead looked at theorems in that chapter and looked for something to use, which is usually what you would do if setting those equations equal was not helpful for whatever reason

[lyric mountain]

huh

[lyric mountain]

The natural exploratory step should be, the book told me two things cannot happen at the same time, (even and odd). Well, if that is true, what happens, so you set the two definitions to be equal and examine the equation you get.

So here, you're talking about theorem 7 right?

[dense rain]

It's a stupid example, but it's like if someone tells you that you cannot pat your head and rub your belly at the same time.

[lyric mountain]

oh I see. The natural thing you'd do is try it right haha?

[dense rain]

The first thing you would do is to try to do exactly that. Only if you cannot do it would you then Google something about human physiology

[lyric mountain]

#help-26 message
So here, we are just setting n to be even and odd right?

[dense rain]

Yes

[lyric mountain]

Hmm

I follow that

Can I use theorem 1.5 now?

[dense rain]

I think you're overthinking it if you are looking at that theorem

[lyric mountain]

Since we can use that to show n is either even or odd

oh

Is it that n cannot be both equations?

n =! n here

[dense rain]

You should take some time looking at what Ann wrote and taking a bit of time to think about what you can do with that, preferably without looking at more theorems

[verbal crater]

cant you just use the definition of even and odd?

[lyric mountain]

Aren't we doing that with what Ann wrote?

[verbal crater]

yeah

[dense rain]

That is using the definition of even and odd.

You need to take a step back and read the contents of what you are pasting into discord

[verbal crater]

oh i thought yall moved away from that when you were talking about the division algorithm thing

my bad

[dense rain]

I wasn't talking about you with that comment

Just that they can't tell that Ann's comment is the definition of even and odd is a problem.

[verbal crater]

i see

[lyric mountain]

wait I know that though

[verbal crater]

and use the reply feature so i dont get confused lol

[dense rain]

So follow what Ann wrote, take an integer, call it n, it is both even and odd. Write down what that means, and think about what you can do with those facts.

[lyric mountain]

No I'm still stumped

[verbal crater]

ok we'll start from the bottom

what proof technique would you want to use here

[lyric mountain]

So this is a intro to discrete math class. I don't think he's expecting us to know proof techniques. I think we're going to build those in the class.

But from my reading of a proof book, I'd want to do a proof by contradiction.

[verbal crater]

ok good

if your statement is: it is not possible for n to be both even and odd

how would you start the proof

[lyric mountain]

Show not(it is not possible for n to be both even and odd)

(sorry idk how to do the not symbol)

[verbal crater]

we're doing a proof by contradiction

so to start, what do we do to the statement

[lyric mountain]

assume it's false right?

[verbal crater]

actually nvm this is correct, got confused a little

so whats the negation of the statement

[lyric mountain]

That it is possible for n to be both even and odd

[verbal crater]

good

btw this is an assumption

we're not trying to show that it is true

we're just assuming that it is true

so to start: lets assume that n can be both even and odd

and by the definition of even and odd numbers, what can you write it n as

[lyric mountain]

n = 2m
n = 2k + 1

[verbal crater]

you should use two different letters here

m and n would do

because they're not always equal

wait nvm we cant use n

lets use k

so n = 2m and n = 2k + 1

[lyric mountain]

k instead of m?

okay

[verbal crater]

ok now since n is equal to both of those

are they equal?

2m and 2k+1

[lyric mountain]

no

[verbal crater]

why not?

if a = b and a = c

does b = c?

[lyric mountain]

Oh that's true right?

[verbal crater]

yeah

so does 2m equal 2k + 1?

they're both equal to n

also we missed one thing: m and k are both integers btw

[lyric mountain]

I can make 2m equal 2k + 1

[verbal crater]

ok good

so 2m = 2k + 1

now what can we do here

[lyric mountain]

are you asking how can I make them equal ?

[verbal crater]

no

im asking are they equal

or not

[lyric mountain]

for certain integers yes

[verbal crater]

for certain integers?

