help-38

[nova spire]

How many words of length 5 are there in total (E and E' different)?

[oblique perch]

because I got 360 +120
600 +720

whihc overall is 1800

[nova spire]

I don't understand where your 600 and 720 come from

[oblique perch]

what i emean by second part was the 5 letter overall

720 if its 5 letters for 1 E

600 if its 2 E's

for 5 letters

[nova spire]

and for no Es?

[oblique perch]

but why would we go no E's?

[nova spire]

why wouldn't we?

[oblique perch]

but that is inculded in the answer is it not?

I assumed we do a case for 1 or 2 E's since there is an E in the question. If we put a case for no E, wouldnt that mean that we are also able to include any other letter as a chance ?

because the work we did so far got us 1800

[nova spire]

ok but where are words such as CHAIV counted in your counting?

[oblique perch]

ok, now im confused haha

the asnwer is 1800 and this method led me to it

if we add another case that would make the answer higher

[nova spire]

this is an example of "wrong method and correct answer" which shouldn't be promoted

[oblique perch]

Like, the method I used wasn't exactly what you showed me.

I did for 4 letters:

[nova spire]

I think you went wrong in computing "exactly 1 E"

[oblique perch]

6C4 x 4! (this would be for 4 options availbale and 1 E)
6C5 x 5! (samwe thing)

for 2 E's:

5C4 x 4!/2!
5C3 x 5!/2!

The last part is choose 2 and 3

not 4 and 3

[nova spire]

2E is correct, it's 600

Exactly 1E is 600 too

[oblique perch]

the last one is assuming 2 E's are already in place

[nova spire]

And No E is 120

[oblique perch]

okok, so its either 2 E or no E?

[nova spire]

or 1E

0E, 1E, 2E are all three possible cases

[oblique perch]

okok

idek at this point, im getting brain fart so imma save this and come back to it to see what wactully happened

im losing it haha

thank you fo your help though

🙂

[nova spire]

no problem

Do you want me to show you both approaches?

[oblique perch]

if possible yes

then I can clear some understaidng

[nova spire]

So, What you wrote for 2E is correct

For 1E, you have to choose the other 4 letters and then order them

so 5C4*5! = 600

For 0E, you choose the 5 letters and order them, so just 5! = 120

So 600+600+120 = 1320

(and then 1320 + 480 = 1800)

Other technique :

Different words of length 5 with A C H I E V E' : 7 x 6 x 5 x 4 x 3 = 2520

Words that don't have E or E' : 5 x 4 x 3 x 2 x 1 = 120

Then words that have at least E or E' is 2400

but then we're overcounting all of those 2400 words

so it's actually 2400/2 = 1200

and so the total number is 1200 + 120 = 1320

[oblique perch]

then add 480 and boom

okok

ill write this better for myself so i understand the mechanism

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[harsh pier]

50whole3/4 kilograms of rice will be packed equally in 5whole1/2 kilograms packets FIND : how much rise will be there in 8 of packets of mass 5whole1/2

[harsh pier]

help me i cant solve this question

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[lyric kiln]

hi

[lyric kiln]

the cost of items is given by the function C(x)=10x+600

suppose the max cost is 2100

how do I find the domain and range of this

[winter rune]

c(x) = 10x + 600,

the domain is the set of all possible input values, (x values), since there is no limit on x in the function, the domain is all real numbers, or (-inf, inf)

the range is all possible output values, (y values), given that the cost must be less than or equal to 2100, set up an inequality, 10x + 600 <= 2100, solving for x will give you x <= 150, therefore the random of the function given the maximum cost would be [600, 2100]

[lyric kiln]

wait why is there a max limit?

shouldnt it be infinite the graph x=150 goes on and on

does it not

is it because of the original equatoin

[winter rune]

wdym exactly, im confused by what ur asking

[lyric kiln]

u said the range is between 600 to 2100

is that because of the original equation? because when u look at x=150 - it is infinite

[winter rune]

I mean technically it would extend to infinity, but in the context, we were given a maximum cost of 2100, thats why we have the maximum value in the range

[lyric kiln]

oh thanks so much bro

ur the man

[winter rune]

x = 150 is the maximum quantity that can be produced given the constraint of 2100, beyond that itd go beryond the limit

ye

np

[lyric kiln]

wait bro

what would the domain be then

would it just be 150?

[winter rune]

you're right, the domain would be (0, 150), in a mathematical context, it is infinity, but since you have a limit of 2100

my bad, just was writing

didnt realize, good catch

[0, 150]*

[lyric kiln]

wait why would the domain be 0, 150 if x=150 only

doesnt it just go straight up with nothing ont the sides

[lyric kiln]

It was right, but how??

