help-17

[tulip nebula]

Whenever before factoring you find whether D is greater than or equal to 0 or not

If it's less than 0 then it has complex roots that is no real roots and thus can't be factored

In this case D>0

[wicked ice]

okay thats the case then since these can't be factored the GCF for these are 1

[tulip nebula]

No

These can be factored

Because D>0

Because in the format ax^2 + bx+ c, b^2-4ac which is called the D, Discriminant is greater than 0

[wicked ice]

oh i thought you were using a equal sign

[tulip nebula]

I mean, if it's equal or greater to sign then it means the quadratic expression can be factored

Lol just ask what is confusing and I'll explain that part

I mean the ultimate aim is to find the zeros and quadratic formula gives direct answer in that case

But if we can factor it out then that's easier than using Quadratic formula

It's used in both

lol

I asked this because I m not sure if he knows about Discriminant or quadratic formula as of yet

No

This is the question I repost it for you ary

Just go ahead it's public server

[wicked ice]

yeah i'm here

wassup

yup

yeah idk how you were taught it but my teacher taught me to do next is to find factors that can both be add to find 7 and multiplied to find 4

so pretty much this

[tulip nebula]

Well I've already factored it out

But my method of factoring is different from one your teacher and you use

[wicked ice]

yeah for all the real number idk why I can't finding ones that can be both placed here

i might try using the ac method

[tulip nebula]

You can write 2t^2-7t-4 as 2t^2-(8-1)t-4

2t(t-4)+1(t-4)

That's it you have factored it to (2t+1)(t-4)

The process aim is usually to substract or add two factors of the product of a and c in the factorable quadratic ax^2+bx+c

[wicked ice]

wait shouldn't these have variables?

or no since it's part of the original problem

??

[tulip nebula]

What variable

I'm confused because there is only one variable in our quadratic which is t

You can use your method to verify it but I want to tell you that my method always works

[wicked ice]

yeah the t in -7t shouldn't we put it with -8 and -1

[tulip nebula]

No I didn't use negative sign

Like in 2t^2 - 7t - 4 , we select 2 and 4, not 2 and (-4)

That's how my method works

[wicked ice]

ahh okay

[tulip nebula]

I don't know about your method

It's confusing to try knowing it

Maybe our method in essence are same

Or there is alternative method the one Ary spoke of, completion of square

But it seems that doesn't work here

[wicked ice]

yeah

[tulip nebula]

Basically you can use the resultant factors to see if your method can be used to factor the same

I alr factored it out for you

In my case I used the product of 2 and 4 which is 8 and then it's 2 factors 8 and 1, used arithmetic operation between them of +/-, to get 7

The latter part of my method is as you saw

If you're convenient with the factoring out process you can go ahead and find zeros since it should be easier after factoring

[wicked ice]

okay got you

let me get this down

[tulip nebula]

Ok

[wicked ice]

alright finally got it done

t = -1/2 and t = -4

@tulip nebula

[tulip nebula]

it's t=4 though

Not -4

That's error

[wicked ice]

okay one sec

ik it looks terrible but what you think?

[tulip nebula]

Yeah it's good

Although I don't understand your method but that's not important

[wicked ice]

i used a similiar method you said its called the ac method

[tulip nebula]

I called it middle term factorization

The motive is somewhat similar but I use it differently like I told above

At first I thought it's same method but I don't get the process you used by +- there

[wicked ice]

yeah its close but not the same

[tulip nebula]

Yeah

Anyway we get same answer so it doesn't matter

Ig the essence is same

[wicked ice]

alrighty then but what now since now I gotta use evidence to write my answer

[tulip nebula]

Lemme repost original question

Time can not be negative

So the negative answer is eliminated

So there is only one answer

[wicked ice]

alright so we have one answer which 4

[tulip nebula]

Rest is your English wording

Just explain what you did and that's your evidence or whatever

[wicked ice]

alright one sec

alright what do you think ?

[tulip nebula]

Yeah 👍

The reasoning is perfect

[wicked ice]

alr coolo

okay one more small thing

[tulip nebula]

Well

[wicked ice]

the first thing you look at factoring is just if there a GCF right?

[tulip nebula]

The first thing that comes to my mind is factors/common terms but the technical answer would be zeros ig

[wicked ice]

alright cool

and thats it we've been here for awhile and I apperciate your help a whole lot

[tulip nebula]

Well I had my fun helping you. Appreciate you for asking questions too

Now you can close the channel and goodbye

[wicked ice]

alrighty cya man

.close

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[vapid crater]

I need help, I absent yesterday and now I missed my math class I hope someone is willing to let me understand this part... how do I get the n = 10 ?

[vapid crater]

That's the only thing I don't understand 😅

[vocal sleet]

@vapid crater Has your question been resolved?

[vapid crater]

Ahh now I got it

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@vapid crater Has your question been resolved?

