help-28

[opal isle]

idk

anyways

what would be the limit

[lament rivet]

Yep!

[opal isle]

okay so you got the answer

[lament rivet]

Thank you guys all so much!

I had one more question, how do you know you’re supposed to times everything by 1/n!

[opal isle]

you divide by the thing that grows the fastest as n --> infinity

i mean, multiply by 1/n!

[lament rivet]

Ohhh yeah, is dividing by n! And multiplying 1/n! The same

[opal isle]

yes

diving by n! = 1/n!

multiplying by 1/n!... well = 1/n!

[lament rivet]

thank you ! i need to go back to my basics so bad

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[full forum]

Please don't occupy multiple help channels.

[eternal summit]

my second answer came out to be the same but with the signs inverted

it is correct still, right?

cuz it just means unit vector but in opposite direction, which would still be considered parallel.

[gritty rose]

!1c

[full forum]

Please stick to your channel.

[eternal summit]

what

[gritty rose]

Read

[gritty rose]

And read

[eternal summit]

but both questions are different

[gritty rose]

Doesn't matter

[eternal summit]

so which one do I close, now that you are here?

[gritty rose]

Also doesn't matter

[eternal summit]

closed

now pls help me

[open igloo]

In case of vectors, parallel would usually mean that when they are overlapped they form an angle of 0⁰

If they are opposite/form 180⁰ angle they would be antiparallel

[eternal summit]

okay

so my answer

correct?

oh shit

then it is not correct

shucks man

but then

how would I know what is the direction of the second diagonal?

[eternal summit]

lorentz man

[open igloo]

By knowing what vector the second diagonal is
If the first diagonal points in the direction as a+b vector then the second one would point at direction of a-b

You can draw a rough diagram of a and b, their tails touching together and check it out

[eternal summit]

look

how do i show you

how do i show you

tell me please

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@eternal summit Has your question been resolved?

[eternal summit]

no

[eternal summit]

hellp someone

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@eternal summit Has your question been resolved?

[eternal summit]

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[willow inlet]

why is it wrong?

[willow inlet]

The first picture is what I got for a and the second and third are what I got for b

[minor crater]

lmao photomath

[willow inlet]

yeah I don’t have a graphing calculator

[minor crater]

fair

[limpid moat]

we are not rivh like you

[minor crater]

rounding error

change the last digit to 4

[minor crater]

the second one too

[willow inlet]

thank you

[willow inlet]

btw what site is that?

[minor crater]

desmos

very good graphing calculator

[willow inlet]

thank you again

I’ll start using that one

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[sullen raft]

just wondering if this is correct

[sullen raft]

example 8

[golden agate]

yup it seems correct

[sullen raft]

wicked thanks

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[unborn tiger]

i need help

[unborn tiger]

how do you integrate 2 ln 5y?

[limpid moat]

do you know how to integrate ln y?

[unborn tiger]

i don't think so

the derivative of ln y is 1/y right?

[limpid moat]

yes... actually it is 1/y

[unborn tiger]

oops yeah

then how do you integrate ln y?

[limpid moat]

but the integral of ln y is yln(y)-y (try to derive it)

[unborn tiger]

y/y-y?

[fast peak]

do you know integration by parts?

[unborn tiger]

i did

but i forgot

[limpid moat]

😭

[fast peak]

then look it up and as a practice problem integrate ln(y) = 1*ln(y)

[limpid moat]

hence try to train your memory

[unborn tiger]

Okay let me look it real quick

wait hold on

is the derivative of 2*ln(5y) = 2/5y?

or is it wrong?

[limpid moat]

it is right 🙂

[fast peak]

no

you forgot chain rule

you also forgot to use correct parentheses

[unborn tiger]

my goodness

i remember chain rule tho

hold on let me use chain rule

nevermind i'm not getting it

@fast peak

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[sleek quest]

why is my answer wrong?

[sleek quest]

i used u-substition with u=8-cos(x) and du=sin(x)dx

[grizzled mulch]

Integral (8-u)u⁹du = 8u¹⁰/10-u¹¹/11+C

[sleek quest]

where did you get that from

[grizzled mulch]

What?

As you said substitute u=8-cosx

Theres a cosx in the beginning which would become (8-u)

8-cos would be u and rest as you mentioned du

What step is bothering you?

[sleek quest]

i found it to be $\int{cos(x)u^9\mathrm{d}u}$

[glossy valve]

talk_less

[next sail]

no, you shouldn't have any x left

you need to get rid of the cos(x) as well

[sleek quest]

but how

[next sail]

u = 8 - cos(x) so cos(x) = 8 - u

[sleek quest]

oh

right

thanks

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[harsh elk]

what does the .88 represent? 88% decay?

[viral jasper]

Close, it is a decay, but not 88%. Imagine if the number were 1.00. Is that a 100% decay?

[harsh elk]

no

well 1-x=.88

,calc .88-1

[glossy valve]

Result:

-0.12

[harsh elk]

so its a 12% decay

so 88% of price?

but what does .88

represent

[viral jasper]

you already said it

[harsh elk]

the price?

but 24500 is

[viral jasper]

There's a lot of things you can call it

rate of depreciation, rate of remaining value, decay rate

[harsh elk]

depreciation yes

that was the word i was looking for

.clos

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[sullen berry]

Going in with quadratics I get

2.97 seconds

It’s not right so I’m not too sure where I went wrong

[full forum]

Show your work, and if possible, explain where you are stuck.

