help-38

[covert gazelle]

What do you want to ask?

[alpine lava]

nothing your asking a question just wanted to show smth like it, my question is in #help-5

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@wraith hinge Has your question been resolved?

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[wraith hinge]

hello

[wraith hinge]

how is called this thing

i only need name

i know how to use

but not name

[magic skiff]

product operator

[wraith hinge]

but can you name the operation how it is so i can have the idea

[wraith hinge]

like this operation

[stoic iron]

multiplication

[wraith hinge]

yes

but it need a special name

[magic skiff]

like the factorial?

[wraith hinge]

yes

[main sigil]

It's not factorial

it's called zero

[wraith hinge]

not the result

how do i say it

[stoic iron]

https://mathmaine.com/2018/03/04/pi-notation/

[main sigil]

Product of all integers between 0 and 10 including both endpoints

[wraith hinge]

oh, thanks

🤠

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[violet nest]

how did they know that velocity = v =f' ....

where did that -4 * sin*t come from

[primal condor]

velocity is the derivative of position, so they just derived 4 cos t

also remember it's sin(t) not sin TIMES t

[violet nest]

cos t derivative is -sin t

[primal condor]

yes it is

[violet nest]

so that negative goes infront of the 4

[primal condor]

yes

[violet nest]

oh

that makes more sense

[primal condor]

lol

did that answer ur question

[violet nest]

so f'' is the derivative twice?

[primal condor]

yeah

there are different ways of writing it but I always just use ''

it just means the derivative of the derivative

[violet nest]

wow

epic

[primal condor]

you just gotta know that velocity is the derivative of position, and acceleration is the derivative of velocity

[violet nest]

why are they multiplying that 7/4

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[hoary brook]

So I'm pretty sure my math was right, I found the derivative of p and got 3/20 x^(1/2)

then I plugged in 40 and got .948

which then I multiplied by 1000 since its in thousands

whoops I just realized I put the wrong screenshot

anyways I got that the quantity demanded is 948.6 radios when price is $40?

wait but why would I have to get the derivative of p if this isnt a rate?

[trim jolt]

@hoary brook Has your question been resolved?

[hoary brook]

<@&286206848099549185>

[cursive musk]

what

price is a function of demand (x)

so you are finding dp/dx

[hoary brook]

oh

so would I just multiply every term by d/dx and then fill in its following value?

[cursive musk]

what

[hoary brook]

or how would I go from there

[cursive musk]

for p'(40)?

[hoary brook]

no for the original function

[cursive musk]

its the exact same as p'(6) in the previous question

do you know how to take derivatives

[hoary brook]

yeah I found the derivative and plugged in 40 for p

p'*

[cursive musk]

okay so whats the question

[hoary brook]

but it wasnt the right answer

[cursive musk]

40 for p?

its 40 for x

dp/dx is a function of x

you cant plug in p in dp/dx

[hoary brook]

OH so I'm solving for x and then finding its derivative

?

[cursive musk]

no

there are many ways you could have messed it up but most of them come from a tiny algebra/calcualtion error

show your work

[hoary brook]

which value am I finding the derivative for then?

[cursive musk]

just cause your answer is wrong doesnt mean you dont understand it

you are finding dp/dx at x = 40

[hoary brook]

wait maybe theres a misinterpretation

err I'll just show my work gimme a scond

@cursive musk

[cursive musk]

looks good

[hoary brook]

this is the answer it shows in the book

OH am I supposed to plug in the 948 into another function?

[cursive musk]

i dont think you have any other function

[hoary brook]

well back into p?

[cursive musk]

no

i think the textbook is wrong

[hoary brook]

That'd really suck then cause I was stuck on the problem for a hot minute LOL

also what would that be as a rate?

I'm lost on how to word that bit cause I have to interpret it

[cursive musk]

what I would have said is at the demand = 40 thousand, for every thousand increase in demand the price would go up by around $0.95

ngl was a bit tricky for me too

and I did this years ago

[hoary brook]

why is it back to cents?

oh cause you said 40 thousand

[cursive musk]

because p'(40) is a price

not a demand

[hoary brook]

so you couldnt say an increase of $948/quantity demand increase of 40 units?

