help-13

[idle tusk]

hint: remember sin^2 + cos^2 = 1

(essentially the same idea as what sssssssssssvvvvvvvvvvccccccccccc suggested)

[cedar kiln]

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[obtuse coral]

For 2d I got 49/64

Am I right?

[ancient lodge]

,w 1-\frac{1+2+3+4+5}{64}

[wraith dagger]

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[ancient lodge]

[obtuse coral]

Thx sm

Also

,rotate

[obtuse coral]

I got 1/2 for 3a

@ancient lodge

Don’t think it’s right, tho

[ancient lodge]

,w \frac{\frac{1}{2}*(6+3)(6)}{54}

[wraith dagger]

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[ancient lodge]

eh seems fine to me

assuming that each pt is equally likely to be hit ofc

[obtuse coral]

Thx

Could I get some help w/ 5a as well?

@ancient lodge isn’t it, like, a lot of info?

How do I create a tree diagram?

[ancient lodge]

I have to go, but start off with the type of dog then move onto the type of bun

should be 9 branches

slightly tedious but not horrible

[obtuse coral]

Ty

[cedar kiln]

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[vast pilot]

Labelling to make it easier (Left to right -> A [4x4] , B [4x1] , C [4x1])

I'm not sure how to approach this / read it - i've tried to read it as AxB(-2xC) and that didnt work, due to B and C being unable to multiply since the rows in C don't match the columns in B.

[warm crescent]

I don't see why you can't

[vast pilot]

oh okay so you read it as AB-(2C)

[warm crescent]

first multiplication

[vast pilot]

okayy thank u

[warm crescent]

and luckily for you there is an identity matrix there

[vast pilot]

so would AB have all zeros except; a1,1 and a4,4 as 2's?

[warm crescent]

the size of AB is 4x1. If you meant $a_{11}$ and $a_{41}$ yes

[wraith dagger]

sssssssssssvvvvvvvvvvccccccccccc

[vast pilot]

yes thank u very much i get it now

😁

.close

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[knotty saffron]

With l'hopitals rule how should i rewrite it?

[runic garnet]

think about how u can have a fraction with g(x) in the numerator and f(x) in the denominator

how would u go about doing that

[knotty saffron]

f^-1

[knotty saffron]

i could bring it down with a negative power

[runic garnet]

So what does it look like as a fraction

[knotty saffron]

g(x)/f(x)^-1

Like that?

[runic garnet]

Yes, and as x goes to infinity, what does that fraction tend to?

[knotty saffron]

0

right?

[runic garnet]

how?

[knotty saffron]

becasue the numerator

is getting really big

wait

no because 0 devided by something is indeterminate

[runic garnet]

So g(x) in the numerator

as x goes to inf, what does g(x) go to

[knotty saffron]

oh so the numeratior is getting infinately large

so wouldnt it just be infinity

but its devided by 0

[runic garnet]

ok so now look at the denominator

we have (f(x))^-1

[knotty saffron]

im confusing myself lol

[runic garnet]

as x goes to infinity, what does (f(x))^-1 go to

[knotty saffron]

I mean

the function

it equals 0

so 0?

[runic garnet]

no

as x goes to infinity, what does f(x) go to

[knotty saffron]

a?

i think im confused to what your asking

were approaching a

which is an unkown

theirs a function

which we also dont know

[runic garnet]

oh wow

could barely see that

thought the ‘a’ was an infinity

[knotty saffron]

sorry that screenshot is so bad

here ill send in a new one

[runic garnet]

alr thx

[runic garnet]

ok i can see it now

hmm lets see

[knotty saffron]

okay great

for some reason my screenshots are terrible

[runic garnet]

what does it give on the drop downs

cuz i think its still the same idea as before

[knotty saffron]

Its the same on the other side too

[runic garnet]

Ok so

If we want 0/0

[knotty saffron]

are my answers that i put correct?

[knotty saffron]

yeah?

[runic garnet]

yes i believe those are right lol

nicely done

didnt even see u put in an answer

[knotty saffron]

Yeah

after reading my textbook i got a better idea

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[inland scroll]

does anyone know how to solve a laplace eqn when they have both first and second shift theorem?

[inland scroll]

the question im lookin at specifically is: L [ H(t - 8) * sin(6t - 48) * e^7t ]

[cedar kiln]

@inland scroll Has your question been resolved?

[cedar kiln]

@inland scroll Has your question been resolved?

[inland scroll]

<@&286206848099549185>

[inland scroll]

😭

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[misty maple]

Can someone help me understand why the two methods yield different answers? I understand one may be wrong but I do not understand how.

[cedar kiln]

@misty maple Has your question been resolved?

[misty maple]

<@&286206848099549185> 🙏

[cedar kiln]

@misty maple Has your question been resolved?