[winter rune]

because X is just the maximum amount of items that can be inputted in the function that'll reach the limit of 2100

[lyric kiln]

ohhh

[winter rune]

assuming you cannot have negatives, 0, 150 would become the domain

[lyric kiln]

so 0-150 is the maximum

[winter rune]

yes

[lyric kiln]

so if we didnt have the context we really wouldnt know right

if we were given strcitly x=150

[winter rune]

if you didnt have the context, you wouldnt really know, itd have to be (-inf, inf) because all x values could work, because there is no defined limit

i mean if you were given strictly x = 150 then yeah, itd just be 150 if thats what you meant

[lyric kiln]

yeah thats what I meant, thanks a lot bro

[winter rune]

sorry im very bad at explaining

[lyric kiln]

I didnt realize the importance of context

[winter rune]

yeah no problem

[lyric kiln]

nah ur way better than a lot of people on here

[winter rune]

yeah gotta pay attention to what they ask and whatnot, otherwise you make big mistakes

[lyric kiln]

have no idea how much I appreciate you

[winter rune]

tyty, hope that helped

[lyric kiln]

sure did

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[lyric kiln]

h

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[silent kiln]

idk whats wrong

[dry holly]

that should be right

[twilit dome]

is f(x) given?

[dry holly]

considering ff(x) is the given function

your domain is right

[night zodiac]

What's your f(x) equation?

[twilit dome]

it says "find ff(x)" which kinda implies that ff(x) isn't given

[silent kiln]

why does that matter? i have f(f(x)) above and it asked for the domain for f(f(x))?

does it also have to be within the domain of f(x)?

[twilit dome]

if I have f(x) = x^2 and g(x) = sqrt(x), we would say fg(x) = x, even though f(g(x)) is actually only defined for nonnegative x

[silent kiln]

ahh okay thank you

I get it

[night zodiac]

Because if f(x) had a restricted domain, you still need to include that

[silent kiln]

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[waxen forge]

help

[waxen forge]

idk

pls

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[waxen forge]

or this pls

xd

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[proper wigeon]

How does this problem work?

[zinc ginkgo]

Factor the numerator

Oh you did

[dull temple]

factoring is how you'd do it algebraically

[proper wigeon]

oh wait

im so dunb

how did i not see that

im sorry

im just wondering how to do the graph part

table******waoidhwaiodhawiodhawoid

[dull temple]

you just pick numbers close to -3

getting closer and closer

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[wraith hinge]

factorize the expression: 32x^2 - 4x . which i did heres what i did: 2 * 2 * 4 * 2 * x * x - 2 * 2 * x
but what do i do now?
how do i subtract them

[scenic mango]

32x^2 is the same as x * 8 * 4x

Do you see anything they have in common?

[wraith hinge]

WHAT

oh

well 8 times 4 is 32

[scenic mango]

Shocking, right

[wraith hinge]

but isnt factoring all about getting the lowest number possible

you can divide 8 by to

and get 4

and divide 4 by 2

[scenic mango]

To the factor, a number means to break it up into numbers that can be multiplied to get the original number

[wraith hinge]

oh

but

[dark summit]

what is going on here

when you factorize a function you get the lowest possible x forms

the answer is 4x(8x - 1)

try to separate out the x^2

[wraith hinge]

wha

why

[dark summit]

O_O

because it whats the question is asking you to do

[wraith hinge]

BUT

isnt what i did correct

[dark summit]

not even close

[wraith hinge]

but isnt there differnet methods to do it

[dark summit]

yes, try to separate out the x^2 terms, factor the x terms to the lowest form

[scenic mango]

What you did was prime factorisation, not really what you're supposed to

[wraith hinge]

oh

what about this? 2x(4x+3)-x(2x+4)

wait

i think i can do this

gimme a minute

nvm

i have no idea how i would do this

not when theres abstraction in the paranthes

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[remote thistle]

For this one it might help if you draw a picture, but you have a line segement RT and a midpoint S. If S is halfway between RT, then you can get the distance between R and S (in both x and y) and use that to find T

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[wraith hinge]

need help figuring out a formula

[cyan zinc]

Not enough info

[stoic iron]

^ what are you suposed to be doing?

[wraith hinge]

what is the formula of this

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[oblique perch]

I have been stuck on this for a while. I tried to understand what was going on the quesito itself and looked up stuff, but Im confused quite a bit

Like, 4c is the previous question, 6d is based off of it. And It really confused me

Orignially, I used pascals identity to get the answer for 4c

(n-m+1)C(m) was my answer I think for 4c

<@&286206848099549185>

<@&286206848099549185>

If someone could help expalin thst would be great

<@&286206848099549185>

The struggle is real

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[oblique perch]

not yet

srtill waiting

<@&286206848099549185>

[oblique perch]

Anyone 😦

<@&286206848099549185>

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[oblique perch]

<@&286206848099549185>

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[dire citrus]

Can anyone help me

[dire citrus]

With easy geometry

[plush yew]

send question

[lethal anvil]

hi feel free to post the problem and tell us where you're stuck

[dire citrus]

I'm doing these sorts of questions, I kind of know how to do them however not too well. Is there anything I should remember when doing them

[wraith hinge]

I would say just makesure to really understand what your doing and memorize stuff cause it will help in higher math after geometry if you can remember how the angles work if you know what i mean.