[verbal crater]

look back here

you said:

n = 2m
n = 2k + 1

2m and 2k+1 are both equal to n yes?

[lyric mountain]

we wrote that yes

[verbal crater]

so is 2m and 2k+1 equal to each other?

since they are both equal to n?

[lyric mountain]

okay sure

I thought you were trying to get me to show they are equal with certain integers

[verbal crater]

no..

im just asking you are they equal to each other

its a yes or no question

[lyric mountain]

yes

[verbal crater]

ok good

so 2m = 2k + 1

now what can we do here

[lyric mountain]

I don't know

[verbal crater]

hmm we have a 2m on the left and a 2k and the right

any ideas?

[lyric mountain]

no

I don't know what the plan is

rn

[verbal crater]

maybe we can try factoring the 2 out?

[lyric mountain]

why

[verbal crater]

you'll see why

so we'll try moving the 2k to the left

so 2m - 2k = 1

anything we can do here?

[lyric mountain]

m = 1/2 + k
k = -1/2 + m

[verbal crater]

no no no

we're not solving for m or k here

we're trying to do a proof here

not solving equations

maybe we can try factoring the 2 out?

[lyric mountain]

2(m - k) = 1

[verbal crater]

ok good

now do you see a problem here

[lyric mountain]

Is it that the rhs is an odd number?

[verbal crater]

yep yep

and the left is?

[lyric mountain]

probably going to be an even number

[verbal crater]

be more confident

is it or is it not

[lyric mountain]

It is

[verbal crater]

so we have even number = odd number

which is obviously false

and since our assumption of n being both even and odd is wrong

n cannot be both even and odd

yes?

[lyric mountain]

Yes

[verbal crater]

and that completes the proof

[lyric mountain]

I don't think I would have been able to do that on my own. Thank you for batteling through that with me

Maybe I'm just tired not sure.

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[true temple]

Can someone check the answer for my hw

[topaz sinew]

@true temple Has your question been resolved?

[true temple]

<@&286206848099549185>

[outer delta]

What you have looks correct to me

[true temple]

can u help me on how to estimate the instantaneous velocity at t =2 seconda

[true temple]

<@&286206848099549185>

[hollow rose]

Draw a tangent at that point then find the gradient of the tangent

I think

[native vortex]

which qs brother?

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[limpid wave]

I know that 11x - 3 = 5x - 9 here because they are a linear pair but don’t get how to find m<PST after that

[drifting swift]

why not find x first

[limpid wave]

Got -1

[limpid wave]

Yeah how to plug it in

[drifting swift]

i mean plugging it in should not be an issue

but also show your work?

i think you may have messed up

tho let me reproduce it

[limpid wave]

Ok lemme

[drifting swift]

oh yeah... no you're right tho

x does end up as -1

wait

[limpid wave]

Only thing I did was 11x - 3 = 5x - 9

[drifting swift]

holy shit what the fuck

i got bamboozled!!!

11x-3 and 5x-9 aren't equal lmao

[limpid wave]

My friends got it for some reason but I don’t get it

[drifting swift]

they are supplementary

[limpid wave]

oH

[drifting swift]

they add up to 180

[limpid wave]

OhH

I have Covid rn so

[drifting swift]

oh fuck

[limpid wave]

My brain not working

They literally told me from school

They are linear pairs so they equal each other

💀💀💀

[limpid wave]

Yesterday at midnight I was trying to do this

BRUH I get it now

[drifting swift]

if you have covid you should be resting the fuck out

[limpid wave]

Or am I missing something

I plug it into 11x - 3 then right

You can close now right

Tysm Ann

[sweet shard]

you do it yourself

[sweet shard]

read

[limpid wave]

I did that one

.close

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[limpid wave]

Ohh okay thanks

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[zinc loom]

are these equivalent? If not, at which point is it not the same?

[zinc loom]

hmm, it is not the same

putting this in to quadratic formula on the left, can you see where i went wrong

[topaz sinew]

@zinc loom Has your question been resolved?