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[ember tapir]

how to solve without a calculator $\frac{25}{4}^\frac{-3}{2}$

[hushed pewter]

$(\frac{25}{4})^{-3/2}$

[ember tapir]

thanks

[twin meteor]

SWR

[hushed pewter]

Also, only surround math with dollars signs. e.g. $ax^2+bx+c$

[twin meteor]

SWR

Idle_Wild

[ember tapir]

that's better!

[soft walrus]

also use \left and \right to make parentheses more visually appealing

$\left(\frac{25}{4}\right)^{\frac{-3}{2}}$

[twin meteor]

XxMrFancyu2xX

[soft walrus]

is that your problem?

[ember tapir]

that's the problem yes

[halcyon quail]

finding the perimeter of a square is that finding the sum of all 4 or can i take one side and multiply by 4

P = 4s

[vocal sleet]

Please read #❓how-to-get-help

[halcyon quail]

oh my bad

[soft walrus]

how well do you know your properties of exponents?

[soft walrus]

ur good

[ember tapir]

I know them fairly well

[soft walrus]

Do you know how to deal with exponent when a fraction is being raised: $\left(\frac{m}{n}\right)^{k}$?

[twin meteor]

XxMrFancyu2xX

[ember tapir]

but I have tried to manipulate this a few times and I can't find a method of solving it, I've tried looking at websites and the approach taken suggests I'd need a calculator

[soft walrus]

for this you don't my friend

start with the fraction property

[ember tapir]

so for the exponent, the demoninator is the root-power

and the numerator is the new exponent

[soft walrus]

oh lol that's fractional exponents

[ember tapir]

the negative is 1 over

[soft walrus]

i mean this

although you are right about that

[ember tapir]

it's just m to the k divivded by n to the k?

[soft walrus]

yes $\left(\frac{m}{n}\right)^{k}=\frac{m^k}{n^k}$

[twin meteor]

XxMrFancyu2xX

[soft walrus]

Ok good you know that

so just distribute your $\frac{-3}{2}$ out to 4 and 25

[twin meteor]

XxMrFancyu2xX

[soft walrus]

To yield $\frac{4^{-\frac{3}{2}}}{25^{-\frac{3}{2}}}$

[ember tapir]

m ^ -3 / n ^ 2 ?

[twin meteor]

XxMrFancyu2xX

[ember tapir]

oh right I see

[soft walrus]

Ok so you all good there?

Now, back to your fractional exponents properties

what do you notice about 4 and 25 in particular?

[ember tapir]

so 1/8 / 1/125 ?

[soft walrus]

^

[ember tapir]

$\frac{\frac{1}{8}}{\frac{1}{125}}$

[twin meteor]

Idle_Wild

[soft walrus]

you're trying to go too fast and its messing you up

just what do you notice about 4 and 25? keep it simple

[ember tapir]

root 4 is 2 and root 25 is 5

[soft walrus]

Yes, they're both square numbers

so this fraction can be written (gimmie a sec this may take a min to type)

$\implies\frac{(2^2)^{-\frac{3}{2}}}{(5^2)^{-\frac{3}{2}}}$

[twin meteor]

XxMrFancyu2xX

[soft walrus]

right? because $2^2=4$ and $5^2=25$

[twin meteor]

XxMrFancyu2xX

[ember tapir]

ok yes, I follow

[soft walrus]

Ok, so now when we have $(m^n)^k$

[twin meteor]

XxMrFancyu2xX

[soft walrus]

what can do you do with those exponents?

[ember tapir]

multiply them

[soft walrus]

yes so what do you with $(2^2)^{-\frac{3}{2}}$?

[twin meteor]

XxMrFancyu2xX

[soft walrus]

note this is just the numerator

[ember tapir]

2^-3?

numerator

[soft walrus]

Yes! and now repeat for dinomiator

[ember tapir]

5^-3 denominator

[soft walrus]

god i spelt that word WRONG

but yes

so we have $\frac{2^{-3}}{5^{-3}}$

[twin meteor]

XxMrFancyu2xX

[soft walrus]

right?

[ember tapir]

yeah

[soft walrus]

When we have negative exponents in a fraction what can you do with them to make them not negative?

[ember tapir]

you can either flip the fraction, or put 1 over the base

[soft walrus]

Ok actually we'll just do that

so we get $\implies\frac{\frac{1}{2^{3}}}{{\frac{1}{5^{3}}}}$

[ember tapir]

oh ok

[soft walrus]

i apologize this LaTeXing is awful dont pay attention to that

[ember tapir]

no it's fine thanks, it's legible

[twin meteor]

XxMrFancyu2xX

[soft walrus]

no im saying the math was wrong lol

[ember tapir]

oh right

[soft walrus]

ok that's better

ok, so do understand how we did that?

we put the guys on the bottom

but that fraction is pretty ugly

[ember tapir]

well I'd have gone a different direction and gotten it wrong but what I notice is you're at the same point I was at earlier

[soft walrus]

Ok, so you get here no problem?