[languid junco]

which equation did you use?

[sullen berry]

H=ut+(1/2)gt^2

[languid junco]

u is Initial velocity?

that formula is only true if you start from ground zero

[sullen berry]

So what’s there use for this one?

[languid junco]

the general formula has a + y0, an initial height

so ut + (1/2)gt^2 + y0

[sullen berry]

initial velocitytime+ (1/2)gravitytime+y0

Oh it made it squiggly

[languid junco]

gravity*time squared yes

squiggly time is the best kind of time

[sullen berry]

So it’s just solve for t

1.5*t+((1/2)(-9.8)*t+24

[languid junco]

you forgot the t^2 again lol

but otherwise yes, set that equal to 0 and solve

[sullen berry]

Shoot

I’m getting .733

Is wrong

Omfg

I squared wrong :(

Doing something wrong can’t figure it out going insane

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[sullen berry]

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[long solstice]

how can i approach this q?

Let Sn be the number of 110-free bitstrings of length n.
(a) Find S1, S2, and S3.
(b) For n ≥ 4, find a recursive expression for Sn.

[sharp lagoon]

OK, what do you get for part a?

Or are you stuck on that?

[long solstice]

oh hey chai long time no see

how ya doing

[sharp lagoon]

I'm doing fine. How are you?

[long solstice]

im good

ive just got stuck on a bunch of my courses

like data structures 2 and operating systems

its getting hectic lol

[sharp lagoon]

Is the operating systems course where you create one or more of an IT one?

[long solstice]

sorry?

[sharp lagoon]

Oh, does the course teach you to make operating systems?

[long solstice]

its like learning linux and c programming

[sharp lagoon]

Oh, I see.

Systems programming.

[long solstice]

yeah lol

well the course is supposed to go in depth in how os works

and kernels etc.

[sharp lagoon]

Ahh, OK.

[long solstice]

thats fine i like learning about that

but MATH

i hate it

like discrete math

[sharp lagoon]

OK, let's try this discrete math problem.

[long solstice]

ok give me a sec if thats ok

[sharp lagoon]

OK.

[long solstice]

im watching a vid on it

i want to see if i can figure it out

[sharp lagoon]

OK.

[long solstice]

(a) Find S1, S2, and S3.

is that supposed to be a geometric sequence because ik S was depicted for that way back when

do i hv to make a gemotric sequence?

[sharp lagoon]

No, first, what is S1?

[long solstice]

the number of 110 sequences

so when we have one 110 sequence?

[sharp lagoon]

No, it's 110-free bitstrings.

[long solstice]

yea srry -free

[sharp lagoon]

So, bitstrings that don't have 110 in them.

[long solstice]

yes correct

[sharp lagoon]

Like 01011

[long solstice]

so S1 would be when we have size 1 string?

[sharp lagoon]

Right.

Which bitstrings are in S1?

[long solstice]

1 and 0

so just 2 for S1?

[sharp lagoon]

No, for S1.

[long solstice]

i meant S1 lol srry

[sharp lagoon]

OK, so S1 is 2.

What about S2?

[long solstice]

yes

11, 00, 10, 01

so 4

this is ezier than i thought

i overcomplicated it

[sharp lagoon]

OK, what about S3?

[long solstice]

111, 000, 011, 100, 001, 100, 001, 010

theres supposed to be 9

but we have 8

[sharp lagoon]

You have 001 twice.

[long solstice]

oh

damn too many sequences to keep track

[sharp lagoon]

Well, you can do it in base-2 order.

[long solstice]

i forgfot 100

2^3?

thats 8

[sharp lagoon]

000, 001, 010, 011, 100, 101, 110, 111

[long solstice]

but theres supposed to be 9?

[sharp lagoon]

No, 9 is incorrect.

[long solstice]

oh

so 2^3

and we dont need 110

[sharp lagoon]

Almost.

Right.

[long solstice]

kk

betski

[sharp lagoon]

So, S3 is 7.

[long solstice]

correcto

thnxc

[sharp lagoon]

Now, we need to look at how to proceed from here.

Let's look at 011.

[long solstice]

wdym

arent we done with a?

[sharp lagoon]

Yes, but now we're doing b.

[long solstice]

ok

im assuming we need 2^n

[sharp lagoon]

So, let's look at 011.

What bits can come after that?

[long solstice]

as in with n of length 3?

[sharp lagoon]

No, like 011, then add a bit.

Which bits work?

[long solstice]

i dont think im following sorry? we can only have 1 or 0 after the bit 011

[sharp lagoon]

Right.

So, is 1 allowed?

[long solstice]

oh

1 is allowed

0 isnt

[sharp lagoon]

OK.

Let's look at 0111.

What bits are allowed?

[long solstice]

only 1 again

and again

and again

[sharp lagoon]

Right.

[long solstice]

ahhh

i see

[sharp lagoon]

Once you get two 1 bits, you're stuck with only 1 bits.

[long solstice]

so at some point we only have thje option 1

[sharp lagoon]

So, let's look at something else.

How can you avoid getting two 1 bits in a row?