[dire citrus]

Ok, thanks. Also what is the method when solving 3e

Without a protractor

[night zodiac]

There's a hint

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[knotty glacier]

How do I write these in interval notation? I only need to do 51 and 53

[chilly cloak]

51. (-2, -1]

( is exclusive

[ inclusive

for infinity use inf)

[knotty glacier]

Oh I get the open circle is a ( and the closed circle is a ]

So 53 would be ( inf , 4]

[chilly cloak]

-inf

but yeah

[knotty glacier]

Oh right

Thank you 🙂

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[lusty thorn]

!status

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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

[lusty thorn]

To show that they are equivalent, show that both imply each other

[lusty thorn]

To show that they are not equivalent, find m, n such that one holds, but not the other

[bright tree]

guys how do i formulate a hypothesis <@&286206848099549185>

i forgot hwhshahaha

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[lusty thorn]

please read #❓how-to-get-help

[azure pebble]

i just figured out a) but am still stuck on how to start with b)

[azure pebble]

how do i find these values

[lusty thorn]

Can you find m,n such that one of the predicates hold, but not the other

[lusty thorn]

What have you tried

Can you list some m,n that satisfy both predicates

[rocky dune]

What are you guys talking about what is hypothesis?

Can you explain

[lusty thorn]

You can read all the messages in this channel

[rocky dune]

Ok

[lusty thorn]

Starting from the currently pinned message

[rocky dune]

Ok got it

You can continue

[azure pebble]

for the first one i used the logic that if m<n is true then by logic of transendency that m<x<n will also be true

[lusty thorn]

And then if you don’t understand any of the terms at all, google them

[azure pebble]

but i don't see how it would be different

for D=Z

[lusty thorn]

What is logic of transcendency

[azure pebble]

if m<x and x<n then m<n

[lusty thorn]

D = Z means the number between them has to be an integer

[azure pebble]

and that is what A(m,n) is

[lusty thorn]

did you mean transitivity?

[azure pebble]

yes ops

[lusty thorn]

transitivity assumes that there exists such a number; you’re trying to prove that such a number exists

[azure pebble]

i got it

i used m = 1 and n = 2

thanks

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[maiden nova]

Please can someone help, what did i do wrong

[maiden nova]

the notepad is my working out

[solid kiln]

Dyssrupt

[maiden nova]

oh yeah its 225

ok so square root of 189 is 13.7477

so i put my answer as 13.74

[grave pagoda]

,calc sqrt((15)^2 - (6)^2)

[solid kiln]

Result:

13.747727084868

[maiden nova]

13.75

[grave pagoda]

yup try 75

[maiden nova]

yes got it, tysm

ok ima do my last one

thanks @grave pagoda finished!

[grave pagoda]

yay good!

yw

[maiden nova]

tyhsmm

@grave pagoda

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[worldly junco]

Yo it’s the myth the legend the one I am back

Ok so I understand the first two upper questions

I’m stuck on the trig function one

Using my calculator I got 0.004215 and I wanted to check if my calculation was right

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[molten copper]

What mode is your calculator on ?

[nova spire]

If you calculator is in degrees you have to change it to radian mode

Or convert pi/4 and pi/3 in degrees

[worldly junco]

Radian

[nova spire]

Can you show what you inputed in your calculator? Don’t forget parentheses

You can either write it or send a screenshot/picture

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[runic slate]

hi can someone help me w hw?

[runic slate]

i don't understand this

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[jaunty scarab]

You're given a few angles.
You're asked to find WHZ and WPN angles.
With that, you're asked to find x and y.
With that, you're asked a bunch other angles.

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[sage cloak]

I need help simplifying with the questions the variable h in them 🥲

[idle galleon]

I think most of them are just hidden derivatives

[sage cloak]

I just don't understand how to do it

[idle galleon]

You know what the definition of the derivative is right?

[sage cloak]

Nope I haven't learned that yet

[idle galleon]

Oh

You're using stewart calculus right?

[sage cloak]

I don't think so, the textbook is McGraw-Hill Ryerson

[idle galleon]

Ok

Have you at least learned about derivatives yet?

[sage cloak]

Not yet, I'm learning limits before derivatives

[idle galleon]

I'll see if there's any alternate way

[sage cloak]

Okay thanks 👍

[idle galleon]

Part a b and d should be solvable just by expanding and simplifying

[sage cloak]

Yeah is it like that for all of them?