[ember tapir]

yeah I follow you, but I was thinking (1/2) ^ 3 / (1/5)^3 and I'm not sure that's the same

[soft walrus]

no, that's multiply 1/2 three times the one I posted above is 1 over 2 multiplied three times

[ember tapir]

and much earlier I said (1/8) / (1/125) following a different route and that seems to be back where we are?

[soft walrus]

which ig is the same, but when you don't have 1 in the numerator it's bad

[soft walrus]

yes ok

[ember tapir]

although no it's not is it

oh it is

oh no it isn't 1/75 right

oh no 1/125 it is

[soft walrus]

I only have like 2 mins so ill try to be quick here

[ember tapir]

ok thanks

[soft walrus]

$\frac{\frac{a}{b}}{\frac{c}{d}}\implies\frac{a}{b}\div\frac{c}{d}\implies\frac{a}{b}\cdot\frac{d}{c}\implies\frac{a\cdot d}{b\cdot c}$

[twin meteor]

XxMrFancyu2xX

[soft walrus]

i have to go now

[ember tapir]

oh I see

ok thank you very much for your help

superb

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[crisp yoke]

can someone explain to me how to do this one

[onyx totem]

!status

[vocal sleet]

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

[onyx totem]

try to go over the requirements of what makes a differentiable function

[crisp yoke]

when the limit is finite?

[onyx totem]

I'd start with 'it must be continuous'

as additional hint, it all revolves around the point at ||x=1||

It seems like you know what to do, if any help is needed please ping

[crisp yoke]

do I have to choose the values for which at the x=1 the functions are the same?

[onyx totem]

that is one criteria

continious means no empty spaces or jumps

but there is another

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@crisp yoke Has your question been resolved?

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[shy bone]

Hi, I need help with this question, thanks!

Two balls with masses of 0.2 kg and 0.4 kg collide. If the 0.2 kg ball is traveling at a speed of 5 m/s and the 0.4 kg ball is at rest, what are the velocities of the balls after the collision?

[hushed pewter]

Is the collision elastic or inelastic?

[shy bone]

It is elastic

Because the question is asking for the velocity of each ball

[hushed pewter]

There's not enough information then

[shy bone]

What about inelastic

[hushed pewter]

Wait

I forgot about energy conservation ignore me

[shy bone]

Ok

[hushed pewter]

You have two properties : conservation of momentum and conservation of energy

You have two unknowns : the final velocity of each ball

Two equations and two unknowns

[shy bone]

Do you solve each ball by using the formula v = p/m where p (momentum) is the total from ball1 and ball2

@hushed pewter

[hushed pewter]

Not sure what you mean

[shy bone]

@hushed pewter like this

.close

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[grizzled tusk]

I’m trying to do number 6

Is this right for c

And for the other ones should I use y=-x+1 and x^2+y^2=1 to substitute them all

And integrate from 0 to 1 and 0 to 1

Or do I need to use the length of the lines in any way

[vocal sleet]

@grizzled tusk Has your question been resolved?

[grizzled tusk]

<@&286206848099549185>

Please I just need help on c

The integral of x should be from 1 to zero

.close

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[formal pond]

https://byjus.com/question-answer/when-one-litre-of-water-is-added-to-a-mixture-of-acid-and-water-the/

should help

[vocal sleet]

@obsidian cliff Has your question been resolved?

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[gaunt panther]

how is the norm sqrt 69?

isnt it just the sqrt of 4^2 + 3^2

which is 5

?

[flat whale]

No

Use the information they gave you

[gaunt panther]

ah crap

yh mb

thanks

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[unreal sparrow]

Is there a digestible video that covers the topic relating to all four of these questions? I already have the answers but i don’t know how the process works

[grizzled tusk]

https://www.youtube.com/watch?v=2_6H5UE_Nkk&list=PLV_e97dP47FE0KsQwaGYpRlQ1c2cv-eiI&index=6

[unreal sparrow]

Thanks

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[light kiln]

@fluid obsidian I’m back sry

[light kiln]

Confused by this problem

So is the direction of maximum increase at a point always the gradient vector at that ppoint?

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@light kiln Has your question been resolved?

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[fluid obsidian]

Ah you

[fluid obsidian]

Yeah

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[vocal sleet]

Please don't occupy multiple help channels.

[rancid flicker]

.open

[keen umbra]

Ok I think I know how to do this

[boreal remnant]

Write out the first few terms

[keen umbra]

And see the sequence

[vocal sleet]

@wanton talon Has your question been resolved?

[wanton talon]

first few terms are 1/2, (1/2)^2, ((1/2)^2)^3?

so then it is approaching 0 as n goes to infinity

does that mean it converges ?

since its 1/2 or less always

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@wanton talon Has your question been resolved?

[wanton talon]

.close

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[untold hill]

hello!

[untold hill]

so

I'm gonna send an image

I just want to make sure I got the right answer

as in I'm not sure if what I did was correct

[fluid obsidian]

Yeah good

[untold hill]

yeah just a sec

so my biggest ifff is the (x^1)/(x^1/2)

[fluid obsidian]

Nic

[untold hill]

yes?