[long solstice]

like mathematically?

[sharp lagoon]

No, I mean by thinking like we did with the 01111 thing.

What are some ways of not getting two 1s in a row?

[long solstice]

well if we know what the last two bits are if we know they are 1 then place 1 again

[sharp lagoon]

No, I mean, let's say we don't want to have two 1s in a row.

So, we don't have two 1s in a row so far.

How can we maintain that?

Like with 010.

We don't have two 1s in a row.

[long solstice]

i see that

[sharp lagoon]

How can we keep it from getting two 1s in a row?

[long solstice]

im not sure srry

as of yet

[sharp lagoon]

OK, what bits are allowed after 010?

[long solstice]

both 1 and 0

[sharp lagoon]

OK, what bits are allowed after 0100?

[long solstice]

both again

[sharp lagoon]

OK, what bits are allowed after 01000?

[long solstice]

both

[sharp lagoon]

OK, so when the last bit is 0, you can have either next.

[long solstice]

oh ok

[sharp lagoon]

What about 0101?

[long solstice]

btoh

[sharp lagoon]

OK, what about 01011?

[long solstice]

when lasy bit is 1

dont put zero?

[long solstice]

1

[sharp lagoon]

What do you mean?

Right.

So, that doesn't avoid two 1s.

So, 0101.

What has to come next to avoid two 1s?

[long solstice]

0

[sharp lagoon]

OK, so 01010.

What can you have next?

[long solstice]

both

so do we always put 0 after 1?

[sharp lagoon]

Yes, if you want to avoid two 1s, you have to do that.

[long solstice]

i see

how can i describe that as an expression

[sharp lagoon]

Well, first, we want to think of it in English.

[long solstice]

wouldnt i need a mathematical one

how can i translate that to math

[sharp lagoon]

We want to get a more intuitive sense of the rules here.

[long solstice]

ohh i see

[sharp lagoon]

So, the rules are that if you get 11, you're stuck with 1s forever.

[long solstice]

yess

and we dont want that

well actually

isnt that fine

cant we just put 1s forever

[sharp lagoon]

Yes.

[long solstice]

and its still 110 free

[sharp lagoon]

We're getting rules for what sequences work.

So, once you get 11, you're stuck with 1s.

When you have 01, you can follow that with 0 and then do whatever you want, or you can follow that with 1 and be stuck with 1s.

When you have 00, you can do whatever you want.

When you have 10, you can do whatever you want.

So, we need to know the previous two bits to see what we can do next.

[long solstice]

ye

s

would i use fibonacci

[sharp lagoon]

Why?

[long solstice]

im assuming so

so i can get two bits?

last bit

and bit before

or am i tripping

[sharp lagoon]

What do you mean by using Fibonacci to get two bits?

[long solstice]

srry i might be overthinking it

[sharp lagoon]

OK, so we need to know the last two bits to know what we can do from there.

[long solstice]

yeah

[sharp lagoon]

So, let's look at S2.

We have 00, 01, 10, and 11.

With the 11, we have one possibility for the next bit.

So, 11 as the previous 2 bits gives us one result with 3 bits.

11 -> 111.

Does that make sense?

[long solstice]

yes

[sharp lagoon]

OK, and then that 111 will become like 11 for the next bit after that.

So, we have 11 -> 111, which gives us 11 for the next time.

With 01, what options do we have?

[long solstice]

2

010, 011

[sharp lagoon]

OK, so we have 010, which gives us 10 for next time.

We have 011, which gives us 11 for next time.

What about 00 and 10?

[long solstice]

001, 000, ans 100 and 101

so is this logarithmic

[sharp lagoon]

OK, so we have two ways to get 00 and two ways to get 01.

No.

[long solstice]

ok

[sharp lagoon]

It's a recurrence relation.

[long solstice]

yeah i get that

[sharp lagoon]

So, let's look at S2.

We have 00, 01, 10, and 11.

• 00 -> 1 * 00 + 1 * 01
• 01 -> 1 * 10 + 1 * 11
• 10 -> 1 * 00 + 1 * 01
• 11 -> 1 * 11

Those are the count * the two bits for the next turn.

Does that make sense?

[long solstice]

umm

gimme a sec

srry

wuts happening there

i cant seem to decrypt it

[sharp lagoon]

Well, if you have 00, you can get 00 or 01 for the next stage, right?

[long solstice]

OHHH

and last one we cant have zero

11 -> 1 * 11

i see

[sharp lagoon]

OK, so we add all those together.

[long solstice]

why do we always multiply by 1 tho>?

[sharp lagoon]

Because that's how many ways there are to get from 00 to 00, for example.

[long solstice]

for ex.

00 -> 0 * 00 + 1 * 01

wouldnt that make sense

[sharp lagoon]

No, you get 1 way to get from 00 to 00.

Not 0 ways.

[long solstice]

oh

i didnt see last message

kk

[sharp lagoon]

OK, so we add up the results.

2 * 00, 2 * 01, 1 * 10, 2 * 11.

[long solstice]

ok

wait shouldnt we start from 4 bits

because n>=4

[sharp lagoon]

No.

Now we start again:

• 2 * 00 -> 2 * 00, 2 * 01
• 2 * 01 -> 2 * 10, 2 * 11
• 1 * 10 -> 1 * 00, 1 * 01
• 2 * 11 -> 2 * 11

Does it make sense what I did there?