[cursive musk]

none of that is right

[hoary brook]

yeah I think im having a hard time interpreting this part

[cursive musk]

40 is where the slope is

so at demand = 40

demand is in thousands

price is in $

so its not 0.948*1000/d but 0.948/1000d

[hoary brook]

and price is p where x is demand

so

[cursive musk]

ye

[hoary brook]

what is p'?

the rate of change where price is...

uhhh

[cursive musk]

think about it for a moment

[hoary brook]

im trying to think out loud rn lolol

so if p' = dp/dx then

price with respect to demand

so

$.95 per 40,000 units demanded

oooooooooooooooooh

[cursive musk]

almost

[hoary brook]

or would it be

[cursive musk]

40 is just the point we know the slope at

dx is still just x

so its $0.95 per x at x = 40

[hoary brook]

Oh so $.95 per quantity demanded when quantity demanded is at 40?

[cursive musk]

perfect

[hoary brook]

my brain

is fried LOL

[cursive musk]

thats good

your brain is like a muscle

you work it out and get tired, come back the next day and its smarter

[hoary brook]

so how did you know that it's just when it's at 40 and not that quantity demand is 40,000?

[cursive musk]

cause x is 40

we only know the slop at 40

i think youre getting x and quantity demanded and dx confused

40 and 40000 depend on the context but they are the same

but the rate is just delta p / delta x

delta x is whatever you decide it is

delta p is $0.95

[hoary brook]

oh yeah cause delta p is the same as dp

[cursive musk]

i think a drawing would help one sec

[hoary brook]

yeah that kinda helps paint the picture

so also in general

this is more a generalization, but with these types of problems, I can assume that x is not gonna be a constant value and rather that when it's instantaneously at that moment that value temporarily?

maybe thats the word I was looking for, instantaneous

[cursive musk]

which x

you are determining the instantaneous rate of change of p with respect to x (dp/dx) at x = 40

[hoary brook]

i meant the x = 40

[cursive musk]

x = 40 is constant

but p'(x) is a function of x

[hoary brook]

im pretty much trying to get a more solid foundation of when to look out for how the wording works to make it that the answer will be "when x = 40" rather than accidentally saying "per x"

[cursive musk]

so you need both of those

i think for the "per x" dont say x cause then its confusing

say in context

so when the demand is 40, for every increase in demand the price is expected to increase by p'(40)

its also not just "per something"

its per increase in something

so that we can use dx

[hoary brook]

this because it's a rate right?

[cursive musk]

yes

since we know dp/dx, if we know dx we know dp

[hoary brook]

and dx is the change of the demand right?

[cursive musk]

yes

[hoary brook]

so then dp would be the change of the price

[cursive musk]

yes

[hoary brook]

okay random request,

do you think you could switch up some of the letters and maybe some of the wording to quiz me? lol

if not that's fine i know its probably a strange request

[cursive musk]

i mean there are probably just other problems in the book you could do

its not strange

[hoary brook]

oh probably like the other question I accidentally posted earlier

[cursive musk]

i can think of one though one sec

if the time delay on a highway in minutes is dependent on the number of cars on the road, where t = f(cars), if t'(10) = 0.2, what does that mean

[hoary brook]

the time is at .2 when there are f = 10 cars?

[cursive musk]

note the '

[hoary brook]

the time changes by .2 minutes when there are f=10 cars?

[cursive musk]

no

[hoary brook]

wait delay isn't a rate right?

[cursive musk]

delay is a function of the cars

but dt/dc is a rate

[hoary brook]

dt/d(10) is the change in time when there are 10 cars right?

which = .2?

or am I misinterpreting somewhere

[cursive musk]

you dont touch dc

its not d * c

look at the photo i sent

[hoary brook]

so dt/d(10) isnt the same as t'(10)?

[cursive musk]

t'(10) = dt/dc evaluated at c = 10

[hoary brook]

oh

[cursive musk]

dt/dc is a function of c like 2c

[hoary brook]

So it's not .2 minutes have passed if there are 10 cars on the highway?

[cursive musk]

correct

[hoary brook]

what is the .2 minutes then?

that's where Im tripped up the most I think

[cursive musk]

brb

[hoary brook]

cause delta t = .2 which means the change in time is .2 when it's evaluated at c=10

[cursive musk]

No

t is 0.2

But not delta t

Delta t is dependent on dc

Which we decide

It’s not 10 or 0.2

Say t = c^2

dt/dc = 2c

dt/dc at c = 0.5 => 2(0.5) = 1

[hoary brook]

so we have to find what dc is first?

didnt mean the reply my bad

[cursive musk]

dc isn’t a variable that you find

dt/dc is one variable

[hoary brook]

well not "find" i mean figure out

like what it means

but you're saying its conjoined

so the change in time with respect to the change in amount of cars on the highway

when c = 10

[cursive musk]

dt/dc is a function just like t’(c)

You don’t find what dc is

Like you don’t find what t’ is

You’re like breaking it into letters

[cursive musk]

Yes perfect

[hoary brook]

so how would we put that in words

for an answer i mean

uhhh

[cursive musk]

Use this

Plug in the numbers you know

[hoary brook]

the change in time with respect to the change in amount of cars is .2 when there are 10 cars?