[idle galleon]

I think so, it works for c too actually

E requires rationalizing the numerator though

[sage cloak]

Yeah, the only problem is that I don't remember how to simplify them through expanding and rationalizing , so I need a bit of help with that

[idle galleon]

Oh ok

Do you know about the binomial theorem?

[sage cloak]

I think I have heard of it but I don't remember

[idle galleon]

How about FOIL?

[sage cloak]

Yes I think so

[idle galleon]

So can you use that to expand them?

[sage cloak]

Yes I tried that but I don't know what to do next

[idle galleon]

What did you get?

How about let's do b first since it's the easiest

[sage cloak]

Yeah I'll try that in a bit

This is what I have so far

[idle galleon]

Can you simplify it further?

The 4 and -4 cancel out and you can factor out an h after that

[sage cloak]

So would it just be left with h-4?

Or is it h-4h?

[idle galleon]

Yes it's h-4

[sage cloak]

I see thanks

[idle galleon]

Do you need help with the other ones?

[sage cloak]

So when I divide by h, it applies to all the h's on the numerator?

[idle galleon]

Yes, because of the distributive property

[sage cloak]

I think I'll need help with c, e, and f or at least have a good idea of how to do them

[idle galleon]

We'll start with c

First focus on the numerator

You can subtract the two terms using common denominators

[sage cloak]

Does a and c look correct so far?

[lusty thorn]

for a, you need to check the third step

you only divided h^3 by h, not the other terms

[sage cloak]

Oh right, I didn't see that 😅

Is c correct though?

But I don't know what to do after those steps for c

[idle galleon]

What did you get for c?

[sage cloak]

Well I don't really know what to do after that step and I don't really know what to do after that step

[idle galleon]

I believe you got h^2+12h+48 after simplification?

[sage cloak]

Oh yes, I got 48 as my answer

[idle galleon]

Ok that's good

[sage cloak]

I was talking about question c, which is the one with the fractions

[idle galleon]

Yes I know

Let's move on to e since f is similar

[sage cloak]

Okay let me try that right now

[sage cloak]

For e, do I have to rationalize the numerator first?

[idle galleon]

I think that's the intended solution

Your textbook should have an example using this method

[sage cloak]

Yeah it does but it doesn't have an example with fractions

[idle galleon]

Ok

Here's an example

Typing...

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

[sage cloak]

Then how do I solve the rest of the problem after this step?

[idle galleon]

In the example I gave you should proceed by dividing the numerator and denominator by x so that you don't get a 0/0

[sage cloak]

I see, then I just plug in the number to find the limit?

I think I just got it now

I just need a bit of help with the fractions one and I'll be done, thanks for the help so far

[idle galleon]

You mean part f?

[sage cloak]

Yes

[idle galleon]

It's pretty much the same as c

First focus on the numerator

And then subtract the terms

[sage cloak]

Well I didn't quite get c as well

I was stuck on one of the steps and I didn't know what to do next

[idle galleon]

Oh yeah I forgot

Just use the property (a/b)/c=a/(bc) and then expand the numerator

[sage cloak]

Is it like this?

[idle galleon]

Yes

[sage cloak]

I see, yeah I have to get more used to using that

I'm on part f now and I'm stuck on what to do after this step

[idle galleon]

Try repeating the steps I described above

[sage cloak]

Should I expand (2+h)^2?

[idle galleon]

Yes

[sage cloak]

I expanded it but I'm not sure what to do next

[idle galleon]

What did you get for the numerator?

Try factoring out an h term

[sage cloak]

This is what I got but I'm not sure if it's correct

[idle galleon]

I'll check real quick

Yes that's correct

[sage cloak]

Thanks a lot

😊

I do need more help with other questions but I'll ask a bit later, I'm good for now

[idle galleon]

Ok, I got to go to sleep in a bit though

[sage cloak]

Good night, I could just send the questions here but I won't be able to respond for about an hour or so

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[trim jolt]

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

[desert ice]

How did we do a ratio test on this

I wasn't done writing my question 💀

So I solved basically 90% of the question

[molten comet]

I realized after "user typing" sorry my bad 😅

[desert ice]

And got to this point

Lol its fine

And its been such a long time since I've done calculus that I'm getting confused by ratio test

First of all we should do a ratio test on this right?

[molten comet]

Ratio tests were to determine whether an infinite series converge or diverge... from what I remember

[desert ice]

Yeah

lim t->0 so

hmm

We just have to know which of denominator/numerator is bigger

right

Since t and (-1)^n term is the same

We dont have to compare them

So if the 1/(2n!-(2n+1)!) is bigger than 1/(2n+1)!

The whole thing diverges

Am I correct?

anyone..

[winged hinge]

hm

I think it'd be easier to just do the ratio test on each of the terms 1/2n! And 1/(2n + 1)! Separately

oh wait

What are you trying to show exactly

Just that it absolutely converges or not?

Or are you tryna find the value of the limit as t goes to 0?