[shut meadow]

i think the 2nd method doesn't work due to repetition

like lets do set 1, qu a,b,c,d,e,f. in the 6C2 u could have a,b or b,c when ur 10C1 could pick set 1 c or set 1 a and that's a repeat

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[fair copper]

im doing question c rn

and i do not understand anything from the second page onwards

[shut meadow]

i think it wants you to find the gradient of the graph at 8 hours and whenever the time where the gradient is double that

[cedar kiln]

@fair copper Has your question been resolved?

[fair copper]

nah it wasnty

i figured it out tho

.close

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[coarse blaze]

Hello

[coarse blaze]

I'm having an absolute brainfart right now

Can somebody find my mistake

$\frac{(2x)^2}{(2-x)^2} = 36 \rightarrow 4x^2 = 36x^2-72x+144$

[shut meadow]

maybe directly square root everything to make the calculation easier for yourself?

[gusty forum]

72x

[wraith dagger]

dp

[shut meadow]

[coarse blaze]

$0=32x^2-72x+144 \rightarrow x = \frac{72\pm\sqrt72^2-4\times 144\times 32}{2\times 32}$

[wraith dagger]

dp

[coarse blaze]

And the discriminant is negative

[gusty forum]

although im sure its actually 144x lmao

you expanded it wrong

[coarse blaze]

however when I square root both sides I get an answer

[shut meadow]

yea -4*36 is 144

[coarse blaze]

that's it

[shut meadow]

and 4*36 is also 144

[coarse blaze]

I should sleep more :)

Thanks :)

.close

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[icy mirage]

<@&286206848099549185>

[shut meadow]

so the amount of permutations of all those is what?

*less than 8 children = 0-7 children

so try multiplying all the possibilities together

[icy mirage]

8 x 26^2 x 365?

[shut meadow]

remember february 29th?

[icy mirage]

oh 366

[shut meadow]

yes and u times all thos together

[icy mirage]

ohh i get it now ty

[shut meadow]

but wait

[icy mirage]

what

[inland wasp]

nvm

[shut meadow]

it is all of them the same

[inland wasp]

ye thats what i was thinking

[shut meadow]

so it will take some more thinking about getting everything the smae

but thats the 1st step pretty much

[icy mirage]

its 26 000 000/ # ways right

[shut meadow]

yea if it doesn't divide perfectly then round down

if it divides perfectly round down one

do u know why?

[icy mirage]

uhh wait a minute isn't it round up

[shut meadow]

no always round down cuz u can;t have 1/2 a person

it is always round down when u think about it

*for qu like these

[inland wasp]

no because if its 0.5 round up innit?

fr tho its round up

[shut meadow]

lets do an example

[inland wasp]

AHHHHHH

ok i understand g

[icy mirage]

wait but if u hv like 13 pigeons and 4 pigeon holes then u need 3*4+1 pigeonholes which is round up?

[shut meadow]

if u have 5 types of socks how many socjs do u need to randomly pick to make sure you have a pair

[icy mirage]

6

[shut meadow]

yea

2 :0

[inland wasp]

same pair or random pair?

if same then 6

if dif then 2

[shut meadow]

so how many pairs would be in 20 pairs

[inland wasp]

10

[shut meadow]

'randomly pick' make sure

bro man stop throwing maths so hard

[icy mirage]

11

[shut meadow]

...

[inland wasp]

bro

[icy mirage]

21

[shut meadow]

stop trolling u 2

[inland wasp]

wth

[inland wasp]

not troling

[shut meadow]

...

[icy mirage]

lol mb typo

[shut meadow]

ok i give up but u got the 1st step

[icy mirage]

lol ok thx

.close

[cedar kiln]

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[shut meadow]

i hope u had a calculator for this i hope

also i worked out the answer as :||10||

[cedar kiln]

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[sharp harness]

when we have an equivalence relation, do all the equivalence classes have always the same topological properties of the equivalence relation ?

[buoyant latch]

What do you mean by topological properties of an equivalence relation

[sharp harness]

like if the relation is F_sigma then all its classes will be always F_sigma

[buoyant latch]

I’m probably out of my depth soz

[sharp harness]

its ok dw

[cedar kiln]

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[cedar kiln]

@sharp harness Has your question been resolved?

[cedar kiln]

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[crimson sedge]

I will first square everything in order to convert it ti -x^2+2x+6+16-9=0 right?

[sage field]

!status

[cedar kiln]

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

[crimson sedge]

So it’d become -x^2+2x+23=0 I’m stuck here

[sage field]

Do you know how to solve a quadratic equation?