[fluid obsidian]

Nic

[untold hill]

that's the naem

[fluid obsidian]

No I mean that's nic

[untold hill]

I'm confused

aren't you supposed to teach me math?

[fluid obsidian]

Nic answer

[radiant yacht]

Pls help

[untold hill]

nono

[ornate ember]

Nice

[fluid obsidian]

Yeah

[untold hill]

you get you're own channel

get the fuck out of mine

[fluid obsidian]

Alright

[ornate ember]

whoah bro don't be so hostile

[untold hill]

WHATT!!à

[fluid obsidian]

Sorry but why?

[radiant yacht]

I am pls help bro

[untold hill]

my bad sounded more funny in my head

[ornate ember]

Hey friend. This channel is being used. Head to #❓how-to-get-help and open a channel

[fluid obsidian]

Yeah that's true

It sounded funny

[untold hill]

I don't think so

[untold hill]

my bad for being hostile

[fluid obsidian]

Okay

[fluid obsidian]

It's okay np

[radiant yacht]

Bro ✅ my bad😅 I can’t solve questions

[fluid obsidian]

No that's not your fault

Your mistake is to ask in the wrong channel

[untold hill]

ok

for real though

when do I get an answer

[fluid obsidian]

You already got

[untold hill]

this

wdym

[fluid obsidian]

Yes that

[untold hill]

you just repeated my name 1000 times

is that logic fine?

[fluid obsidian]

Yeah

You did it nicly

[untold hill]

OOOHHH

NICE

YOU MEANT TO SAY NICE

YOU FORGOT THE E

[radiant yacht]

O 😅 what’s correct channel then

[fluid obsidian]

Why do you think this is problem?

[untold hill]

because I've never really worked with halves in exponentiation that way before

[fluid obsidian]

I'm pretty bad at English, I apologize for any inconvenience from my end

[untold hill]

no worries

as long as you can do math and explain it, that's all we can expect from you

@radiant yacht It's here.

Just write in one of the channels your math problem and someone will come to help you

[fluid obsidian]

Are you worried about $\frac{x}{\sqrt{x}}$ being equivalent to $\sqrt{x}$ or $-\sqrt{x}$

[twin meteor]

fäf

[untold hill]

no

It just worked against my intuition

[fluid obsidian]

So what does you intuition say?

[untold hill]

it says there may be something wrong

cause with whole numbers

right?

there is like x * x * x / x * x, then it's obvious to see how the answer is = x

but with x / sqrt(x)

it's like can you just substract both exponents then?

I'm not sure what that would look like

but if you were to represent sqrt(x) as it's own variable call it c

it would be c*c = x

[fluid obsidian]

Why not?

[untold hill]

so you can just do c*c/c = c

c being the sqrt(x)

But I didn't C that before

[fluid obsidian]

You don't need to

Just keep in mind, for $x>0$ we have $\frac{x}{\sqrt{x}}= \sqrt{x}$

[twin meteor]

fäf

[untold hill]

Obviously there's a rule for it but for me this technique is just much more comprehensive

It's using something I already know to figure it out.

Anyways I think I'm good now

thanks for the help

.close

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[vast shale]

$\text{show that } p^{k+1} = \frac{1}{a+b}\begin{pmatrix}
b+a(1-a-b)^{k+1} & a-a*(1-a-b)^{k+1} \
b-b*(1-a-b)^{k+1} & a+b*(1-a-b)^{k+1}
\end{pmatrix}$

in latex

[twin meteor]

! matthewzz

[vast shale]

im on the k+1 step

in a induction proof

[vocal sleet]

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[vast shale]

.close

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[vocal sleet]

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[tall pasture]

I'm confused about (e). Workings in second screenshot.

(I did make an earlier post but it timedout)

[tall pasture]

@flat whale Hope you don't mind the ping. I saw your comment in the other channel but couldn't reply

dp=(dp/dt) dt, so dp=p' dt

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@tall pasture Has your question been resolved?

[tall pasture]

<@&286206848099549185>

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@tall pasture Has your question been resolved?

[tall pasture]

<@&286206848099549185>

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@tall pasture Has your question been resolved?

[tall pasture]

.close

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[hoary frost]

We consider the set C([a,b],R):={f:[a,b]→R| f is continuous} as a subset of the vector space B([a, b], R) of bounded functions provided with the metric induced by the supremum norm. Decide and justify whether C([a, b], R) is open.

Do you guys think the set is open or closed?

[hard atlas]

do you think its helpful if I say "open" or "closed" now?

you have to find out yourself which it is

try examples

[hoary frost]

I was think we use ε > 0 cause of the definition of open sets and all and define g(x) = f(x) + ε/2

Thinking *

As a counter example

[hard atlas]

why is that a counterexample?

[vocal sleet]

@hoary frost Has your question been resolved?