[cursive musk]

Yes but put some more context in there

what is .2

[hoary brook]

.2 minutes

[cursive musk]

Okay

[hoary brook]

the change in time with respect to the change in amount of cars is .2 minutes when there are 10 cars?

isnt there an easier way to put "the change in time with respect to the change in amount of cars"?

[cursive musk]

it’s kind of the same thing as what I do but I think there is a better way

So use this

[cursive musk]

^

[hoary brook]

when there are 10 cars, the change in time with respect to the change in the amount of cars is .2 minutes?

[cursive musk]

kinda?

I would use the “for every increase in…”

Or “for every additional”

Say it like you are predicting values

[hoary brook]

when there are 10 cars, .2 minutes pass for every additional car?

[cursive musk]

Not quite

.2 is the increase in highway delay for all cars

When there are 10 cars on the road, every additional car is expected to increase…

[hoary brook]

.2 minutes pass for every additional car?

[cursive musk]

no time is passing

This is about how long the traffic takes

[hoary brook]

When there are 10 cars on the road, every additional car is expected to increase .2 minutes of time?

[cursive musk]

What is time in this context

Be clear

[hoary brook]

travel time

[cursive musk]

Okay

Now add that back in

[hoary brook]

When there are 10 cars on the road, every additional car is expected to increase traffic by .2 minutes of travel time

[tawny girder]

2+2=?

[cursive musk]

Replace traffic with travel time

Otherwise you’re saying it twice

[hoary brook]

When there are 10 cars on the road, every additional car is expected to increase travel time by .2 minutes

[cursive musk]

You got it!

[hoary brook]

jesus

[cursive musk]

Lmao

It’ll be a lot faster next time

[hoary brook]

i hope so lol this is really tricky for me

[cursive musk]

Try the satellite one now

[hoary brook]

satellite one?

[cursive musk]

67

[hoary brook]

oh this one

when x = 40, the price is $.95 per additional unit demanded

the more I think about the dp/dx the more the "per" part makes sense when I remember that it means change in price with respect to change in demand

its finally connecting a bit now lol

[cursive musk]

better

but you dont want to have just x = 40

and its not really "the price is"

we know the price at x = 40

but the price increases per unit demanded (p'(t))

[hoary brook]

when the demand is 40 units, the price increases by $.95 per additional unit demanded?

[cursive musk]

yep!

just one nitpicky thing though, since the function is often not a straight line, the derivative isn't the same if we change x by even just a little bit (like to 40.00001), so the slope is different, meaning the tangent line isnt a perfect estimation

does that make sense

[hoary brook]

color changed lol

[cursive musk]

ooh helpful role yay

anyways

[hoary brook]

yeah this makes sense

[cursive musk]

alright cool

so I just add "expected to increase"

[hoary brook]

the tangent line is an estimation essentially

[cursive musk]

yep

[hoary brook]

vs if we used a secant line wouldnt it technically be more accurate?

cause it uses 2 points

[cursive musk]

i've never actually learned that

but I'm guessing it depends on the function and the points

[hoary brook]

yeah how much info we're given essentially

too bad its all so convoluted sometimes LOL

but thanks so much for your help, I definitely feel more confident in interpreting this stuff now

.close

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[echo jasper]

Help please? how is this wrong

[wraith hinge]

show ur working out

[wraith hinge]

oh it wants standard form

not slope intercept

[echo jasper]

OH

Omg

I gotta read

thanks

.close

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[robust turtle]

I am struggling help

[cursive musk]

!status

[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

[cursive musk]

!show

[trim jolt]

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

@robust turtle Has your question been resolved?

[robust turtle]

1

[cursive musk]

when is a function not continous

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@robust turtle Has your question been resolved?

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[fallow zinc]

What are the answers to these 3 questions?

[cursive musk]

!nosols

[trim jolt]

As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.