[crimson sedge]

Yep, but not this one. I usually find the second’s terms sum

[low vine]

Are you sure it's correct

[sage field]

ig there could be some mistake here

[crimson sedge]

That’s what it happened when I simplified

[unique valley]

can you show how did you do it?

its not correct

[sage field]

let me simply it

[crimson sedge]

I squared everything

In order to cancel

The root

[sage field]

there should be √x Term too

[unique valley]

show me

how you squared

[sage field]

show it

[unique valley]

im 99% you squared incorrectly

[sage field]

I guess you missed the 8√(2x+6)

In rhs

[unique valley]

also

you can ubstract 4 both sides

[crimson sedge]

???

[unique valley]

the hell

its completely wrong

[crimson sedge]

What’s the first step then?

[unique valley]

substract 4 both sides

to get sqrt(2x+6)=x-1

[sage field]

Take 4 to the RHS

Then square

[crimson sedge]

So it becomes sqrt2x+6=x-1?

[unique valley]

yes

[sage field]

Yes correct

Square it and tell us what did you got

It will be different from what you sent

[crimson sedge]

2x+6=x^2+1

[unique valley]

RHS is wrong

[sage field]

Wrong

[crimson sedge]

…..

[sage field]

There will be a -2x in rhs

[crimson sedge]

Oh

[unique valley]

(x-1)^2=(x-1)(x-1)=x^2-2x+1

[sage field]

(a+b)² = a² + b² + 2ab

[crimson sedge]

Is that the expansion?

[sage field]

Yes

[crimson sedge]

What’s rhs?

[unique valley]

yeah

[sage field]

Right hand side

[crimson sedge]

I will study that first

[unique valley]

right hand side

it really mean right side of an equation

[crimson sedge]

So do I have to study expansion here?

[unique valley]

do you know how to multiply (x-1)(x-1)?

[sage field]

Do you not know the a+b whole squared expansion?

[unique valley]

yeah it strange

[crimson sedge]

x^2-x-x+1

[sage field]

Yes

Then -x-x = -2x

[crimson sedge]

I’m still confused on the expanding part

I will study it first

[sage field]

Let me simplify the RHS for you

[crimson sedge]

Wait I will try

-x^2+2x+5=0 ?

Oh wait no

[unique valley]

no

[crimson sedge]

What am I missing here

[sage field]

Yes

[crimson sedge]

I’m confused

[sage field]

Noo

Wait

[unique valley]

its wrong

[sage field]

You didn't bring the 2x to rhs

[unique valley]

2x+6=x^2-2x+1

subtract 2x both sides

you get 6=x^2-4x+1

[unique valley]

and subtract 6

so you get x^2-4x-5

[crimson sedge]

I am so confused sorry

[sage field]

write -4x as x-5x

[sage field]

Which part confuses you?

[crimson sedge]

May I know which part I am missing

So that I can work on it

[low vine]

Can u send

[crimson sedge]

The part after squaring

[sage field]

You understand this much?

[sage field]

How did I wrote (x-1)² = x² - x - x +1?

[crimson sedge]

After expanding (x-1)^2

[sage field]

Oh

How did I wrote (x-1)² = (x-1)(x-1)?

[crimson sedge]

(x-1)^2 becomes (x-1)(x-1) when expanded and after you multiply

[sage field]

oh

[crimson sedge]

Thus x^2-x-x+1

[sage field]

Do you know 2² = 2×2?

[crimson sedge]

Yep

[sage field]

Then what's (x-1)² ?

[crimson sedge]

(x-1)(x-1)

[sage field]

This right?

[crimson sedge]

Yep

[sage field]

Then multiply x in 1st bracket to the x in 2nd bracket

Then multiply the same x with the -1 in another bracket

Same thing you do with -1 in the first bracket

[crimson sedge]

x^2-x-x+1=x^2-2x+1

[sage field]

Yes, you understand this much right?

[crimson sedge]

Yep

[sage field]

Then this should be your right hand side?

[crimson sedge]

Yep

[sage field]

Correct

Now what is our left hand side?

Write the combined equation of right and left hand side

[crimson sedge]

2x+6 but we gotta arrange them all to the right side

[sage field]

Correct

Now arrange it and tell me what did you got

[crimson sedge]

So -x^2+2x-2x+6-1=0

[unique valley]

its -2x

-x^2-2x-2x+6-1=0

[crimson sedge]

Oh wait

[sage field]

2x in lhs should be -2x in rhs right?

[unique valley]

no wait wait

you moved right to left

[crimson sedge]

But -2x here become +?

[unique valley]

so its actualyy +2x+2x

2x+6=x^2-2x+1

[sage field]

No that's correct

[unique valley]

so -x^2+2x+2x+6-1=0

[sage field]

But when you move it to the right, then -2x become +2x

[unique valley]

move to the right

its easier

[crimson sedge]

Wait let me do it again

I’m lost

Sorry guys

[sage field]

Take your time

[unique valley]

this is wrong dont lookt at it

[unique valley]

this is the right one

[crimson sedge]

Since -x-x=-2x but on the left one it’s +2x

Since it gets converted

Am I right from here?