[zinc loom]

<@&286206848099549185>

[young hornet]

the quadratic formula has been applied correctly to the equation.

[zinc loom]

but when i calculate the value of this and sub that value of lambda into the lower picture it doesnt equal zero

and it is different to the value of the pic at the top right

[young hornet]

first, let's simplify the expression under the square root:
[9e^{4}-30e^{2}+169]

Now, let's calculate the discriminant:
[D = (3e^{2}-1)^2 - 4(e^{2}-7)(6)]
[D = 9e^{4}-6e^{2}+1 - 24e^{2}+168]
[D = 9e^{4}-30e^{2}+169]

so, the discriminant is correct.

[thorny flame]

clovercat.

[zinc loom]

can you not use $e$ as a number in this way?

[thorny flame]

CharlesWorthingtonShire

[zinc loom]

to to calculate a single number value for lambda? (obv it might not be an exact number)

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[trim gust]

I am stuck at this question. I dont really know how to start solving it. I wrote down the definition of derivative and I am unsure what should I do next. I was thinking of using L'Hopital's rule or Mean Value Theorem. (things written in blue are just my thoughts/assumptions/notes so they arent really important)

[snow nimbus]

Hint: You can add a 0 in the middle with 0 = -f(x)+f(x)

[dense rain]

Take a linear combination of the Taylor expansion of f(xi+h) and f(xi-h)

[trim gust]

ok thank you guys! I will try it out and if i am stuck again i will ask for more help! Will close it for now! Thanks again!

.close

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[snow nimbus]

You can dm/ping me if you still have a question. This question is pretty cool

[trim gust]

Thank you! Might take you up on that offer haha

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[odd hedge]

My math knowledge is quite limited but I am trying to find the interception (more or less the x value) between y=0 and the derivative of the function f(x) = ((cosx+sinx+1)/sin2x) when X is on the interval between (0 ; π/2). I hope that my calculations are correct, but for the derivative i get: f'(x) = ((cosx.sin2x - sinx.sin2x - 2sinx.cos2x - 2cosx.cos2x - 2cos2x)/(sin2x)^2). Then i let that be equal to 0 and try to solve, but I cant. And I am sure it has a solution in the interval because when I graph the derivative on desmos the point is (π/4 ; 0 ). I understand that there always is the graphic way of solving it, but I really wanna know if there is an algebraic way. I have tried factorising it so that it's something times something equals 0 and then just use basic trigonometric equations but I dont seem to be able to factorise it in an adequate manner where that works. I have tried changing the trigonometric functions so that everything is connected to sinx and then I let it be equal to lets say T. Then after solving I tried to return to the function and check the values for the interval, however I didnt manage to make that work either.

[topaz sinew]

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[ivory sorrel]

!status

[topaz sinew]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

@errant mesa Has your question been resolved?

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[rain bobcat]

How do I do b, d, e

Someone help me.

.close

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[half sage]

how can i find general term of sequence: $f(0) = 1, f(1) = 2, f(i) = f(i-1)+f(i-2)+i$ ? tried to express them in terms of fibonacci numbers, but didnt work, can anybody help with that? 😦

[thorny flame]

nana

[half sage]

<@&286206848099549185>

[jade rune]

This is not fibonacci number

Those are expressed in f(i) = f(i-1)+f(i-2)

[half sage]

i know, but i wanted to express terms of this sequence in terms of fibonacci numbers

[jade rune]

I don't think you can

[gleaming reef]

hi nana how are you doing

I will attempt to help you solve this problem

[topaz sinew]

@half sage Has your question been resolved?

[topaz sinew]

@half sage Has your question been resolved?

[half sage]

<@&286206848099549185>

[lofty fiber]

its not possible cause there is a homogeneous and non-homogeneous part to it, so i guess u could trial and error but i dont think there is a method

[half sage]

is it not solvable? or not through fibonacci...

[royal glacier]

As I know there's no general method

[lofty fiber]

half of it is fibonacci

half of it is non homogeneous

[royal glacier]

but I think your question is special case

[lofty fiber]

so this

[royal glacier]

Do you know about solving linear recurrences?