[fallow zinc]

Mb how do I solve these questions?

Can you help me through the steps @cursive musk

[vague citrus]

I can help with 3rd

Could you just send a clearer picture

[fallow zinc]

@vague citrus

[vague citrus]

Notice curve is downwards

So coefficient of x^2 is negative

It is also clear one zero is -8

And do you know the relation between vertex and the coefficients?

[fallow zinc]

Vertex is like the middle point right?

[vague citrus]

That topmost point

[cursive musk]

not always

its the middle

[vague citrus]

Let me complete

[cursive musk]

alr

[vague citrus]

I mean a point where a function has its maximum or minimum value

Here it is maximum

At -5,3

You know the relation? @fallow zinc

[fallow zinc]

It’s the maximum cause it’s at the top?

[vague citrus]

Yes

Since the curve is downwards there is a maximum value
Had the curve been upwards there would be no maximum value

Okay the co-ordinates of vertex are -b/2a , f(-b/2a)

a is coefficient of x^2 and b is the same of x

[fallow zinc]

ok go on

[vague citrus]

you can use relation of zeroes

Let zeroes be p,q

So p+q=-b/a

But you know one zero

Which is -8

So -8+q=b/-a

Now use vertex formula

-5=-b/2a

b/a=10

So q = 2

[fallow zinc]

Ok

[vague citrus]

No

Wait

Actually I did it wrong there

This

[fallow zinc]

I got this

@vague citrus

I found an example of the problem in my photos

[vague citrus]

Okay, I couldn't help you

[fallow zinc]

I still need help on the first problem

That one I don’t get at all

[vague citrus]

I don't know how to determine nature of solutions in a cubic but I can help with answer

[fallow zinc]

I’ll take anything

[vague citrus]

1 real 2 complex

And yeah the real one is negative

[fallow zinc]

I don’t understand

Do I enter the numbers like this?

[vague citrus]

See I am 100% sure about 3rd one

Since it is asking roots

Or zeroes

[vague citrus]

Wait there are no positive real zerp

0,1,2

This is what I thikb

[fallow zinc]

Ok

Thanks

Do you mind reviewing one more question?

I wasn’t entirely sure on this but I think I did it right

[vague citrus]

Ok

[vague citrus]

I have not studied about them

I'm sorry

[fallow zinc]

Dw

You’ve already helped me on the last two questions

.close

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[wraith hinge]

I don’t know how to do this

[ocean mural]

you know $\log_y z = \frac{\log_x z}{\log_x y}$

[solid kiln]

fäf

[wraith hinge]

Ys

[ocean mural]

make all base equal to a

[wraith hinge]

How?

[ocean mural]

using this

[wraith hinge]

Hmm

Could u show me that(?

[ocean mural]

wait for a bit

[trim jolt]

@wraith hinge Has your question been resolved?

[solid kiln]

fäf

[wraith hinge]

Like this (?

[ocean mural]

ok

what do you get

[wraith hinge]

b equal c

How about a?

[ocean mural]

x=y=1 so a=b=c

[wraith hinge]

Ooo

Thx

.close

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[autumn dagger]

How can I get length?

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[wraith hinge]

Is this correct?

[trim jolt]

@wraith hinge Has your question been resolved?

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[drifting rose]

how do you intergrate this?

I simplified the bottom by doing completing the square

so I got this new bottom bit

[cursive musk]

mate what

just do partial fraction decompoisition

[drifting rose]

and then I got this

[cursive musk]

i understand

dont do that

just do PFD

[drifting rose]

they want it in trig ratios

[cursive musk]

oh

idk then

[drifting rose]

:V

you know partial fraction decomposition but not trig

[cursive musk]

yeah

didnt cover trig

[drifting rose]

also why would I do PFD if I want to make it easier for me

wait

you can just split it up into smaller fractions

ok nvm

[cursive musk]

pfd is just so much more straightforward

you dont have to memorize specific methods

[drifting rose]

yea but -3+x-x^2 is not factorisable

its going to be a quad equation

[cursive musk]

-(x^2-x+3)

,w factor -(x^2-x+3)

[solid kiln]

Results provided by WolframAlpha

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Requested by Kefir101Awesome#7665

[cursive musk]

ah

I assumed it was

carry on

[drifting rose]

so your method wont work either way

so...

you mind helping?