[sage field]

Correct

Now simplify the terms with same degrees and multiply with -1 and find roots

[crimson sedge]

So -x^2+4x+5=0

what am I supposed to do now when the first coefficient is -1?

[unique valley]

its correct tho i recommend you to move terms to the side where the coefficient next to the biggest power is positive

[sage field]

Multiply all terms with -1

[unique valley]

if you dont want to deal with -1 you can multiply both sides by -1 or move every term to right side

or even factor out -1

[crimson sedge]

I’m sorry to ask this but why do I multiply -1? I feel like I need to understand so that I can counter this questions better next time

It’s not the GCF right?

[unique valley]

so the coefficient next to x^2 is positive

[sage field]

You understand that if we multiply numbers with the same number on both side then it remains same?

[unique valley]

its not needed to solve but its helpful

[crimson sedge]

Ohhh

[sage field]

Since there is 0 on the right side, so even if we multiply with the -1, it will remain 0

[crimson sedge]

So it becomes x^2-4x-5=0?

[unique valley]

yes

[sage field]

And the x² term which has the highest degrees will become positive

[sage field]

Yes

Now either factorise it or use quadratic formula

[crimson sedge]

So (x-5)(x+1)=0

[unique valley]

yes

[sage field]

Correct

[crimson sedge]

Thus x=5,x=-1

[unique valley]

yeah

[crimson sedge]

Thank you!!!

[sage field]

np

[unique valley]

important thing

[crimson sedge]

Thank you both

[unique valley]

check if those solutions are correct plugging in original equation

!

[crimson sedge]

Aight!

[sage field]

I second this

[unique valley]

beacuse inside of sqrt cant be negative

and if it would be after plugging the particular solution is not correct

[crimson sedge]

But this is a very limited question that should be answered in like a min. So it’s ok to just move on once I find the solutions in the real test right?

[sage field]

I checked it and there are no such cases

[sage field]

Yes

[unique valley]

in this example no

but they might be in other

[sage field]

But it usually takes 10 secs hardly

[crimson sedge]

Aight thanks I will close

[unique valley]

👍

[crimson sedge]

.close

[cedar kiln]

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[sage field]

Yes do take care of this

[cedar kiln]

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[sonic epoch]

How much does an average mall pay for electrical bills?

[sonic epoch]

this has been on my mind for a long time

and i need answers

[runic garnet]

maybe it'd be better to consult google.

or a Sir.

@flint plinth @royal loom thoughts?

[sonic epoch]

oh didnt even thought about that, hold on

[solid juniper]

[sonic epoch]

oh $40k lul

[sonic epoch]

ight ty

[wanton sail]

damn, is that per month?

[sonic epoch]

ya

apparently

from opera

.close

[cedar kiln]

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[runic garnet]

opera user

[sharp lotus]

https://www.sciencedirect.com/science/article/abs/pii/S019689040200167X#:~:text=The annual electricity use per,the total building electricity use

[sonic epoch]

oh i mean quora

[solid juniper]

quora

[cedar kiln]

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[tulip pecan]

how do i go about doing this question?

[coral jewel]

what have you tried

[sage field]

!status

[cedar kiln]

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

[tulip pecan]

made four cases, x => 3; x < 3; x + 4 => 0; x + 4 < 0

the answers I got don't match with the answer key though

[unique valley]

then show your work

[tulip pecan]

I don't have my phone right now buthold on

i'll type it out if i can

[unique valley]

im not sure those are cases you want to consider

[tulip pecan]

okay yeah so I took a different approach

took -4, 0 and 3 on a number line

and took the values of x in each interval

[unique valley]

first case id consider is x<-4 when both terms under the absolute are negative

[unique valley]

whats the x in this case?

[tulip pecan]

yeah I'm getting the sum of roots as -7 and the difference as 5

neither of which are in the options

gotta move on to the next interval then

[tulip pecan]

-1, -6

[unique valley]

are you sure?

[tulip pecan]

the expression becomes (-x-3)(-x-4)-6= 0

which is x^2 + 7x + 6 = 0

right?

[unique valley]

yeah

ok it is

[tulip pecan]

yeah i oughta move on to -4 < x < 0 then innit

[unique valley]

right

[tulip pecan]

which is (-x-3)(x+4)-6 = 0

yeah?