@desert ice

[desert ice]

limit

@winged hinge

as t goes to 0

And the numerator and denominator are each maclaurin series

That I generalized into that form

[winged hinge]

Oic

Well I really don't see how ratio test helps u here

That just tells u whether or not a series is absolutely convergent

So probably don't wanna do a ratio test

Heck you probably don't even want to write (cos(t) - sin(t)) /sin(t) in terms of the McLaurin series

Honestly I'm surprised you remembered these things but not how to find the limit of this :p

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@desert ice Has your question been resolved?

[desert ice]

No the question specified

No lhopital, just mclaurin

That's why

[winged hinge]

L'hôpital wouldn't help tho wot

[desert ice]

Then what do I have to do?

How do I evaluate that

I have no idea

[winged hinge]

I've no idea why the problem is asking for you to use mclaurin

Well the limit doesn't actually exist for starters

Even in the sense of going to infinity or negative infinity

It goes to both

[desert ice]

lim t

[winged hinge]

Oh

[desert ice]

Original q btw

[winged hinge]

OK ic

Well now for starters you wrote the bottom wrong

says t - sint not tsint

As for the top I missed the t in cost actually haha

[desert ice]

That is what I wrote tho

I don't even know if I mentioned the original problem but

anyways

I do think I converted that into mclaurin series without errors to

[winged hinge]

Where's the standalone t?

yeah you did that right

[desert ice]

I already accounted for that

[desert ice]

that's why we got this denominator right here

[winged hinge]

Even if you decided to cancel out the t from the num and denom it should still be 1 minus something

[desert ice]

What

No

t-sint

[winged hinge]

Yeah I was wondering if you decided to write t(1 - sint) instead and cancel out the t that way

[desert ice]

sint starts out with t+t^3/t or something

[winged hinge]

Then wheeeeeeere is the t

[desert ice]

which means

[winged hinge]

Oh

[desert ice]

-t from there

..............

[winged hinge]

Bet

[desert ice]

Anyways I'm already over with that step

[winged hinge]

Wait not bet

Youe index is written incorrectly

If the t cancels out then it should start at 1

[desert ice]

What..?

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[winged hinge]

yeah cus were starting from t^3

[desert ice]

Yeah

[winged hinge]

So it should start at n = 1

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[desert ice]

No

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[desert ice]

n=0 cause

-1^0

starts out positive

t-(t-t^3/3! . . . )

[winged hinge]

And make it (-1)^(n + 1) instead then it's fine

Yeah but you canceled out the t

[desert ice]

Yeah

So the first term is positive

-1^0= 1

so the first term is positive

[winged hinge]

but you have t^(2n + 1)

So the first term will be t

Which you said you canceled out

[desert ice]

Ok the t^2n and the numerator

Should also be t^2n

[winged hinge]

I think your numerator's fine

[desert ice]

hmm ok

[winged hinge]

now hmmm let me first cheat with l'hôpitals to see what the answer is lol

OK so we're supposed to get 0 I think

OK so all I got so far is the factorial difference part of the numerator can be rewritten as 2n/(2n+1)!

Cus you have that it equals ((2n + 1)! - 2n!)/((2n + 1)!(2nl!))

Which is 2n!(2n +1 - 1)/((2n + 1)!(2n!))

rechecked and limit is actually -2 p sure about it this time

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[desert ice]

Hmm how does this become -2..?

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[winged hinge]

Well on the bottom you have - sum_(n =1)^(infty)(-1)^nt^(2n + 1)/(2n + 1)! Sooooo I'm thinking you can factor out the 2 and somehow the remaining sum on the top cancels out with this but I dunno what function gives that mclauren series yet 🙃

Or at the very least that it's a function such that its limit as t goes to 0 with respect to this is 1

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[cosmic gate]

,rotate

[cosmic gate]

I know this is a phys question, but hopefully it should be fine 😁

My guess is that it is c purely off the linear torque formula T=FD

But I don’t think that linear torque applies here

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[cosmic gate]

<@&286206848099549185>

[woeful cobalt]

my guess is C too

[woeful cobalt]

whys that?

[cosmic gate]

Cause there’s angular velocity

[subtle mango]

would it be a?

since the torque can be maximied with the same amount of force then?

[cosmic gate]

Woah

I’m confused

[subtle mango]

like t=f*d

a fatter handle increases the radii

thus we can use the same amount of force to get a larger torque

[wraith hinge]

Yup sure it's a

Coz the torque should be along the middle axis not the end of screwdriver

So the radius is directly proportional to torque

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[trim jolt]

@wide charm Has your question been resolved?

[wide charm]

How to do this question?

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[grand pilot]

I set the elements from r(t) to be in the parabolid

and it simplifies down to t(2t+5)

t = 0, t = -5/2

then i plug back in r(t) why isnt this correct?

i see where i messed up.