[cursive musk]

i thought I could help

whenver I saw problems like those it was for PFD

[drifting rose]

aw rats

[cursive musk]

sorry I cant help

[drifting rose]

aw thats ok

:((

[verbal gulch]

perhaps use the fact that the derivative of arctan(x) is 1/(1+x^2)

[cursive musk]

how though

do you see a solution in your head

divide both sides by 11/4 and then get the 11/4 into the (x-1/2)^2?

[verbal gulch]

u-substitution to convert it into the form 1/(x^2 + a)

then factor the denominator so you get 1/(a((x/sqrt(a))^2 + 1)

u substitution again to make it

1/a((u^2 + 1))

[cursive musk]

ah

[verbal gulch]

there's probably a more optimized way

[cursive musk]

,w derivtative of arctan(ax)

[solid kiln]

Results provided by WolframAlpha

Click here to refine your query online
Upgrade to WolframAlpha Pro!

Requested by Kefir101Awesome#7665

[verbal gulch]

,w integrate 1/(-3+x-x^2) dx

[cursive musk]

yeah thats what I thought

[verbal gulch]

yeah looks like you have to do something like that

[cursive musk]

I could help yay

right nosols

@drifting rose have you been following this convo

[drifting rose]

uhhh

hold on...

no I am a bit dazed because I DO know how to do it

is just the answer is

[cursive musk]

that looks incorrect

or at least not what wolfram says

[drifting rose]

it does show the whole working out

but I have no clue how it goes from one step to another

it goes the top to the bottom

and I'm dazed by how they did it

I kind of get this

I can see using that to get to there.... kind of

.close

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[grand aspen]

Hello

[grand aspen]

Can I get your help? Please

[wraith hinge]

Send your question 🫡

[grand aspen]

Here it is

Thank you

[wraith hinge]

It’s asking for the integral?

[grand aspen]

It’s asking to solve the equation

And then give the solutions

[wraith hinge]

oh

[grand aspen]

I did one

But it’s not the same

Or similar

Do you know how to start?

[wraith hinge]

I think you can use a couple trig identities here

[grand aspen]

Which one?

[wraith hinge]

$cos^{2}x + sin^{2}x = 1$

[solid kiln]

pulse

[wraith hinge]

you have $2sin^2{x}$ in your equation

[solid kiln]

pulse

[wraith hinge]

See how we can manipulate that into $cos^2{x}$?

[solid kiln]

pulse

[wraith hinge]

@grand aspen

[grand aspen]

Yeah

I’m trynna take it in

[wraith hinge]

Hint: You can rearrange this identity into $sin^{2}x - 1 = cos^{2}x$

[solid kiln]

pulse

[grand aspen]

Is (2sinx)^2 the same as sin^2x?

[wraith hinge]

yes

well

$(sinx)^2 = sin^2{x}$

[solid kiln]

pulse

[grand aspen]

Ok cool

So then the 2sin^2(x) becomes cos^2(x)

[wraith hinge]

nono

think

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

[solid kiln]

pulse

[grand aspen]

Ok

[wraith hinge]

And how we can change 2sin^2x into cos^2x’s

[grand aspen]

So the sin^2(x) - 1 turns into cos^2(x)

[wraith hinge]

Yes

[grand aspen]

Ok cool

But does it matter that the one is positive?

Or does that first minus make it negative?

[wraith hinge]

It’s gotta be -1

NO IM TRIPPING

IM SORRY i shouldn’t do math at 1:42am my bad but

https://cdn.discordapp.com/attachments/908078008609431674/1088712029210157056/725155247621799976.png

$cos^2x = 1 - sin^2x$

[solid kiln]

pulse

[wraith hinge]

That’s better

Sorry I goofed that

[grand aspen]

Lol it’s ok

So

The first cos becomes 1 - cos^2x

1-sin^2x

My bad

[wraith hinge]

$2(sinx)^2 - 5cosx + 1 = 0$

[solid kiln]

pulse

[wraith hinge]

this is the original equation

[grand aspen]

Yes

[wraith hinge]

So the goal here is to turn all the sinx’s into cosx’s so we can factor this

you can use the identity to change the sinx’s into cosx’s pretty easily here

https://cdn.discordapp.com/attachments/908078008609431674/1088712029210157056/725155247621799976.png

[grand aspen]

Ok

= 1-cos^2(x)

[wraith hinge]

so with this identity, you can find what sin^2x equals

yes

you would replace (sinx)^2 with that

[wraith hinge]

so now you can get
$\newline
2(1-cos^2x) - 5cosx + 1 = 0$

[solid kiln]

pulse

[wraith hinge]

which is also
$-2cos^2x - 5cosx + 3 = 0$

[solid kiln]

pulse

[wraith hinge]

@grand aspen do you see how I got to this point?