[unique valley]

yes

[tulip pecan]

yeah so i get x^2 + 7x + 18 = 0

[unique valley]

ok

[tulip pecan]

roots of which are irrational

so none of the options match for this interval either

[unique valley]

i mean determinant is negative

so yeah, skip

[tulip pecan]

yea

moving on to 0 < x < 3

[unique valley]

why 3?

why x<3?

[tulip pecan]

isn't the first term of the equation (|x| - 3) though

[unique valley]

it is but 3 isnt under absolute

value

[tulip pecan]

ah fair

[unique valley]

so you get (x-3)(x+4)-6=0

and x^2 +x-18=0

determinant is 73 right?

so its -1+-sqrt(73)/2

[tulip pecan]

yeah but which interval did we take x under though

[unique valley]

x>0

[tulip pecan]

oh okay

hold on lemme do that

[unique valley]

so your solutions are -6 and -1+sqrt(73)/2

[tulip pecan]

yeah right on

[unique valley]

-1 isnt solution here btw

beacuse interval there was x<-4

[tulip pecan]

why -6?

i'm getting [-1 + sqrt(73)]/2 and [-1 - sqrt(73)/2]

as the roots for x > 0

[unique valley]

thats the solution we got in interval x<-4

[tulip pecan]

ah okay

[unique valley]

i meant it for final solutions

[tulip pecan]

if i use these though I get the sum of roots as [0.5]

[unique valley]

wait

look

-1-sqrt(73)/2

is negative

right?

[tulip pecan]

yeah

[unique valley]

so we throw this solution out

beacuse its in interval x>0

[tulip pecan]

i see

[unique valley]

in interval x<-4 we got -1 and -6, -1 we throw out beacause x<-4

in interval -4<x<0 there are no solutions

[tulip pecan]

I see

hold on I think I really messed up the intervals by putting 3 lmao

[unique valley]

yeah lol

[tulip pecan]

so on the number line the only numbers I mark are -4 and 0 yeah?

[unique valley]

are you allowed to use calculator?

[tulip pecan]

not in exams no

[unique valley]

ok wait so

the final solutions are -6 and -1+sqrt(73)/2

and thats a and b in the question

estimate the a+b and a-b

[tulip pecan]

I see

lemme do the question again tho

with the proper intervals and such

[unique valley]

ok

[unique valley]

its supposed to be a floor function am i right?

[tulip pecan]

yeah so in -4 > x I get x = -1 , -6

[tulip pecan]

yeah pretty much

[unique valley]

yeah

[tulip pecan]

and i throw away -1 here?

[unique valley]

yes

[tulip pecan]

because it's greater than -4

alright

[unique valley]

no its less than

x < -4

so for example -5, -6 etc are less than -4

to be clear

and -3, -2, -1 etc are greater than -4

[tulip pecan]

ahhh gotcha now

[unique valley]

yeah we thorw out beacuse its greater than -4

i read it wrong

i thought you meant beacuse x is greater than -4

do you understand

sorry for confusion

[tulip pecan]

yeah i get it now

[unique valley]

ok

[tulip pecan]

no problem

okay for 0 < x i get x = [+- sqrt(73) -1]/2

we throw away the negative value because it's less than 0

[unique valley]

yes

[tulip pecan]

okay so that leaves us with -6 and [sqrt(73)-1]/2

alright

[unique valley]

yeah

sqrt(73) is between 8 and 9

if you cant use calculator i think its important to know

[tulip pecan]

yeah I took it as 8.5

[tulip pecan]

yeah cus *^2 is 64 and 9^2 is 81

[unique valley]

yes

[tulip pecan]

yeah so [alpha + beta] gives [2.25]

as per my calculations

which isn't in the options

[unique valley]

you sure?

its (-12+8.5-1)/2

[tulip pecan]

yeah das what i did

(-13+8.5)/2

[unique valley]

so its -2,25 right?

[tulip pecan]

oh shoot yeah

mb lmao

which is -3

[unique valley]

i think its 2

under this function

[tulip pecan]

-2

shouldn't be -3 nah

[unique valley]

the function is called "the greatest integer"

-2 is greater than -3

[tulip pecan]

the greatest integer nearest to -2.25 would be -2 no

yeah

[unique valley]

it is

[tulip pecan]

yeah so we lock option B?