.close

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[flat wing]

Does anyone know if this is right

[knotty locust]

Undo your substitution to complete the problem

And don’t forget plus C

[flat wing]

Ty

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[cunning cairn]

hey everyone. I am trying to determine the MLE for the parameter p for the geometric distribution. Unfortunately I am struggling therefore I'd appreciate some help a lot !
What I got so far is in the picture.
I dont even know if what I am doing is correct. I follow the instructions in my book but somehow I feel like I am doing it wrong as I am not really understanding what exactly I am doing. Maybe someone could help me understand it better by providing some guidance. Thank you !

[cunning cairn]

t is the estimator

the next step according to my book would be to determine the log - likelyhood function, which I tried to do in the second picture right here

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[daring brook]

P(A) = 1 − P(A^c) is always true right

[daring brook]

given P(A) cannot be 0

[knotty locust]

well if P(A)=0 then P(A^c)=1

[daring brook]

so its true even if P(A) is 0

[steep patio]

yes

[daring brook]

so its always true

ok thx

P(A U B) = P(A) + P(B) is always true if A and B are mutually exclusive

right

im like 90% sure

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[silk gust]

I been stuck on this page

[nimble stone]

isnt that a page of solutions or am i missing something

[silk gust]

Trynna find the correct answer for each problem and find the error

[nimble stone]

have you checked through any?

[silk gust]

I try to

But I don’t get it

Like my first day of real math and the teacher

Is like

Can’t understand

[nimble stone]

if youre looking for errors you have to look for two things for each line of work: what were they trying to do, and what did they end up with

for example

if you look at karens work

on the second line it has 14x-14
to me this shows they were multiplying by 7 to try turn the 2/7x into 2x

however they made 2/7x into 14x by mistake

which is a multiplication of 7^2, while everything else is multiplied by just 7

[nimble stone]

if you look carefully with this in mind, you should be okay. Just see what they tried to do and check if it was done properly at each step

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[astral merlin]

Completing the square, i think I messed up the signs somewhere

[nimble stone]

second line is an issue

also, should f(x)=x^2+12x-5

[surreal summit]

Ummmm

[astral merlin]

Ohh

[nimble stone]

if so then the second line is -[x^2-12x]-5
then -[(x-6)^2-(-6)^2]-5

[astral merlin]

okay let me rewrite and try it over

No wait

If you are factoring out the -1

Wouldn't that make it -12

[nimble stone]

i wrote -12x?

[astral merlin]

Isn't that what you said here

Maybe I didn't understand

[nimble stone]

i was asking if thats what f(x) is supposed to be (i did miss the - on the x^2 though)

its because you wrote f(x)=-x^2+12-5

[nimble stone]

this is when i factor the -1

[astral merlin]

This is correct

[nimble stone]

really?

[astral merlin]

Right

[nimble stone]

you cant complete the square on this

thats just f(x)=-x^2+7

[astral merlin]

I don't understand

[nimble stone]

are you saying f(x)=-x^2+12-5

rather than f(x)=-x^2+12x-5

[astral merlin]

Its question D)

[nimble stone]

so this

[nimble stone]

then this follows

[astral merlin]

Yes

[astral merlin]

Okay

So when youre moving it outside the bracket it would be +36

-5

[nimble stone]

it would

[astral merlin]

You used a different method

[nimble stone]

?

[astral merlin]

They way im learning it, you take the negative sign from the -12x and use the (-6²)

[nimble stone]

thats what ive done?

x^2-12x -> (x-6)^2-(-6)^2

[astral merlin]

So would it not be this

Or would it be positive because

Of the two négatives

[nimble stone]

thats the answer

its just your method doesnt make sense since you wrote the function wrong at the start

you wrote -x^2+12-5 and you never corrected the 12 to 12x

[astral merlin]

But that's a bit confusing because the of the negative sign and the -6

[nimble stone]

i get how your method works
you create a quadratic thats has one root

if i do it your way:

f(x)=-x^2+12x-5
=-[x^2-12x]-5
=-[x^2-12x+(-6)^2-(-6)^2]-5
=-[x^2-12x+36-36]-5
=-[x^2-12x+36]-5+36
=-[(x-6)^2]+31

when you pull the -36 out it becomes -(-36)=+36

[astral merlin]

I think I went wrong because i didn't square the 6

Which would've made it positive

I just stuck in the negative 6

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[tepid trench]

5

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Please don't occupy multiple help channels.

[neat vine]

!onechannel

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Please stick to your channel.

[knotty locust]

.close

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[uneven eagle]

what is this exactly

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[dreamy tinsel]

no you count because not everything is multiplied by eachother

*cant

but one part on the top is addition and therefore you can't

[night zodiac]

$\frac{a + b}{a} \neq b$

[solid kiln]

dldh06

[night zodiac]

You can't cancel across addition and subtraction like that

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[patent whale]

Is someone able to explain to me how I can form a 3-degree polynomial with the following properties?