[grand aspen]

Ok

So

Yup

Light work amigo

Alright

So i’m there

After distributing

[wraith hinge]

Cool

you can factor this I think

@grand aspen It’s like how you’d factor $-2x^2 - 5x + 3$, but with $cosx$ instead of x

[solid kiln]

pulse

[grand aspen]

Yeah i got that part

So now

I factor out

[wraith hinge]

so you end up with

[grand aspen]

I hate using the box method

[wraith hinge]

damn, i like it

fold hurts my brain

[grand aspen]

Can you show me how to factor quickly

I can do it

And its satisfying

But like i feel that people got the edge on me

When it comes to that

But i’ll do it

[wraith hinge]

Fair

[grand aspen]

Bruh

I’m messing up💀

[wraith hinge]

so you should get that
$(-2cosx + 1)(cosx + 3) = 0$

[solid kiln]

pulse

[grand aspen]

Wait

Why is it like that?

Don’t we keep the x substitute?

[wraith hinge]

well

it’s asking about cosx so i’d keep it

but from here, you can set each factor = 0 to find what cosx is equal to

[grand aspen]

Oj shiy

I got it

I think

WIt

Wait

I got (2x -3 ) (x - 1)

[wraith hinge]

one sec

[grand aspen]

Oh i messed up the negative

[grand aspen]

Damn bro

[wraith hinge]

i don’t know how to use f.o.l.d. factoring method tbh lol

[grand aspen]

Damn

I tried using the x method

I messed up

[wraith hinge]

but from here on out:
$\newline
-2cosx + 1 = 0
\newline
cosx + 3 = 0$

[solid kiln]

pulse

[wraith hinge]

with algebra:

[grand aspen]

1/2 and -3

[wraith hinge]

$cosx = \frac{1}{2} \newline
cosx = -3$

[solid kiln]

pulse

[wraith hinge]

Do you know your unit circle?

[grand aspen]

Yeah

But hey do you know how to dictate whether the 2x or x will be on the left side or top in the box method?

[wraith hinge]

Doesn’t matter where they go

[grand aspen]

Oh ok

[wraith hinge]

if I put cosx + 3 on the top and -2cosx + 1 on the side, it would be the same

[grand aspen]

Hmmmm ok

Did you use the x method to get the two numbers for the box method

[wraith hinge]

i just try tons of numbers in my head until they work

keeping in mind that I need to get -2cos^2x and 3 as my results when i multiply

[wraith hinge]

So with unit circle knowledge, when does $cosx = \frac{1}{2}$?

[solid kiln]

pulse

[wraith hinge]

@grand aspen

ok I need to go to sleep so I’ll quickly finish this process

$cosx = \frac{1}{2}$ when x =
$\frac{\pi}{3}$ or $\frac{5\pi}{3}$

[grand aspen]

My bad

My goddamn cat spilled tea everywhere

Alright so

[solid kiln]

pulse

[grand aspen]

Yeah I got the angles it’s pretty easy stuff

The x coordinate is 1/2

So it’s both of those

And then

The -3 is crazy

[wraith hinge]

Yeah so

cosx will not be a number less than -1 or more than 1, which means -3 has no solutions

[grand aspen]

Oh yeah

Because the boundaries

[wraith hinge]

cos(0) and cos(pi) are the max and min, respectively

yes

[wraith hinge]

so now,
1/3, 5/3
should be the correct answers

because it asks for the 0 to 2pi interval only

[grand aspen]

Yup and negative 1 is under

So no answer

[wraith hinge]

yeah cos(x) will never be -3

does 1/3, 5/3 count as correct?

@grand aspen

[grand aspen]

Checking

YESSIR

THANK YOU VERY MUCH

[wraith hinge]

np

Sorry for messing it up earlier

[wraith hinge]

https://mathsux.org/wp-content/uploads/2022/04/Screen-Shot-2022-04-26-at-9.38.44-PM-1024x560.png

This is a good resource to use

you should memorize these identities

well, just one from each of the top 3 columns

if you know 1 you can just use algebra to manipulate it however u want to

[grand aspen]

Sweet

Thank you bro

Have a goodnight

.close

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[lost citrus]

Temperature for entire june $30X$ \
Temperature for first 13 days $13X - 130$ \
So the last 17 days should be $30X - 13X + 130$ \
$17X + 130$ right ?