[unique valley]

lets check a-b first

depending how much time you have on exam im recomending to check other options

[tulip pecan]

[a-b] is [-9.75]

which would be -9 right

[tulip pecan]

yeah thats the thing

its not that this process in particular isn't valid

its just really time taking lmao

yeah but anyway I'm getting options B and D

[unique valley]

wait

a<b

need to check for that

if we are subtracting its important

[tulip pecan]

oops

[unique valley]

to know if its -9 or 9

[tulip pecan]

yeah that flew past my head entirely

that part

yeah aight

[unique valley]

but -6 is a

so its valid

[tulip pecan]

oh alr

huh

the answer key says its A and C

whereas I got B and D

[unique valley]

so maybe we didnt understand what this function meant 😭

[tulip pecan]

yeah 💀

gahdamn

[unique valley]

its really strange they didnt call it floor or ceiling function

[tulip pecan]

yeah thats what i hear all the time too

[unique valley]

ok

i googled

and as im reading you can call floor function as "greatest integer function"

and it really give -3 and -10 for our answers

as i checked

[tulip pecan]

ohhh

[unique valley]

dont worry i got confused too

[tulip pecan]

isn't -2.25 nearer to -2 than it is to -3 though

[unique valley]

its not really about being nearby

[tulip pecan]

oh right

[unique valley]

also we just approximated sqrt(73)=8.5

and we really just sure its between 8 and 9

so its not -2.25 but -2.someting

[tulip pecan]

ah okay

[unique valley]

but as isaid its not really amter

[tulip pecan]

we're still getting -3 and -10 even if we take sqrt(73) as 8.5 though

[tulip pecan]

yeah

i got it now

[unique valley]

floor(-2.0001) would give you still -3

[tulip pecan]

it all just boils down to the definition of the floor function lmao

[tulip pecan]

yeahh

[unique valley]

yes yes

[tulip pecan]

aight that helps a ton thanks a bunch man

[unique valley]

np

glad i helped

[tulip pecan]

.close

[cedar kiln]

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[fathom star]

Im not sure if im looking over something in my notes

Im not seeing any identities that match

[hollow trail]

do you have anything on power reduction identities?

[fathom star]

OK, so was wondering about that, but wasnt sure how the 8 gets transfered

[hollow trail]

you can rewrite as 8(cos²x) then distribute the 8 afterward

[mighty shuttle]

I'd suggest they don't, the identity involves 2cos^2(x)

[fathom star]

so 8+8cos2x / 2

[hollow trail]

yes, (needs more parentheses), now you can simplify a bit further

[fathom star]

4+4cos(2x)

[fathom star]

I think I got it but curious what you mean

[rich field]

4*(2 cos²x - 1 + 1)

i think he means this

[fathom star]

Hm, alright then. So quotient identity variant im guessing? Not sure how that get me to the answers provided, but also guessing its something above my level as well.

[rich field]

do you remember the formula for cos 2x?

[rich field]

you can substitute that here

and get the same answer

[fathom star]

cos(2x) = 2cos^2x - 1. so times 4 is the 4cos(2x) idk that i completely understand the + 1 part. Like it makes sense with the multiple choice, but not how you end up with it if that makes sense

[rich field]

so the question is 8cos²x
the options have cos 2x
so to use the identity of cos 2x i did
8cos²x
=> 4*(2cos²x)
this kinda looks like the identity its just missing -1
so i add and subtract 1
=> 4*(2cos²x-1 +1)
then u can substitute the identity and get
=> 4cos 2x + 4

adding and subtracting the same thing doesnt change the expression

[cedar kiln]

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[cedar kiln]

@obsidian elm Has your question been resolved?

[cedar kiln]

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[turbid ether]

Determine the value of k for which the function f(x)=4x^2-3x+2kx+1 has two zeros. Check these values in the original equation

[turbid ether]

Any idea how to solve

[dusty hazel]

Do you know what the discriminant is

[mighty shuttle]

D>0, if you know discriminants

[turbid ether]

Yeah b^2-4ac

[dusty hazel]

Then this

[turbid ether]

Wait but what do I do with the discrimination

Discriminate

Do I put -3 + 2k for b?

Ok I ended up with 4k^2 -12k-5

Now quadratic formula?

[cedar kiln]

@turbid ether Has your question been resolved?

[cedar kiln]

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[winged marsh]

hi im not sure what to do here?

[winged marsh]

i tried to find the time when it's traveled 5m vertically

[void glen]

the 5 should be negative since we are traveling 5m downwards, and you used downwards as negative

[winged marsh]

o right thanks

.chlose

.chlose

wtf

.close

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[cedar kiln]

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[vagrant sail]

ok

[vagrant sail]

so

i need to solve a parametric i believe

all i know is velocity angle and time

time is 150

velocity is 53.358m/s

angle is 20

i dont know what to do with this

the formula give

given*

was

X=velocitytcos(angle)

he says im really close with 3266.16639814

[cedar kiln]

@vagrant sail Has your question been resolved?

[polar bone]

radians or degrees?

i believe thats probably the problem

[undone epoch]

Probably missing rounding the answer up.

[cedar kiln]

@vagrant sail Has your question been resolved?

[cedar kiln]

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[long arrow]

similarity

all these three triangles are similar to each other

set some ratios

ah wait

There's simpler way

Just use area of the triangle...