[half sage]

yes

but not much...

[royal glacier]

I would say "special case" because we can get simple general term of sequence of $a_n=a_{n-1}+a_{n-2}+n$ if we ignore about initial value conditions

[thorny flame]

Dri111

[royal glacier]

because if $a_n=-n-3$, it meets the recurrence but not satisfies with initial values

[thorny flame]

Dri111

[royal glacier]

Then think about b_n, where it satisfies not only recurrence but also the initial values

[lofty fiber]

is there a non trial and error method

i didnt find one

[royal glacier]

idk about non trial one

[lofty fiber]

because i have a solution

but it was trial and error

[royal glacier]

me too

[lofty fiber]

we're finding values for ai+b where a and b are constants we dont know

right

[half sage]

actually my task is to compute f(n) for O(logn) and i know how to compute n-th term or linear recurrence for O(logn), but idk how to do it with this one 😦

[jovial pasture]

wait im not sure but i kind of found a solution

[lofty fiber]

explain

[jovial pasture]

so, let me just clarify

f(2)=5, f(3)=10, f(4)=19 etc. right?

write the sequence for f(n)-f(n-1) for every n starting with 1, and you would get 1, 3, 5, 9, 15, ....

now find the differences between those consecutive terms and you get, 2, 2, 4, 6, 10 etc.

notice with the 1, 3, 5, 9, 15, .... the nth term is the sum of the previous two terms +1

[jovial pasture]

from this we can see that this sequence is 2(1), 2(1), 2(2), 2(3), 2(5) etc.

where the brackets are fibonacci numbers

and then you can do some manipulation to find the general formula for the question in terms of a fibonacci number

[lofty fiber]

interesting

[jovial pasture]

im still working on it

also i am pre-university, so im quite bad at explaining myself mathematically, but i just found patterns like this

[lofty fiber]

so this question shares the first two terms of fibinacci

[jovial pasture]

yes i think

[lofty fiber]

mhm

then its trial and error from here

[jovial pasture]

its not really trial and error

you can prove it i think

i just need some time

[lofty fiber]

at least no systematic way to do it

at least i didn't find one

[jovial pasture]

hmmm

[lofty fiber]

plug it into python lol

[jovial pasture]

haha

[royal glacier]

did you use matrix for it?

[lofty fiber]

if it helps u can have the solution and work backwards

$[ f(n) = \frac{1}{8} \times 2^{-n} \times \left( 2^n \times (1 - \sqrt{5}) \times (n + 2) + (1 - \sqrt{5})^{n + 1} + (1 + \sqrt{5})^n \times (5 + 3 \sqrt{5}) \right) ]$

[thorny flame]

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

[half sage]

yes

[royal glacier]

oh then

wait a sec

can you express your recurrence with matrix?

because as I know exponential can be calculated in logn

[half sage]

no, i can only express linear recurrences without free term

[royal glacier]

does this make sense to you?

[half sage]

yes

[royal glacier]

so it goes like this

then

srry if image is small

oh think n as i

miswrote

[half sage]

so the matrix with 0 and 1 is matrix of transition?

[royal glacier]

I think so

[half sage]

okay, thank you so much, it was huge help ❤️

[royal glacier]

glad it helps

[half sage]

also @lofty fiber and @jovial pasture thanks a lot too

.close

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[violet hornet]

I need a solution for this problem please. the cyclist one.

[topaz sinew]

Please don't occupy multiple help channels.

[thorny flame]

Snöwdinger

[violet hornet]

Would summing the moments around point O be correct ?

@thorny flame

[thorny flame]

Snöwdinger

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[violet hornet]

@thorny flame can you show me how t solve using the moment method ?

.reopen

[topaz sinew]

✅

[violet hornet]

<@&511231220735279104> can you show me how t solve using the moment method ?