• has 3 complex roots
• each root has a modulus greater than 2
• only has complex coefficients

[patent whale]

So far, what I have tried to do is pick 3 complex numbers

z=1+2i
z=2-2i
z=0+3i

and then use those as the roots to form a polynomial
(z-1-2i)(z-2+2i)(z-3i)=0

Expanding into the polynomial
z^3 - (3 + 3 i) z^2 + (6 + 11 i) z + (6 - 18 i) = 0

The only problem is the the first coefficient is 1, but I need it to be a complex number

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@patent whale Has your question been resolved?

[tropic smelt]

Hello. You will always get a 1 in the leading coefficient because each factor has the form (z-a)

a fast solution is to multiplu the polynomial by i 🤔

or just change z by iz in some factor

[patent whale]

I tried this, but then this changes the values of the roots and then the moduli of one of the roots is no longer greater than 2

I'm not sure if there is some trick to it

[tropic smelt]

Mmm I don't see how that could happen (?

mmm wait

,w roots of (z*i-1-2i)(z-2+2i)(z-3i)

[solid kiln]

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[tropic smelt]

,w expand (z*i-1-2i)(z-2+2i)(z-3i)

[solid kiln]

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[tropic smelt]

ok..

[tropic smelt]

these have length 3, sqrt5, 2sqrt2

Let me know if that's ok, maybe I don't understand the problem correctly

[patent whale]

Oh! I see what you mean. Sorry, I misunderstood what you said about adding i to the polynomial. I understand now, thank you!

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[lime star]

having trouble with this problem

tried a couple different ways but none of them have led to the answer. I think i am getting the wrong induction step

pls lmk

<@&286206848099549185>

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[next raptor]

Please don’t ping them before 15 mins are done

[lime star]

sry

[spring hull]

First of all why are you equating in all steps that's not what we do in a induction proof

[lime star]

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[quaint kindle]

Three students are chosen at random from the whole group

Find the probability that only one of them studies spanish

how do i approach this? 🤔

[wraith hinge]

@quaint kindle What are all the ways for only one student in a group of 3 students to study Spanish?

[quaint kindle]

study S, dont study S, dont study S

[wraith hinge]

Order does matter

Although...

[quaint kindle]

and 2 more of that

[chilly cloak]

S !S !S

!S S !S

!S !S S

[quaint kindle]

yeah

[wraith hinge]

wow

[wraith hinge]

I had a brain glitch, nevermind that

Basically in each case you have any one of the 3 students studying Spanish and the 2 remaining students not studying Spanish

The reason I phrase it like that is that the calculations basically work like that

[quaint kindle]

yeah

[wraith hinge]

@chilly cloak You seem to be an active helper, I bet I'm not the only one to think you'll join the helpers lounge soon

[wraith hinge]

@quaint kindle Speaking of which, do you have any idea at this point how we'll calculate the probability?

[chilly cloak]

what is that?

[wraith hinge]

The channel for people with the Helpful™️ role

[quaint kindle]

nope 💀

[chilly cloak]

20*10*9*3/30/29/28?

[wraith hinge]

I- what?

[quaint kindle]

what

💀

[chilly cloak]

how many ways of choosing 1 spanish person?

[quaint kindle]

3

[wraith hinge]

Oh I see...

!nosols

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[chilly cloak]

ways of choosing 1 spanish and 2 not spanish over total

[quaint kindle]

ohhh wait

is it 20/30 x 10/29 x 9/28

[quaint kindle]

then times 3

[wraith hinge]

I had another brain glitch but yes

@quaint kindle That appears to be correct

[quaint kindle]

aright

alright

[wraith hinge]

Come to think of it I could've thought of a better explanation

Dangit

Oh well...

[quaint kindle]

thanks to the both of yall 😄

[quaint kindle]

what is it

?

[chilly cloak]

ok..

[chilly cloak]

you got it

[wraith hinge]

I was thinking something like "What's the probability that one of the people in the group studies Spanish? Then what's the probability that the other 2 don't study Spanish" but TimK's explanation (though he did not get to complete it either) made more sense

[quaint kindle]

ah yeah this is def easier to understand than the previous one 🤣

thanks again to the both of you guys

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[chilly cloak]

umm, thanks

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[loud wasp]

Could someone explain this

Not sure where to start

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[serene osprey]

I think this question is either missing something or its worded badly with not that many pertinent information

If I understand the question otherwise, It's saying the baker can produce 27 pastries per day

let x be the number of loaves of bread
let y be the number of cakes

x + y = 27 for any day
x <= 4

The baker must produce at least one pastry of each type so
x >= 1
y >= 1

So they are asking what's the max number of cakes?