[cosmic steppe]

Geometric mean theorem

[long arrow]

and that's sufficient

[brittle terrace]

BC will be the base

BC

[old notch]

or you could use sin cos and tan

[wraith dagger]

Couldn't find an attached image in the last 10 messages.

Mar 26, 2024, 8:25 PM

[cedar kiln]

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[sonic musk]

in question B here, is this even true? because i am not getting (a, p)=0 or (b,p)=0 (which im trying to calculate to see if they lie orthogonally)

[main needle]

p is the vector inside V so it's a combination of a and b

[sonic musk]

yeah, p is 0.5a + 0.5b

[main needle]

so the dot products are positive yea

the normal vector would be axb

[sonic musk]

yes, but if the products are positive, then they cant lie orthogonally, wich means that p is not a projection of y onto V right?

[sonic musk]

wait no, I am supposed to do (a, (y-p))=0 and (b,(y-p))=0 right?

[main needle]

oh right yea

it's the difference that's normal

[sonic musk]

ah thank you very much, have a good one

.close

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[crimson sedge]

how do i write this in simplest form

[crimson sedge]

i did a ² + 2ab + b ² = (a+b ). (a+b)

[runic garnet]

now factor everything else

[crimson sedge]

then used one of the (a+b)s to get rid of the left one

the one on the left

but i cant do the rest

[runic garnet]

a^2 - ab + a - b

whats the greatest common factor of the first 2 terms

[crimson sedge]

a

?

a(a-b) + a -b . a + b
-----
a(a+b) + a +b

is it like this

[runic garnet]

well u got the a(a-b) correct

so we have a(a-b) + a - b

now whats the gcf from the last 2 terms

[crimson sedge]

a - b

wait aaa

[crimson sedge]

a + b

a(a+b) + a +b
?

u talking about that

[runic garnet]

no

ok look

a(a-b) + a - b

[crimson sedge]

yes

[runic garnet]

now look at the a-b part

whats the greatest common factor of that

[crimson sedge]

a-b

[runic garnet]

well, i meant, what is the greatest common factor between a and b

[crimson sedge]

a

[runic garnet]

a is not a factor of b

[crimson sedge]

sorry my english is bad

1?

[runic garnet]

yes

[crimson sedge]

oh

[runic garnet]

so we can write it as

a(a-b) + 1(a - b)

now we can group the terms

[crimson sedge]

ohhh

[runic garnet]

when we group the terms together, we get?

[crimson sedge]

a-b(a + 1)

[runic garnet]

u need parentheses

(a-b)(a+1)

and there u go

[crimson sedge]

oh ok

[runic garnet]

$\frac {(a-b)(a+1)}{(a+b)} \cdot \frac {(a+b)(a+b)}{(a+b)(a+1)}$

[crimson sedge]

yes

we do the same thing for the right?

a(a +b) + a + b

[runic garnet]

yes

keep going

[crimson sedge]

a(a+b) + 1(a+b)

[runic garnet]

yes

[crimson sedge]

(a+b)(a+1)

[runic garnet]

yes

[crimson sedge]

ok now we have that

[wraith dagger]

Stephen

[runic garnet]

now just cancel what u can

[crimson sedge]

a+b

both

on the left and right

idk what its called the therm on the below

[runic garnet]

denominator?

[crimson sedge]

yeah

so its (a-b)(a+1)
-------------
a+1

so its a-b

?

[runic garnet]

yes

[crimson sedge]

yes its on the options

thanks man

i think most of the math is about seeing things

do u acquire that skill by solving questions?

[runic garnet]

yes

[crimson sedge]

ok thanks so much i guess i gotta solve more questions 😅

.close

[cedar kiln]

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[crystal halo]

can someone explain to me how they got to that step in the red

[crystal halo]

im using green

[modern compass]

from your work, they didn't. What is the original question?

[crystal halo]

find interveral of convergence

and radius

here is all the work i did previous to that

this was from a tutor and he put this step after

could this be my next step

[modern compass]

looks like the red answer is wrong. that would converge at 75/32, but your series shouldn't converge there (i don't think)

[cedar kiln]

@crystal halo Has your question been resolved?

[cedar kiln]

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[pseudo trellis]

Hey, I have this problem and I'm not really sure how to solve it

[wraith dagger]

Someone

Someone

[paper pike]

That's a good start but

[wraith dagger]

Someone

[paper pike]

If you found an antiderivative g'(x) of g"(x)

Which could be like
g'(x) = -3cos(x)-2sin(x) + C

[pseudo trellis]

right

[paper pike]

You have to immediately make sure that g'(0) = -3

So g'(0) = -3cos(0)-2sin(0)+C = -3

[pseudo trellis]

yeah

so C is -3?