[hoary frost]

What about f(x) = 1/(x-a) with x in [a,b]

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[winged snow]

An archer can make 30 arrows in one day, or put quills on 20 arrows. How
how many arrows does he have time to make and put feathers on in one day?

[winged snow]

!status

[vocal sleet]

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

[winged snow]

1

[fluid obsidian]

How much time does he take to make one arrow and feathor it?

[dark kiln]

you can be tricky and notice that in 5 days you can make 60 arrows with all the swag

[winged snow]

yes

but i know that the answer is 12

but i dont know how to get there

[viral copper]

"all the swag"

[fluid obsidian]

You know my favorite helper from this server?

[fluid obsidian]

@winged snow

[winged snow]

yes

oh

[fluid obsidian]

What is it?

[winged snow]

1,2 hours to make an arrow

or wait

0,8333333 to make an arrow

[fluid obsidian]

You can keep it in fraction

[winged snow]

and 1,25 to put the quill on

20/24

30/24

[fluid obsidian]

Ok so time taken for one quill arrow will be equal to $\frac{20}{24}+\frac{30}{24}$

[twin meteor]

fäf

[winged snow]

yes

[fluid obsidian]

So how many can he make in 24 hours

[winged snow]

50/24?

[fluid obsidian]

That's the time taken for one arrow

[winged snow]

ah

[fluid obsidian]

Divide 24 by it

[winged snow]

wdym

[dark kiln]

i think you're doing the wrong thing

[twin meteor]

fäf

[fluid obsidian]

Really?

[dark kiln]

not really

[winged snow]

24/50/24

[dark kiln]

just, you don't get 12 if you divide it

so i assumed

[fluid obsidian]

I assumed we get the floor

[winged snow]

bro im sorry im a bit slow

[fluid obsidian]

Greatest integer less than

My man needs to sleep in 24 hours too

[winged snow]

so

[dark kiln]

you;re doing the wrong thing

[winged snow]

then how should i be doing it

[fluid obsidian]

Wait

[winged snow]

ok

[dark kiln]

you;re supposed to add 24/20 + 24/30

[winged snow]

and then?

[fluid obsidian]

Divide it by 24

[dark kiln]

then you get 2, so clearly divide 24 by that so it's actually 12

[fluid obsidian]

Yeah righ

[winged snow]

it makes no sense

what is the reasoning behind that

[dark kiln]

so my method is better in this case

[fluid obsidian]

So you wrote it wrong the thing I gave

[dark kiln]

the reasoning is you add time and you get time

[winged snow]

uhh

[fluid obsidian]

These are the wrong values

[winged snow]

ok

24/20 and 30/24

those are the right ones

[fluid obsidian]

Brah

[winged snow]

24/30

sorry

[fluid obsidian]

Ok

So add these times

To get total time to make a qill arrow

[winged snow]

yep

[fluid obsidian]

Then 24/t gives us the number of quill arrow he makes

[winged snow]

i guess thats right

but it doesnt have to be 24 i guess

it might as well be 1

[fluid obsidian]

What is "it"?

[dark kiln]

the 24 is it

it might be 1 correct

[winged snow]

a day

is "it"

24 hours

[fluid obsidian]

Yeah

[dark kiln]

then 1/20+1/30 = 1/12

[winged snow]

yea

0,833333

I GET IT

oh my goodness

thank you both

.close

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[fluid obsidian]

You're welcome ❤️

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[limber zinc]

hi

[limber zinc]

.close

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[dark jasper]

I'm stuck on how to even start this limit, need help

Without derivatives

[dusky niche]

Why without derivatives?
Looks like L'Hopital

[dark jasper]

Teacher specified he didn't want it. So idk what to do now

How to manipulate it well enough

[muted folio]

Make tan x = sin x / cos x

Then make the top part everything over cos x

so it would be sin x - sin x cos x all over cos x

or sin x(1-cosx)/cos x / x^3

so separate ite

it would be 1/ cos x times sin x / x times 1-cos x all over x^ 2

sin x / x = 1, you can search it's proof in youtube

Then use this for 1 - cos x all over x^2

Then we have 2 cos^2(x/2) all over x^2

then divide 4 on the numerator and denominator

since we want to have (x/2)^2 at denominator and the angle inside

so we have 1/2 times cos^2(x/2) all over (x/2)^2

and this would turn into (cos(x/2)/(x/2))^2

And we find the limit for cos (x/2)/ (x/2)

Change x/2 into a

so we have cos(a)/a

[muted folio]

Ah I got this part wrong, and so forth

I forgot it's 1 - cos x not 1 + cos x

mb

AH YES

You can multiply (1-cos(x))/x^2 with 1+cos(x)/1+(cosx) or its conjugate

so we have sin^2(x)/x^2 times 1/1+cosx

the sin part would become (sin(x)/x)^2 times 1/1 + cos (0)

sinx/x is just 1 and square it it's just 1 again

but 1 / 1+ cos 0 is 1/2

so in the end, we have 1 x 1 x 1/2

or 1/2

[dark jasper]

Lol

[muted folio]

@dark jasper do you get this?