[long solstice]

sorta yeah

[sharp lagoon]

OK, put it in your own words.

[long solstice]

2 * 00 -> 2 * 00, 2 * 01

here there are two ways to get 00?

[sharp lagoon]

Yes. You have 2 ways of starting out with 00, so there are 2 ways of getting 00 and 2 ways of getting 01.

0000, 0001, 1000, 1001

You start out with 000 or 100, you get those four.

[long solstice]

yes

[sharp lagoon]

OK, so can you put it in your own words what happened here ^

[long solstice]

so when we start of with 00 there are to ways to get this, either from a 01 or 00

right?

[sharp lagoon]

No, for the whole four lines.

[long solstice]

like an expression to describe it

[sharp lagoon]

No, like your understanding of what it means.

[long solstice]

i get what it means

its just showing when we start with 2 bits

we can add either a 0 or 1

to get the following 2 bits

the new 2 bits

right?

[sharp lagoon]

That's part of it.

[long solstice]

however

for the last one

were stuck with one option

we cant have 10

[sharp lagoon]

OK, so do the next stage.

[long solstice]

with 3 bits?

[sharp lagoon]

No, using the same technique I used there.

[long solstice]

3 * 00, 3 * 01, 2 * 10, 4 * 11

?

[sharp lagoon]

No, there were four lines.

[long solstice]

wdym

i believe i hv 4

[sharp lagoon]

This has four lines.

I think you got the first part before the arrow.

Now add the arrow and what comes after it.

[long solstice]

3 * 00 -> 3 * 00, 3 * 01
3 * 01 -> 3 * 11, 3 * 10
2 * 10 -> 2 * 00, 2 * 01
4 * 11 -> 4 * 11

[sharp lagoon]

What comes after each arrow?

[long solstice]

did i do it wrong

[sharp lagoon]

That looks fine.

So, let's look at 3, 3, 2, 4 at the start of your lines.

That's for S4.

You have 0000, 0100, 1000. You have 0001, 0101, 1001. You have 0010, 1010. You have 0011, 0111, 1011, 1111.

So, there are three items that end with 00 in S4, three with 01, two with 10, and four with 11.

So, S4 = 3 + 3 + 2 + 4.

[long solstice]

yes ig

[sharp lagoon]

So, using what you put, what's S5?

[long solstice]

S5 = 5 + 5 + 7 + 3?

[sharp lagoon]

Yes.

[long solstice]

ill be honest im just intuitievly doing it i dont rlly know whats happening anymore lol

[sharp lagoon]

OK, let's go back.

[long solstice]

is there an easier way to do this like for example if i get a similar question on an exam

i feel like this method is too long?

[sharp lagoon]

I'm not sure of a shorter method.

[long solstice]

ah unfortunate

[sharp lagoon]

So, we started with S2.

[long solstice]

yes

[sharp lagoon]

• 1 * 00
• 1 * 01
• 1 * 10
• 1 * 11

So, let's use variables this time.

[long solstice]

1 * 00
1 * 01
1 * 10
1 * 11

is this saying we have 1 way to make 00

and 01 etc

[sharp lagoon]

Yes.

For S2.

[long solstice]

just curious do you have to sleep soon, i dont want to take too much of your time

[sharp lagoon]

No, I'm fine for now.

[long solstice]

ok

did something happen lol

[sharp lagoon]

I ran into a dead end, unfortunately.

[long solstice]

ohhh dont worry

so this is a hard question i presume

[sharp lagoon]

Here's where I got to:```
a * 00 -> a * 00, a * 01
b * 01 -> b * 10, b * 11
c * 10 -> c * 00, c * 01
d * 11 -> d * 11

S_n-3 = a + b + c + d

(a + c) * 00 -> (a + c) * 00, (a + c) * 01
(a + c) * 01 -> (a + c) * 10, (a + c) * 11
b * 10 -> b * 00, b * 01
(b + d) * 11 -> (b + d) * 11

S_n-2 = 2a + 2b + 2c + d

(a + b + c) * 00 ->     (a + b + c) * 00, (a + b + c) * 01
(a + b + c) * 01 ->     (a + b + c) * 10, (a + b + c) * 11
    (a + c) * 10 ->         (a + c) * 00,     (a + c) * 01

(a + b + c + d) * 11 -> (a + b + c + d) * 11

S_n-1 = 4a + 3b + 4c + d

 (2a + b + 2c) * 00 ->      (2a + b + 2c) * 00, (2a + b + 2c) * 01
 (2a + b + 2c) * 01 ->      (2a + b + 2c) * 10, (2a + b + 2c) * 11
   (a + b + c) * 10 ->        (a + b + c) * 00,   (a + b + c) * 01

(2a + 2b + 2c + d) * 11 -> (2a + 2b + 2c + d) * 11

S_n = 7a + 5b + 7c + d

[long solstice]

i can continue this queston later

[sharp lagoon]

So, one thing I notice is that S_n-2 - S_n-3 = a + b + c.

[long solstice]

so its about noticing patterns

[sharp lagoon]

Yes.

Then S_n-1 - S_n-2 = 2a + b + 2c.