[lucid junco]

i just want to let you know that

youre talking to a bot

it doesnt talk back

[violet hornet]

Yh but

it's answering somwhow

lol

[lucid junco]

no

that is someone else using the bot commands

,tex hello

[thorny flame]

water beam

[lucid junco]

see

[violet hornet]

oh shi...

Well that feels stupid

[lucid junco]

lol

[violet hornet]

So...

do you know the answer

?

[lucid junco]

i dont sorry

i just saw you talking to the bot and i had to mention it

[violet hornet]

Oh ok thanks

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[pale barn]

The third degree function f(x) = 10x3 – 140x2 + 480x gives us the profit (expressed in thousands of euros) of a company, where x represents the number of months that have passed, since its foundation during the first year (ie x ∈ [0, 12]).

d) Between which months has the company had losses?

[shadow shadow]

When f(x)<0

[topaz sinew]

@pale barn Has your question been resolved?

[pale barn]

and how do i applicate into the formula?

<@&286206848099549185>

[outer delta]

Find its roots, set up an interval between those roots and try a number for each interval. If its negative then less than 0 if its positive more than 0. First and last intervals if your just looking at the first year, will be (0, whatever) and (whatever, 12). If at all, it's (0, whatever) and (whatever, inf)

But there are only a possibility of 3 roots

I am 90% sure it's just the first year, so find which roots are in the interval of (0, 12)

@pale barn

[pale barn]

one by one?

i try first x=1 until x=12?

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[pale barn]

.reopen

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✅

[outer delta]

No, you do algebra

You can factor out an x (which means x = 0 is a root) so x(10x^2 - 140x + 480)

Are you able to go from here?

[pale barn]

you mean x=0 then i solve the equation?

oh wait

[outer delta]

Set the equation equal to 0 and solve, there are 3 possible solutions

[pale barn]

i solve 0>10x^2-140x+480?

[outer delta]

Yes, but it is easier to solve for = 0 then set up intervals between each root and seeing which intervals are negative

So find its roots

[pale barn]

i got x=8 and X=6

[outer delta]

Yes, (along with 0) now set up intervals between the roots and ends

[pale barn]

and how can i know if x<0 or x>0 and x<8...?

[outer delta]

We'll get there

[pale barn]

(6>x<8)

[outer delta]

That's 1 interval, you should have a total of 3

[pale barn]

x<8

x>6

x>0

?

[outer delta]

Those are not intervals

Between x = 0 and x = 6, x = 6 and x = 8, and finally x = 8 and x = 12

[pale barn]

sorry for my knowless i dont really understand

[outer delta]

An interval is a piece of the function between two points of x

[pale barn]

and how with x=0, x=6, x=8 can i find the numer of the month?

[outer delta]

0 is the beginning of the year, 6 is 6 months into the year, 8 is 8 months into the year, and 12 is 1 year

[pale barn]

ok

[outer delta]

x is in 'months'

[pale barn]

sure

[outer delta]

It was stated up here

But at somepoint in those months (mainly the beginning) the function hits 0 whether that is to go into the positives or negatives. Which is why we are setting up intervals. (0, 6) (6, 8) (8, 12) or (0<x<6) (6<x<8) (8<x<12)

Then you can pick a number between those intervals, x = 1, 7, and 9 for this case but it can be any number inbetween and plug it back into the equation and see if it comes out negative or positive. If it's positive the function is positive on that interval, and vice versa if it's negative

x(x - 6)(x - 8) plug in those numbers and solve

@pale barn

[pale barn]

I need solve the f(x) = 10x3 – 140x2 + 480x useing x=7 ?

[outer delta]

Along with 1 and 9

[pale barn]

x=7 f(x)=-70

[outer delta]

What about x = 1, and x = 9

[pale barn]

x=1 f(x)=350

x=9 f(x)270

oh, that's it, tysm

[outer delta]

So this tells you on the intervals of x = (0 to 6) and (8 to 12) the function is positive. Then, the interval (6 to 8) the function is negative

[pale barn]

ok, tysm

.close

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[prisma cove]

can anybody solve that question A truck is to be driven 120 km at a constant speed of x km/hr. Speed laws require that 40 ≤ x ≤ 120. Assume that gasoline costs 40 TL/liter and is consumed at the rate of 1+x^2/360 liter /hours. If the driver is paid 180 TL /hours,find the most economical speed and the total cost for the trip

[topaz sinew]

@prisma cove Has your question been resolved?