[dark jasper]

Im trying to keep up

[muted folio]

Yeah just to be sure I double checked it

[dark jasper]

Here it would end up like this?

[muted folio]

yeah just divide the x^2 to the top

So x^2 would be besides cos(x)

But we don't really want the cos x

So just separate it

[dark jasper]

Yeah, just keeping up

[muted folio]

1-cos x times 1 over 1/cos x

or we will have 1 - cos(x) all over x^2 times 1/cos x

See?

[dark jasper]

Give me 1 sec

[muted folio]

Ah no

You almost had it

Put the x^2 below 1- cos x

not besides cos x

but the idea is there

[dark jasper]

Okk

I just didnt understand how to follow it up from there

What can I do with the 1-cosx/x^2?

[muted folio]

Multiply both the numerator and denominator by the conjugate of 1 - cos x

[muted folio]

Ah no need to distribute the denominator

We only need the top

Separate also the x^2 and 1 + cos x at the denominator

U also got the conjugate at the denominator wrong

[dark jasper]

Yeah, its a +

[muted folio]

Yeah

But no need to distribute it

We only want x^2 at the bottom

Just separate it by making it 1 / 1+ cos x

[muted folio]

yeah

and separate the 1+ cos x at the denominator

so the things at left times 1/1+cos x

the thins at the left side would be 1- co^2x all over x^2

1 - cos^2 x is just sin^2 x

so we will have sin^2x / x^2

Let's use the rule of exponent here

so it would become (sin x / x)^2

And we know that sin x / x = 1

so (1)^2 = 1

1 / cos 0 is 1

sin x / x is 1

so we are only left with 1 / 1+ cos 0

[dark jasper]

Ngl, you made me fell lile a math wizard rn

Ty

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[twin meteor]

fäf

[vocal sleet]

@vast shale Has your question been resolved?

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[pine pilot]

pls confirm answer

I am getting 54,600

[vocal sleet]

@pine pilot Has your question been resolved?

[pine pilot]

<@&286206848099549185>

[wraith venture]

I'm getting 54 400 right now

20*25*111 - 20*5*11

[pine pilot]

yeah thats the given answer

[pine pilot]

can I share my working

?

[wraith venture]

If you want to see what went wrong that would be easier

actually 0 _ _ is 5*5

You want to remove non 3 digit numbers, that doesn't mean numbers with no zeroes

[pine pilot]

but I also considered a third case right

with 0 0 _

that should cover this

I gues

guess*

[wraith venture]

Does it exclude 40 ?

[pine pilot]

oh yeah

got it

thnx a lot man

.close

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[gentle mason]

!help <@&286206848099549185>

[silk comet]

!15m

[vocal sleet]

Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.

[gentle mason]

[elder tundra]

Our reality is a lie

[vocal sleet]

@gentle mason Has your question been resolved?

[vocal sleet]

@gentle mason Has your question been resolved?

[vocal sleet]

@gentle mason Has your question been resolved?

[vocal sleet]

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[wraith venture]

!status

[vocal sleet]

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

[cerulean oyster]

2

I wrote it out in terms of the summation notation

[wraith venture]

by writing v = a v1 + b v2 ?

[cerulean oyster]

no the inner product of v and v1 in the summation form

[wraith venture]

sum of the xi yi ?

yeah don't do that

[cerulean oyster]

where is the x and y coming from

no

[wraith venture]

like the sum of the products of coordinates ?

[cerulean oyster]

in terms of vi and v1i

[wraith venture]

so you're trying to use coordinates

[cerulean oyster]

I guess

[wraith venture]

you may do that

I would advise you choose your basis wisely

[cerulean oyster]

Okay forget everything I

i'm doing **

how would you approach the problem

[wraith venture]

use the information given to you in the most relevant way possible

[cerulean oyster]

where does a and b come from

[wraith venture]

they exist

because v in span(v1, v2)

a, b are real numbers

[cerulean oyster]

oh i see what your saying

replace v in terms of v1 and v2

where to go from there

[wraith venture]

so what does it give ?

compute it

[cerulean oyster]

a+b<v2,v1>+ a<v1,v2>+b

[wraith venture]

you forgot the vectors outside the products

also orthonormal has 2 properties, you only used 1 yet

[cerulean oyster]

is <v2,v1> also 1

[wraith venture]

I would highly recommend you review what orthonormal means

[cerulean oyster]

all basis are orthogonal and length 1

[wraith venture]

hence, <v2, v1> = 0

[cerulean oyster]

I had to go over what dot product lol

yeah I got av1+bv2

thank you

.close

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[wraith venture]

fun fact: this is how sort of a change of basis formula in disguise

[vocal sleet]

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[blazing depot]

i forgot elementray school math 💀 , how do I do it. what the ratios gonna be in a fraxtion

[blazing depot]

or whoever answers could just send me a video i watch

cuz idk what to type

"how to cut a circle 💀 "

[signal mantle]

what are we doing tho

[warped zinc]

yeah

confused as well

[signal mantle]

you can write blue=yellow=x and red=4x

and if youre looking for how many degrees each part is just combine and divide 360 by that

[hushed pewter]

What is the problem asking you to do?