Then (2a + b + 2c) - (a + b + c) = a + c.

Then (2a + b + 2c) - 2(a + c) = b.

So, a and c always have the same coefficients.

So, S_n-3 - (a + b + c) = d.

So, now we have a + c, b, and d.

Let's write S_n-a as t_a.

[long solstice]

is it cool if we do this another time?

[sharp lagoon]

Yes, that's fine.

[long solstice]

i dont think im ready for this question yet

i will save the info u sent me tho

and will talk abt it later

[sharp lagoon]

OK.

[long solstice]

but thnx for helping me with the questions

[sharp lagoon]

No problem.

[long solstice]

as always i appreciate ur help 😄

im guessing ur tired now

lol

[sharp lagoon]

A bit.

[long solstice]

yeah dont wanna take much of ur time

i will try to do some questions tmmrw if i get stuck ill lyk lol

[sharp lagoon]

OK.

[long solstice]

but yeah thanks and gn 😄

[sharp lagoon]

You too.

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[kind cave]

these are the correct answers.
my question is that is subspace R^n determined by the length n of a column of A?

[stiff musk]

the column space is the set of all linear combinations of columns of A
so yea, it's a subspace of R^4 because the columns are length 4

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@kind cave Has your question been resolved?

[silk hull]

Think of 2D -> R^2, 3D -> R^3 so by the definition of it, 4D -> R^4 and column lengths do so

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[flat geode]

What is x (there was no additional info given)

[stiff summit]

Likely the area of DEC

[flat geode]

Yea

Actually i solved it sryy

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[nova island]

Im lost here. Its in the specific section on the monotone convergence theorem

[hidden harbor]

have you studied derivatives?

[nova island]

no

i can do part (a), and to apply the monotone convergence theorem I can see that both sequences are bounded below

but i have no clue how you could determine they are monotonic and bounded above. how could they be bounded above actually??

[dull seal]

You can use this (x-y)^2>=0

[nova island]

yeah thats what i came up with in part a, but im not totally seeing how it applies

[dull seal]

do you mean you don't know how to get to that inequality in part a) from what I said?

[nova island]

No i derived that inequality while doing part a

i dont see how that applies to part b though

[dull seal]

is related to part a because it uses the relationship between the AM and the GM to generate two sequences that will converge to the same limit

assume x_1 <= y_1

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[full forum]

Please don't occupy multiple help channels.

[fervent birch]

<@&286206848099549185> anyone? I tried solving but didn’t get it.

<@&286206848099549185> anyone paleaseeee

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[fervent birch]

Okayyyyyyyyyyyyy

<@&286206848099549185>

[tardy dagger]

Close ur other help channel first

Those ppl alr moved to dm

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@fervent birch Has your question been resolved?

[fervent birch]

<@&286206848099549185>

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@fervent birch Has your question been resolved?

[full forum]

@fervent birch Has your question been resolved?

[fervent birch]

<@&286206848099549185>

[finite ibex]

The minimum coefficient of friction that allows the puck to stay at an angle of 45° with the vertical is 2/square root of 7. In order for the puck to maintain the 45° angle, it must have enough friction to keep itself in place and prevent it from slipping, therefore the minimum friction coefficient must be enough to offset gravity and the centrifugal force of the rotating sphere. The equation that shows the minimum friction coefficient for the puck to remain at the 45° angle is given by tan(45°)=2 square root of 7, which would be 2/square root of 7.

@fervent birch

[fervent birch]

Tysm I am gonna try

[finite ibex]

:)))))

they must give me better helper role

[fervent birch]

Ahah I agree

I keep getting the wrong answer

Do u mind showing me?

[full forum]

@fervent birch Has your question been resolved?

[normal tree]

is this from chatgpt

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@fervent birch Has your question been resolved?

[full forum]

@fervent birch Has your question been resolved?

[silk hull]

Find the vector which satisfies the condition of balancing acceleration dot product gravity

Don’t forget that your acceleration vector will be affected by 45 degrees

[fervent birch]

I didn’t get it

[serene hazel]

"better helper role" it's more like when you use chatgpt and copy paste from here

can't believe you actually wrote all these within seconds

[finite ibex]

nah it is way longer

[finite ibex]

but how i dont use

[serene hazel]

you must have used another ai tool no?

[finite ibex]

i dont even know other thing

[serene hazel]

ok then what happened here after?

you ignored it

[fervent birch]

Omg

[fervent birch]

Wdym I just couldn’t solve it afterwards😭

[serene hazel]

you said "I keep getting the wrong answer" tho

[fervent birch]

Yeah

[serene hazel]

does this mean their help didn't help or what

[fervent birch]

Yeah exactly🌝

[serene hazel]

oh i see

it is like they think ai can do math but its actually wrong

[serene hazel]

^^

[fervent birch]

It didn’t even make sense ngl

[serene hazel]

yea

[fervent birch]

I was just happy someone finally answered

[serene hazel]

honestly im not that enough smart

so im not sure about your problem

[fervent birch]

It’s okay no one rlly could answer it and I didn’t understand

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[vivid berry]

excuse me

[vivid berry]

is there multiple ways i can prove this?

i dont get what "proof by contradiction" means

[nimble dust]

You need to prove in two directions

[vivid berry]

two?