[topaz sinew]

@prisma cove Has your question been resolved?

[whole geode]

!status @prisma cove

[topaz sinew]

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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above

[whole geode]

This is going to be a differential calculus problem. The idea is that you create a function that gives the cost for the trip for a given speed, then differentiate with respect to that speed and try to find the minimum.

There are 3 possibilities, it is either at the min, the max, or somewhere in the middle where the derivative is equal to 0.

[topaz sinew]

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[cold moon]

hello, I have several questions Im gonna work on from the textbook

[cold moon]

however I have no idea if its right or wrong cause theres no solutions

Im wondering if we can go over each question

2.1 i got
b implies f
d imples f
a implies e
c implies e
e and f does not imply any statements

please this is so confusing

its the lack of uncertainty

whether its correct or not

[topaz sinew]

@cold moon Has your question been resolved?

[vernal matrix]

Don't have very long but I think you're missing some implications

[cold moon]

not sure how a would imply e actually, I think it should be e imply a and e imply c instead?

cause cause if e is true then a is also true

which is true

[vernal matrix]

"If there's a girl that every boy has danced with, then there's a girl and boy who have danced"

[vernal matrix]

Not quite either say one couple danced but nobody else did

That's e true but a false

[cold moon]

are you saying a implies f?

[vernal matrix]

Oh yea i misread sorry

I mistook e and f, i can't read

[cold moon]

no no what you said makes sense tho, im missing implication of a implies f, but for a implies e, if a is true, e could be false

which makes a implies e wrong

[vernal matrix]

Yea it is wrong, you were right

[cold moon]

what were all the implications you got? how would you know if you have found all

Im gonna compare a with b,c,d..
then b with c,d,.. and c with d,e,.. but that takes a long time

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[cold moon]

.close

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[white grotto]

how to get the limit on the right and the left side

[sweet shard]

is [x] the floor?

[tired ginkgo]

help

[white grotto]

yeah

[sweet shard]

!occupied

[topaz sinew]

Someone else is already using this help channel. If you need help with a question, please open your own help channel/thread (see #❓how-to-get-help for instructions).

[sweet shard]

try a few numbers with separate one-sided limits

[white grotto]

why few numbers

[sweet shard]

Example 1 isn't exactly the same, but it's the same idea
https://tutorial.math.lamar.edu/Classes/CalcI/OneSidedLimits.aspx

[sweet shard]

really just 1 or 2 is enough

n = 1 eg

[white grotto]

nono i know this and i have the correction but something seems not understandble for me

[white grotto]

look my question is in when x is in n, n+1 why they took the n instead of the n+1 ?? that's my question

[topaz sinew]

@white grotto Has your question been resolved?

[sweet shard]

the solution is right

i don't know what you're confused by

just do an example with n=1

[sweet shard]

and read this

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[deft hemlock]

I thought I got it but I didn't, how do I solve this?

[terse abyss]

Use this diagram

Choose S to max V(s)

[deft hemlock]

S=4 right? Since 24-2x(24-2x-4x)=0

V=(24-2x)(24-2x)x?

[deft hemlock]

Is this right?

[terse abyss]

Yep

And how do you know it’s 4 and not 12?

[deft hemlock]

Since plugging in 12 would be 0

[terse abyss]

But the derivative is also zero

[deft hemlock]

Ohh ok

Thank you!

[terse abyss]

You use the second derivative test

But yeah, good job

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[mental basin]

can someone help with a step-by-step solution? I know how to solve this in principle, but I keep getting different suggestions so I'm obviously doing something wrong.

[mental basin]

a1=0 obviously

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[obsidian gale]

we will integrat (ln(2))2^(t/20) first right?