The max number of cakes is

maximize y given the constraints

so you can set x to 1, and then y=26

it's a very weird question IMO

[loud wasp]

Thank u very muchh

I agree with u how was I supposed to know that a cake and bread is counted as a pastry 😭😭

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[alpine jackal]

hi

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[tranquil widget]

how do i prove this

[tranquil widget]

nvm

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[weary abyss]

https://cdn.discordapp.com/attachments/1098563335173181571/1152891772977037343/image.png
How to do that

[rough pendant]

angle COD is 3 times as big as angle AOB

What do you get from that?

[weary abyss]

idk what is AOB

oh

umm

actually idk

I cant get AOB

[rough pendant]

It is written that Angle COD is 3 times as big as Angle AOB

That means, Angle COD = 3* Angle AOB

Now can you find out Angle AOB?

[weary abyss]

err let me try

[rough pendant]

👍

[weary abyss]

is COD 153

@rough pendant

[rough pendant]

Hey

Lets take it something else

[rough pendant]

We got this right?

Lets take Angle AOB as x

[weary abyss]

ye

[rough pendant]

Angle AOB + Angle BOC + Angle AOD = Angle COD

Remember AOB = x, and COD = 3x (3 AOB = COD)

Try to find out x for now

[weary abyss]

I did 90+66=156 then 360-156=204 204÷4=51 51x3=153

[rough pendant]

Why 360?

[weary abyss]

isnt 360 the full circle

[rough pendant]

No need to apply that. Follow this for now

From this, we get x + 66 + 90 = 3x

Can you find the value of x here?

[weary abyss]

wait

[weary abyss]

(90+66)÷2=1x

[rough pendant]

Yep do it

[weary abyss]

ok

[weary abyss]

So the answer is 234?

[rough pendant]

👍👍👍

Correct

[weary abyss]

thanks

[rough pendant]

You can type .close to close the channel if you are done.

[weary abyss]

ok

[weary abyss]

Can you friend me @rough pendant

.close

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[weary abyss]

.close

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[ivory sleet]

I have derived this negative log likelihood estimator of an exponential distribution parameterized around v,

I have been asked to approximate it's bias and variance using a Taylor series expansion like so:

I'm not very sure what do do here though, I understand that my estimator is a function of the sample mean of a sample drawn from the exponential distribution, but im not even sure what to subtitute into the taylor series formula

[tired ivy]

good luck!

[ivory sleet]

well actually now that i think about it, my mle is not a function of the sample mean, maybe i screwed up somewhere with the derivation?

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[ivory sleet]

i reworked it and got this expression

i mean i kind of get it but im not sure if the answer i am expecting will be a function of the mean and variance of the sampling distribution, or i will be getting an actual value like -1/2 for the bias as an example

cause i can just substitute in the derivatives into the formula and its now a function of sigma square, mu and the sample size

<@&286206848099549185>

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[torn karma]

How, for the last equation (reflected in y =6) is the it 12- f(x+1)

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[oblique egret]

two different formulas for spherical coordinates:

[oblique egret]

and

which is the correct one?

[nova spire]

both are correct, the link between them is $\vartheta = \frac{\pi}{2}-\theta$

[solid kiln]

rafilou2003

[oblique egret]

i dont understand what you mean by the link between them?

because wouldnt changing sin to cos affect the formula?

or vice versa

wait nvm

im an idiot

[oblique egret]

thanks again for the help!

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[earnest breach]

I want to get this equation in terms of x. What are some ways to do this?

[earnest breach]

idk why I'm blanking on this.
y = 4x - x^2 -> y = x(4-x)

Dividing by x doesn't help and dividing by (4-x) doesn't help

the other one is pretty straightforward. y = x^2, just take the sqrt of both and you're left with + - sqrt of y = x

[flint cedar]

can try solving the quadratic equation

x^2 - 4x + y

[earnest breach]

is there another way

like can I do completing the sqaure

I don't feel confident using the quadratic equation when I don't have a calculator.

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[earnest breach]

.close

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[molten comet]

Not sure what to do next

[left oriole]

suggestion, first deal with the possibility that a and/or b is zero, then deal with the case where neither is zero (so you can safely divide by them)

for example, in the equation
2abj = -4bj
if you knew that b was nonzero, you could divide both sides by 2bj and conclude that
a = -2

[molten comet]

Then can I sub what I got for a in the Real equation into the Imaginary equation?

[left oriole]

yep, or vice versa, depending on which equation you worked with first

[molten comet]

Okie, will try

[molten comet]

I did it until here

Is it correct?

If it is, what do I do next?

[left oriole]

yea, that looks fine

so those are the only possible solutions if b is nonzero, right?

so now just investigate what solutions exist if b is zero

[molten comet]

Like this?

None of the solutions I found are here 😢

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[left oriole]

i don't get what you did on the last two lines, starting with "when a is 4/3"

you already know that b=0 in that case

how did you get b = +/- 1.528

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[simple anvil]

hey how would i go about solving this problem?

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