[nimble dust]

Yes
(1) if n is odd then n=4k+-1
(2) if n=4k+-1 then n is odd

[vivid berry]

i just sid this

[nimble dust]

Explain why is this odd

[vivid berry]

it is odd

because 2k is uh even

and then

• or - 1 makes it odd

is that all i need to do

i feel like im doing this wrong

wait so it is =2m+-1 where m equal 2k an integer

[nimble dust]

You can do that but it’s not necessary

[vivid berry]

so is this right?

[nimble dust]

Yeah but what are you trying to prove here

[vivid berry]

that n is odd if and only n=4k+-1

[nimble dust]

What does this prove?

[vivid berry]

that 4k+/- 1 is odd

but it doesnt prove if only

idk how to do that

[nimble dust]

You are proving (2) here

[vivid berry]

ye

oh

so do i also make

let n be 2a+1

[nimble dust]

Now you need to prove (1)

[vivid berry]

idk how to do it

i just did this

[nimble dust]

Try considering the cases where a is odd and a is even

[vivid berry]

wdym by dis?

[nimble dust]

You are trying to prove that if n=2a+1
then n=4k+1 or 4k-1

[vivid berry]

is number 1 the prove n is odd part and the nnumber 2 is the only if part?

[nimble dust]

Yeah

[vivid berry]

can i do like this

wait

take the +1 out of bracket

accident

[nimble dust]

That’s only part of the proof

What if m is odd

You should consider m=2k-1 here

[nimble dust]

That completes the proof

But you should learn how to do proof by contradiction

[vivid berry]

so i just have to do whatever to force it into the form 4k+/-1?

[nimble dust]

Yeah

[vivid berry]

yea can u pls teach me proof by contradiction?

[nimble dust]

First we want to assume the statement we want to prove is false

What does this mean?

It means that there exists some even number m such that

m = 4k+1 or 4k-1

[vivid berry]

oh

ok now whar

[nimble dust]

m is even
So m+1 and m-1 are odd

[vivid berry]

wait is proof by contradiction same as direct proofs?

oh nvmnvm

contradiction we assume that one is false?

[nimble dust]

Yeah

[vivid berry]

why do we have m is even?

[nimble dust]

Because the statement says that n=4k+1 or 4k-1 is odd

[vivid berry]

ohh i see i see

[nimble dust]

If this statement is false
This means that some even number can be written as 4k+1 or 4k-1

[vivid berry]

so that now it is

m is even if and only if?

or no

[nimble dust]

Here is a proof by contradiction

What we want is assume the statement is false
If a contradiction is found
Our assumption must be false
Hence the statement is true

[vivid berry]

is this proved?

can u give me another example so i can try apply it

[nimble dust]

Do you know the proof of sqrt2 is irrational

[vivid berry]

can u use contradiction for this one

[vivid berry]

yes!

can this be proved by contradiction

[vivid berry]

as it cannot be expressed as an integer

[nimble dust]

*fraction, not integer

[vivid berry]

ohhh yehahahehehahahaha

[nimble dust]

This does not require proof by contradiction

[vivid berry]

did u say same number is both odd and even

[nimble dust]

Yeah that is a contradiction we arrived from our assumption

Meaning that our assumption is false

[vivid berry]

what do u mean by same number is both odd and even

[nimble dust]

n+-1 is odd
4k is even

[vivid berry]

ohhhhhhh ohhhh ohhh

ohh

ohh

ohh

[nimble dust]

If they are equal
that means a number is both odd and even

Which is obviously false

[vivid berry]

yeah

is there any resources where i can learn

proof by contradiction

[nimble dust]

Idk
Perhaps you can go to YouTube

They can probably explain this better

[vivid berry]

okok thanks

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[unkempt ivy]

what does it mean by dividing a number by a ratio and why will there be 2 different answers?

[jaunty fox]

It means break the number 62 into two pieces, like x + y, such that x/3 equals y/7

[unkempt ivy]

thanks

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[versed sierra]

how do i solve the ticked part?

[versed sierra]

<@&286206848099549185>

[verbal crest]

YEA?

[versed sierra]

how do i begin to solve?

[verbal crest]

idk

[tame egret]

for the maximum height

[cunning marten]

Ain’t this given

544 ft

[tame egret]

differentiate h(t)

dh(t)/dt = 0

then find the value of t

[cunning marten]

32t +240

=0?

[tame egret]

then differentiate it twice to check if it is the maximum or minimum value
rule:
if d²y/dt² >0 then minimum value
if d²y/dt²<0 then maximm

[tame egret]

-32t+240 = 0

so t = 240/32

[cunning marten]

Ok disdn’t see that

[tame egret]

t = 7.5

[cunning marten]

Good bro

[tame egret]

thanks

[cunning marten]

Tho i dont know differentiation yet

[tame egret]

differentiation?

calculus ?

[cunning marten]

Yes

I haven’t learned that yet

[tame egret]

which grade you in?

[cunning marten]

9

[tame egret]

india?

[cunning marten]

Yupp

[tame egret]

o

you'll learn that in 11 12 i think

[cunning marten]

Yes

[tame egret]

i also am in 9

[cunning marten]

I still know sone basics

[tame egret]

i follow cambridge education board

so i have these topics

[cunning marten]

U in india?