[hidden zinc]

ye ye

[obsidian gale]

ln(2) can go out of the integral as a constant but what do I do about the variable in the exponent?

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[hidden zinc]

integral of a^x

a^x/lna

[obsidian gale]

.reopen

[topaz sinew]

✅

[obsidian gale]

hmm i see. i'll give it a try

but you see... there is a 1/20 with the t so... I'm guessing int of a^x = a^x/lna * dx ?

[hidden zinc]

no what

do u know what is the integral of

f(ax) dx

it is integral of f(ax)/a

u could prove it also

it aint hard

in this case

just take t/20 as u

dt/20 = du

substitute

done

[obsidian gale]

@hidden zinc

[hidden zinc]

that is incorrect

look

u have done everything

but just one step u have forgotten

while integrating

yes u get 2^t/20/ln2

but

u also have to divide by (1/20)

as that is the coeff of t

so it basically gets multiplied

[obsidian gale]

ah so
u = t/20
du = 1/20

so it would be

20*(2^t/20) + C ?

[hidden zinc]

exactly

uve got it pal!

kudos

[obsidian gale]

nice :D

thanks

[hidden zinc]

npp

[obsidian gale]

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[stone verge]

Hi. I'm stuck trying to get ajk instead of aik. I think that maybe I make i = j and that's it, but I would be replacing i with j when j is the index of the sum. So I'm not sure if doing that would still be valid

[stone verge]

Those are matrices

<@&286206848099549185>

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@stone verge Has your question been resolved?

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@stone verge Has your question been resolved?

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[rare eagle]

hi. i'm looking for a game which is dependent only on some form of probability and has a low amount of states (but is still relatively interesting). i want to create a transformation matrix between the states and use it as an example of markov chains

[rare eagle]

i tried snakes and ladders but the issue is that even when having a 3x3 grid i get a 9x9 transition matrix as i can be in 9 possible positions (assuming i start on the first square, 10 if i dont start there)

[odd pagoda]

then make a 2x3 board

[rare eagle]

oh thats neat

thanks

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[half pike]

Cna someone help me double check these?

[shadow shadow]

20=16+4

[half pike]

oh

[half pike]

how do I find out abt the other ones

[shadow shadow]

x²-y²=(x-y)(x+y)

[half pike]

can you help me with the other question first

[shadow shadow]

What questions

[half pike]

17

[shadow shadow]

17=16+1

18=9+9

[half pike]

Ohh ok

[half pike]

can someone double check 14

[onyx igloo]

It’s correct

[half pike]

okk tyy

[half pike]

Can you help me with the last one

[onyx igloo]

Which one?

[half pike]

I covered the number by accident

But it’s the third red strip

[onyx igloo]

Why do you think it’s D?

[half pike]

bc all of them look like (x-y)^2

expect that one but that was is also that basically

so

[onyx igloo]

For that to happen coefficient of x^2 and y^2 have to be positive

you can write x^2-y^2 as (x+y)(x-y)

[half pike]

ohh

[onyx igloo]

A is (x+y)^2 and B is (x-y)^2

But we can’t represent C like that due to the -y^2 at the end.

[half pike]

Ohh

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[finite grail]

how can I solve this?: sin2x sin4x sin6x+sin2x cop9x

[finite grail]

thanks

[snow vine]

what is cop?

[finite grail]

the result?

[snow vine]

Can you maybe send the question again, also using mutlilication symbols

[finite grail]

okok

[finite grail]

sin2x'sin4x'sin6x+sin2x'cos9x=0

[snow vine]

Yeah, you still did not use multiplication symbols in between them

[neon iron]

what is cop9x?

[snow vine]

Can you also use brackets please

and switch cop with cos

[finite grail]

cos

[finite grail]

there are no brackets; it's only: sin2x'sin4x'sin6x+sin2x'cos9x=0

' is for multiplication

[snow vine]

Is it the argument 2x

Or sin^2(x)

[neon iron]

use the identity of sin(A+B/2)sin(A+B/2)

or something like that

[finite grail]

this one