[signal mantle]

nobody knows lmao

[signal mantle]

wanna try my geometry problem

[hushed pewter]

!status

[vocal sleet]

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

[blazing depot]

I want to know the fracton of each part

like blue = 1/4?

[signal mantle]

well

[blazing depot]

yellow = 1/4?

red??

[signal mantle]

a circle has 360 degrees

blue=x
yellow=x
red=4x

blue+yellow+red=360 degrees

6x=360
x=360/6
x=60

and then you sub blue/entire circle

[blazing depot]

oh so 1/6 1/6 and blue

[signal mantle]

and yellow and then red

[blazing depot]

i mean red

4/6?

[signal mantle]

60/360 twice and then red

idk i havent calculated it but probably

[blazing depot]

kk thanks

.close

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[analog torrent]

both the answers c and e are wrong I think but the answer says it is E

[signal mantle]

they all go because theyre a happy friend group

[analog torrent]

yes surely they are why not

but maybe they are sad group and do not go

[dark kiln]

that's what it says

[hushed pewter]

What happens to Daniela if Carlo goes but Anna doesn't?

[analog torrent]

if anna goes we do not know if daniela goes because it gives us only second information

[dark kiln]

we can;t deduce anything about anyone going

basically it's a straight dependency line, Carlo needs everyone to go

[analog torrent]

but the same thing is in e choice we cannot say if bruno doesn't go Anna wont go because it just gives us the opposite information in the second info

[silk comet]

E is correct

contrapositive of statement 3 + statement 2 + contrapositive of statement 1

[analog torrent]

meaning...

[silk comet]

if P, then Q is the same as saying if not Q, then not P

[dark kiln]

my picture explains how it works, B → A means A can't go if B doesn't

all 3 statements are like this, whose going is required

[analog torrent]

why cant we say choice c

[dark kiln]

except the implication is drawn in the opposite direction usually, i complretely reversed it

[silk comet]

consider:
go: A, B
no go: C, D

this satisfies all of the stipulations

but doesn't fit your answer

hence incorrect

[dark kiln]

c says that Carlo has to go, so that Anna can go

that's not true, Anna needs Bruno and no one else

[analog torrent]

hmm that makes sense

[dark kiln]

i mean

maybe you're right actually

it's not like, c is wrong

it maybe actually true

[analog torrent]

daniela needs carlo for go but the given information is told us whether anna is going

[dark kiln]

but we can;t deduce it

[silk comet]

so it's wrong that it can be deduced

[dark kiln]

e however follows

[silk comet]

this is a direct argument that E holds

[dark kiln]

my picture answers it, i hope at least 4 people appreciate it

[analog torrent]

in your picture isn't the arrow between a and d should reversed

[silk comet]

dont think so

X -> Y means if X no go, then Y no go

[dark kiln]

yeah it's tricky

[silk comet]

you should learn what a contrapositive is

that is where some of the arrows come from in the picture

[dark kiln]

the arrow means allowing someone to go

Daniela doesn;t need Carlo

but Carlo "needs" daniela in some weird sense

[silk comet]

in the sense that C cannot go without D

[analog torrent]

so the tails telling us the condition

for the heads

[dark kiln]

yeah

[analog torrent]

okay thank you so much people

.close

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[barren dragon]

.close

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[dusty jay]

Ok so i have a question about probability, so the problem is that you shuffle a regular deck of cards with 52 cards in it and it is split into the 4 groups of 13 (hearts, clubs, diamonds and spades) and you shuffle it and draw 3 random cards, what would be the probability that at least one of them is a spade?

[regal bane]

I don't understand what you mean by "split"

[dusty jay]

as in there is 13 of each type of card

[regal bane]

An easier question:
What's the probability that you draw 3, and there is no spade?

That's (39/52)(38/51)(37/50)

Then to change that to "at least one spade":
1 - (39/52)(38/51)(37/50)

[dusty jay]

uuh you lost me, sec

ok how did you arrive at the (39/52)(38/51)(37/50)?

my original thinking was that as there is 13 cards in the 52 that are spades that makes each of the 3 draws a 25% chance of being a spade of some kind, however the problem i am having is how do i calculate the probability that atleast one would be of the 3

[vocal sleet]

@dusty jay Has your question been resolved?

[dusty jay]

well no but i figured it out on my own

[vocal sleet]

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[vocal sleet]

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[vocal sleet]

@wind dagger Has your question been resolved?

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[desert pier]

I need help with part e

for part e
i get 3x-4y=1

but im not sure if this is a textbook error

[vocal sleet]

@desert pier Has your question been resolved?

[loud walrus]

The book is correct.

[desert pier]

How

[loud walrus]

Show your work first

Did you calculate the Midpoint of AB?