[tame egret]

bangladesh

[cunning marten]

Ohh

[versed sierra]

i am in grade 10

how am i supposed to use differentiation in my board paper

🗿 💀

[cunning marten]

😂

[versed sierra]

im dead

[cunning marten]

Got an idea

U plug the h in the t function

544=16t^2 +240t +544

[versed sierra]

then we are alr taking 544 as the height no?

[cunning marten]

Yes

[versed sierra]

but we have to find out the height

how can we alr take height as 544

[cunning marten]

Hmmm

You can use some physics

Like when the fuel gets exhausted

u=240ft/s

V=0

Take g=-10

-73.152^2 = -20h

[versed sierra]

i tried using v2 - u2 = 2as

[cunning marten]

h=267.5607

So total h = 544+267.5607

Put it in equation to get T

Obviously i am talking nonsense

Because we are given that it is subjected to more forces than just gravity

[versed sierra]

i mean

i should probably use more maths here

but your way makes sense

[cunning marten]

True

😂

Bro u in 10th i am in 9th

U should be way more intelligent

[versed sierra]

only if

[cunning marten]

Wait

The max of a function is c-(b^2/4a)

Dont they teach this in X?

[versed sierra]

its in RD

not in NCERT

[cunning marten]

K

[grim skiff]

The mathematical way is that the max height occurs at the vertex of the parabola, you can apply this. Use that to find the x coord of the vertex then find the y coord and that's the max height

[cunning marten]

@grim skiff thats not in ncert

And our guy is giving board exams

So cant use that

U from Inida?

India?

[grim skiff]

I don't know what ncert is and that's that commonly learned formula for vertex and parabolas

[cunning marten]

Yeah but the grade our guy is in doesn’t teaches him it

[grim skiff]

It's so common that it's part of the quadratic formula

[versed sierra]

i dont really much options left anymore

[cunning marten]

U could ask it from ur teacher

[versed sierra]

when i find out the x and y coordinates

how do i find the height

[grim skiff]

The height is the y coord

[versed sierra]

so -b/2a here is -7.5

[grim skiff]

You applied it wrong

What is the value of a and b?

[versed sierra]

a is -16 and b is 240?

[grim skiff]

Yes

[versed sierra]

oh wait

negative sign mistake

[grim skiff]

Yes that was the mistake

[versed sierra]

(-16 x 7.5 x 7.5) + (240 x 7.5) + 544

?

[grim skiff]

Yes

[versed sierra]

1444?

[grim skiff]

Yes

[versed sierra]

damn

thanks a lot @grim skiff

and you too @cunning marten

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[low mesa]

help guys

[low mesa]

:/

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@low mesa Has your question been resolved?

[low mesa]

<@&286206848099549185>

[agile mountain]

@low mesa The British date '010299' would be read as '99-02-01' in the ISO format and '99-01-02' in the U.S. format. The largest difference here would be between 2nd January 1999 and 1st January 1970, which is indeed 29 years, 11 months, and 1 day.

Therefore, the correct answer is C: 29 years, 11 months, and 1 day.

[low mesa]

tysm

[dire osprey]

yeah

[low mesa]

one question why did u used 1970?

@agile mountain

may u give full explanation

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[torn jolt]

Men:women::5:4
Took ratio as 25:20 for convenience
40 % women unmarried then 8 unit of women un married
Unmarried women number = 30
8 unit = 30
1 unit = 30/8
Total unit of people 45
Then total number of people = 45*(30/8)
But I am getting decimal here...
Where did I go wrong??

[torn jolt]

ping me

<@&286206848099549185>

[rigid gazelle]

i can help

[torn jolt]

Ok

What did I do wrong

@rigid gazelle

[rigid gazelle]

@torn jolt lemme send you my copy

ping me

[torn jolt]

@rigid gazelle

[rigid gazelle]

Let's denote the number of men by ( M ) and the number of women by ( W ).
From point 1 we have:
W = 4/5 M
From point 2, if 40% of the men are unmarried, then 60% are married. So the number of married men is 0.6M
From point 4, we know there are 30 unmarried women.
The tricky part is to understand point 3. Half of the married women came with their husbands, which means the other half did not. Since a quarter of the married men came with their wives, it means that three-quarters did not. But since every married man who came with his wife is paired with a married woman who came with her husband, this should equal half the number of married women.
So let's denote the number of married men who came with their wives as MW (which is also the number of married women who came with their husbands).
Now we can say that:
MW = ¼ times 0.6M
MW = ½ times Number of married women
Since MW = ½ times Number of married women and MW = ¼ times 0.6M, we can set these equal to each other to find the number of married women and thus the number of married men.
Let's calculate these values
Based on the problem and the calculations:
There are 60 men at the gathering.
There are 48 women at the gathering.
So in total, there are 108 people at the gathering.

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[torn jolt]

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[torn jolt]

Two circles are concentric at M ,
AB is a chord in the greater circle and touches the smaller circle at C , if AB = 14 cm
Find: the area of the shaded part between the two circles

I have absolutely zero idea on how to solve this

[twilit leaf]

do you have a diagram?