[paper pike]

This reveals -3 + C = -3

[pseudo trellis]

then I would do the same to g(0)?

[wraith dagger]

Someone

[pseudo trellis]

right?

I get 2 + D

so would that give me D as 3? @paper pike

[paper pike]

In conclusion
g(x) = -3 sin(x) + 2 cos(x) + 3

[pseudo trellis]

wait i'm confused

[wraith dagger]

Someone

[pseudo trellis]

would it not be 3?

[paper pike]

We agreed that g'(x) = -3cos(x)-2sin(x) because C = 0

[pseudo trellis]

so C is 0?

[paper pike]

Do you see why?

[pseudo trellis]

not really

[paper pike]

Here

We need to make sure g'(0) is -3

(this is their given)

[pseudo trellis]

right

we get -3 + C

[paper pike]

So we need to choose C such that g'(0) = -3

[pseudo trellis]

i see

[paper pike]

And g'(0) is -3cos(0)-2sin(0)+C

[pseudo trellis]

so D is indeed 3

[paper pike]

So g'(0) = -3 + C

And this must be -3

So we solve -3 + C = -3

It happens that C = 0

[pseudo trellis]

okay, yeah

[paper pike]

Now we integrate again

[wraith dagger]

Someone

[paper pike]

g(x) = -3sin(x)+2cos(x) + C

[pseudo trellis]

then we do

[paper pike]

Ok but C is zero

[wraith dagger]

Someone

[pseudo trellis]

yeah

[paper pike]

So you can remove it from the integration

[pseudo trellis]

true

[paper pike]

To not complicate things

[paper pike]

In conclusion

[pseudo trellis]

so the answer is 1?

[wraith dagger]

Someone

[cedar kiln]

@pseudo trellis Has your question been resolved?

[main needle]

that's correct 👍

[dreamy void]

yea

cosine at pi is -1

-2 + 3 = 1

[pseudo trellis]

yay, okay

just going through all 10 of my problems, then will close and take the test :P

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[timber oak]

whats the question

!status

[cedar kiln]

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[elder elm]

Sorry, I wnted to check if my answer to 3 and 4 checks out:

[timber oak]

ok ill have a look

well for problem 3, for showing R_n is isomorphic to C_n

you've sketched the right idea but you haven't explicitly given a map and checked its an isomorphism

depends how much detail your teacher is looking for though, since you did say that the group operation corresponds to addition modulo n, which is what it means for it to be an isomorphism (albeit a little informally)

same comment for q4 - your proof is correct, but a little informal - may be better to explicitly write a map that takes g^n -> n and verify that this map is an isomorphism

[elder elm]

Thank you! Lastly, do you think 5 also checks out? Do you think this is a brief enough answer?

[timber oak]

i dont think this actually answers the question

(though its more informative than what i think the desired answer is...)

its much simpler than what youve written

note they arent asking you for which n is there only one group, but rather what can we deduce about our group of order n, if there is only one group up to isomorphism?

though fwiw ur argument for why prime group order => cyclic is correct

again u could be a little more specific, eg given g in G, |<g>| = 1 or p by Lagranges theorem, but 1 \in <g>, so either g = 1 or |<g>| > 1 so either g = 1 or <g> = G, eg G is cyclic (and moreover any non-identity element is a generator)

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[pastel vault]

!status

[cedar kiln]

What step are you on?
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[upper burrow]

2

[pastel vault]

Okay could you send an image of your work?

[pastel vault]

,rotate

[pastel vault]

Yeah so to find dy/dx, move the yk sin kx to the other side

And then factor out (1 + cos kx) from the left hand side

[upper burrow]

Then?

[real tree]

multiply by sin kx on both sides on the final equation

cuz u will get the rhs

I mean lhs

sin kx d^2 y / Dx^2

[upper burrow]

.delete

.close

[pastel vault]

Then sub that into your dy/dx on the last line

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[pastel vault]

A more efficient way would be the quotient rule ngl

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[elder elm]

Could someone check my answer for this problem to see if it makes sense?

[cedar kiln]

@elder elm Has your question been resolved?

[upper abyss]

If they're not the same, then there's two cases:

• |G| > n
• |G| < n

I'd personally go through both cases and show they're impossible

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[outer jungle]

does lcd work here?

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[fair copper]

i dont understand the prcoess between these

[digital cliff]

between which lines

[upper abyss]

It's all common factoring

Just, common factoring things like (x + 3)

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[azure halo]

Hello all! I have a small doubt regarding this question .

What is 8/2(2+2) ?

[cedar kiln]

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[solemn fern]

<@&286206848099549185>

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[solemn fern]

This was my attempt

hello>

<@&286206848099549185>

HELLOOOOOO

[hot crag]

!15m