If you did, you just substitute into the book answer and you'll see it's correct.

[desert pier]

Ohhhhhhhhhhh

I see now

it's working now

[loud walrus]

that's correct

[desert pier]

❤️

.close

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[sinful current]

i need help

[sinful current]

😦

[tender briar]

what part do you need help on?

[desert pier]

that's a lot of marks

[vocal sleet]

@sinful current Has your question been resolved?

[sinful current]

matrixes

[vocal sleet]

@sinful current Has your question been resolved?

[turbid forum]

basically there are 39 at first that are not spades, then there are 38 and 51 cards left, etc. its easier to calculate the probability of no spades in this question and subtract it from 1 than to do all the cases

also sorry for late response

[sinful current]

bruh

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[elfin moon]

How is it continuous?

[flat whale]

https://en.m.wikipedia.org/wiki/Thomae's_function

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[carmine kettle]

So for the matrix A im trying to find all values of t where t is invertible

I tried to get it to rref and see when the rank of t is less than 3

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@carmine kettle Has your question been resolved?

[vocal sleet]

@carmine kettle Has your question been resolved?

[elfin moon]

I didn't understand it@flat whale

[carmine kettle]

Basically trying to show for what values t the matrix A is invertible

[elfin moon]

My question is this

[carmine kettle]

Oh

You can open a new channel to avoid the mess

[strange crater]

your matrix still isn't in RREF

[carmine kettle]

isnt ref enough?

also how would I proceed there if I were to get it to RREF

[strange crater]

row echelon might be enough. to get to RREF you need any column with a leading 1 to have 0s in other rows

you could also calculate the determinant, and solve for values of t to see when det(A) = 0

[carmine kettle]

We didn't learn det yet

[strange crater]

well, go back and make sure all your row operations were done correctly

you might also want to write the augmented matrix with the identity to the right of the vertical bar, that's one way to determine a matrix inverse anyway

[carmine kettle]

( A | I ) you mean right

yea that sounds good I'll try

[strange crater]

actually I just noticed, element (3,3) should be 1 - 2t - t^2

[carmine kettle]

oh snap

ure correct

I get t =/= 1 + sqrt(2)
t =/= 1 - sqrt(2)

[strange crater]

I think you have to negate each

so t != -1 - sqrt(2), and t != -1 + sqrt(2)

[vocal sleet]

@carmine kettle Has your question been resolved?

[carmine kettle]

yeee

ure right

so that sounds good no?

I sent them negated at first but edited for whatever reason

[carmine kettle]

.close

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[verbal turtle]

If the curvature of euclidean spaces is 0, how come we can calculate curvature of curves or surfaces define in the euclidean space to have non-zero curvature?

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[odd dawn]

helo can anyone help me find the value of this

[night oriole]

i can try :D i think i might know

[odd dawn]

i have no idea where to begin

[night oriole]

well

lets start with the first bracket

whats the cube of 1?

[odd dawn]

1

[night oriole]

and 1- 1/1000 is?

[odd dawn]

999/1000

[night oriole]

yessir

theres your first backet

next bracket

cube of 2 is 8

you can either simply 8/1000 or directly subtract

[odd dawn]

oh

[night oriole]

do you want me to solve to give answers

or just explain the steps

[odd dawn]

both

[night oriole]

oh ok

so 1-8/1000

is 992/1000

[odd dawn]

yeah

[night oriole]

next backet

[odd dawn]

evetually it'll be negative right?

[night oriole]

cube of 3 is 27

[night oriole]

why?

[odd dawn]

1- 2017^3/1000

the last part

the brackets

[night oriole]

oh yea that

yea itll be negative

third bracket is 27/1000

which is 973/1000

[odd dawn]

mhmm

[night oriole]

cube of 2017 issss

uhhhh

[odd dawn]

8205738913

[night oriole]

8205738913

yes

1-8205738913/1000

if i was solving this question id turn everything into fractions of 3 d.p

so 0.999

-0.992-0.973

[odd dawn]

oh

[night oriole]

i find it easier but its not a required step

[odd dawn]

now what

[night oriole]

excuse the bad handwriting but
if you reduce the 1000 that is dividing 8205738913
you get 8205738.913

[odd dawn]

does turning the 1 into 10^3 /1000 help

[night oriole]

1-8205738.913
8205737.913

and subtracting it with the other 3 numbers should give you your answer

[odd dawn]

what

[night oriole]

?

[odd dawn]

which one

[night oriole]

i think it was 0.999-0.992-0.973-8205738.913

answer is negative

[odd dawn]

[night oriole]

and to big for me to do without something to write on

-8205739.879 according to google

[odd dawn]

oh

[night oriole]

is that the answer or is it totally off

[odd dawn]

what about this part

[night oriole]

oh its multiply

not subtracting

just multiply the 4 numbers

[odd dawn]

there are 2017 brackets supposedly

yes

there are 2017 brackets

[night oriole]

💀