[torn jolt]

Two circles are concentric at M ,
AB is a chord in the greater circle and touches the smaller circle at C , if AB = 14 cm
Find: the area of the shaded part between the two circles

[twilit leaf]

look at triangle AMC

how can you get the area of the part given the radii of the two circles

[torn jolt]

MA (radius of greater circle) = sqrt(MC^2 + 7^2) ,

Thereis no way to find MC

[twilit leaf]

let MC be little r and MA be big R

[torn jolt]

Okay..

[twilit leaf]

can you write CA in terms of r and R

[torn jolt]

CA² = R² - r²

[twilit leaf]

good

[torn jolt]

R² - r² = 7²

[twilit leaf]

not quite

youre missing something

ok good

how can you write the area you want in terms of r and R

[torn jolt]

@twilit leafπR² - πr²

[twilit leaf]

ok

do you see how the two things i told you to write are related

[torn jolt]

@twilit leaf
πR² - πr² = π(R² - r²) = π7² = 49π 🤯🤯

[twilit leaf]

kaboom

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[full forum]

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[brittle lance]

I just want to make 100% sure that I'm not wrong cause usually I trust the computers here

[brittle lance]

https://cdn.discordapp.com/attachments/622959200535969792/1206773011781517393/image.png?ex=65dd39f2&is=65cac4f2&hm=a1f5eb688c2ca1d97eca91d235fe504c26ac9642c5e43034ad6a9f4aa776bf6f&

[brittle lance]

WolframAlpha is high, right?

https://math.stackexchange.com/questions/232455/is-integration-from-a-to-b-same-or-b-to-a-or-is-negative

Like, wolframalpha is literally just. drunk

I wouldn't put up a question for something so simple but i almost always trust the computers so i wanna make sure the computers are dumb

[cedar hawk]

i have no clue its possible theres some weird exception that its accounting for

[brittle lance]

Yeah I typically trust the computers cause they typically know an exception that I don't know

but WolframAlpha refuses to tell me what the exception is

[languid junco]

i looked this up

Yes, there are some restrictions on when you can swap the limits of integration. One important restriction is that the integral must be convergent, meaning that it must have a finite value. Additionally, the integral must be able to be evaluated from both sets of limits, and the limits must be continuous at the point of swapping.

Reference: https://www.physicsforums.com/threads/swapping-the-limits-of-integration.344128/

idk how picky wolfram is being

they could be picky about continuity

but still shouldn't matter?

strange

[cedar hawk]

feels sort of silly to count the unbounded integral as an 'exception'

like yeah most rules of math dont work if you use infinity lmfao

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@brittle lance Has your question been resolved?

[next ocean]

I would assume this depends on how you define integration

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[torn jolt]

How can I prove $\frac{1}{1-\sin(x)}-\frac{1}{1+sin(x)}=2\tan(x)\sec(x)$

[glossy valve]

BlazeStorm81

[rare dock]

@torn jolt

[glacial pasture]

well, have you made an attempt

[torn jolt]

yes

im typing it out right now

one sec

[glacial pasture]

okie dokie

[torn jolt]

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

[glossy valve]

BlazeStorm81

[torn jolt]

ok so i changed everything to be in terms of sine and cosine ykyk

then i checked for identities and couldnt find anything so i just started experimenting which got me this:

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

[glossy valve]

BlazeStorm81

[torn jolt]

multiplied the left hand side by sine because it looked wonky and the side on the right looked good

which got me when simplified

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

[glossy valve]

BlazeStorm81

[torn jolt]

and thats as far as i got i have no idea how to proceed

lol

@glacial pasture

[glacial pasture]

theres an error here

[torn jolt]

where?

[glacial pasture]

first term numerator

[torn jolt]

how? I just multiplied 1 by 1-sin

[glacial pasture]

(1-sin)(1-sin) is not (1-sin^2)

you meant to multiply by 1+sin

for a common denominator

[torn jolt]

wait lemme foil that out

real quick

[glacial pasture]

sure

[torn jolt]

okay yeah youre right

so what should i have multiplied it by then?

[glacial pasture]

^

[torn jolt]

ohhh

youre right

so multiply both sides by (1+sin)

[glacial pasture]

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

[glossy valve]

AℤØ

[glacial pasture]

you cant multiply both sides by anything

thats not how proving identities works

[torn jolt]

oh yeah nvm youre right

i was referring to the two first fractions not the left side of the equation and the right side haha

but yeah ur right cuz u want same denominator

right?

[glacial pasture]

yeah, you want to combine the terms

[torn jolt]

and wait lemme just clarify rq

[torn jolt]

so the left fraction here was multiplied by 1 + sin and the right fraction here was multiplied by 1 - sin

to get same denominator

correct?

[glacial pasture]

by them over themselves, yes

[torn jolt]

ok that makes sense

[torn jolt]

so now that you have this what can you do here?

[glacial pasture]

what do you think

[torn jolt]

prob subtract

or turn 1-sin^2 into cos

one of those

[glacial pasture]

both

[torn jolt]

so it should look like $\frac{0}{cos}$?

[glossy valve]

BlazeStorm81

[torn jolt]

1+sin-1-sin = 0

nah somethings messed up here what am i doing wrong

does the sin become positive on the right fraction?

[haughty saddle]

multiply each side by 0

[torn jolt]

oh wait it should also be cos^2

@glacial pasture

[glacial pasture]

careful with the signs