[trim lichen]

30X - (13X-130)

[lost citrus]

yeah sorry

[trim lichen]

not 30X - 13X - 130

big difference

[lost citrus]

17X + 130

[trim lichen]

❌

[lost citrus]

but still no answer..

[solid kiln]

Bunnings

[lost citrus]

thanks

got it

daily average divide by 17

.close

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[dark lily]

what was done here to the 3*n?

[dark lily]

.close

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[patent bramble]

The answer is k<9/4

But got k<-9/4

[trim jolt]

Channel closed

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[supple copper]

what's the question

[trim jolt]

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[sick vale]

help please

[sick vale]

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

[trim jolt]

@sick vale Has your question been resolved?

[sick vale]

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

<@&286206848099549185>

bruh hello

[viscid steeple]

......

[solar sequoia]

holy fucking shit

[pseudo pebble]

a is option c

[solar sequoia]

there is no option c

it should be option 3

[pseudo pebble]

like third option sorry

[sick vale]

why

i dont understand the noting fully yet

[solar sequoia]

ok

so

the U means Union

[sick vale]

yes

[solar sequoia]

so you are kinda like "grouping" them all together

so look at the ray x<=4

and then look at the ray x>=7

[sick vale]

its the nmbers that are in both like number lines right

[sick vale]

whats ray

[solar sequoia]

if u want to include both of them at the same time you would write it as the union

[solar sequoia]

or graph

[pseudo pebble]

yes they're basically number lines

[sick vale]

okok

what about b)

[solar sequoia]

what do u think the answer is for b

we are not going to spoonfeed you on every problem

[sick vale]

fine

is it

4?

like the 4th one from the top going down

[solar sequoia]

yes

[sick vale]

@solar sequoia

j curious

do you know

the english igcse spec

[solar sequoia]

I would say the answer is option 4

[solar sequoia]

what is that?

[sick vale]

nvmm

but thank you lots though

i think im beginning to undertstand

[solar sequoia]

ok thats good

[trim jolt]

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[cursive forge]

Are the planes (x,y,z)=(1,2,2)+t(2,1,2)+s(3,-1,1) and (x,y,z)=(3,2,-2)+t(-1,3,2)+s(2,-2,1) parallel?
Can't figure out how to do this one... I've converted to Parametric form, but I'm not sure if I should be solving for s and t using substitution or elimination or something else.

[long basin]

Identify their direction vectors

Then find their normal vectors

Or you can just find their normal vectors @cursive forge

[trim jolt]

@cursive forge Has your question been resolved?

[cursive forge]

Would I do the cross product of the direction vectors such that (2,1,2) x (3,-1,1) = (3,4,-5) and the same for the second plane?

[cursive forge]

And I'm not sure what to do with the normal vectors either. If I have one normal vector and dot it, then they are parallel when the dot product is zero.

[long basin]

Prove that the normal vectors are parallel, that is, one vector is the same as another if multiplied by a scalar

For example, (2, 4, 5) is parallel to (-4, -8, -10)

Because they differ by a multiple scalar of -2

[cursive forge]

So n1 = (3, 4, -5) and n2 = (7, 5, -4)

Therefore 4*5/4 = 5 (for the y's) and that doesn't work with 3 however, thus they are not parallel

[trim jolt]

@cursive forge Has your question been resolved?

[cursive forge]

Any thoughts?

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@cursive forge Has your question been resolved?

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[wraith hinge]

Is there anyway I can solve for x here?

[outer fox]

20,000(1.05) > 25,000 + 500x????

-8

[wraith hinge]

but there is an (x) exponent on top of the 1.05

[crude blaze]

^x

[outer fox]

ahhh wwit

[wraith hinge]

i dont think it ssolvable

[outer fox]

no idk

[trim jolt]

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[grand aspen]

Hello

[grand aspen]

Can I get your help on this problem

[wraith hinge]

for future reference, you don’t have to ask if you can get help, just send the question immediately and someone will help lol

[grand aspen]

np just mannerism

[wraith hinge]

alr

[grand aspen]

I can't even get the top line on this one

[wraith hinge]

oh dear

<@&286206848099549185>

[grand aspen]

The hardest one is number 8 which doesn't even make sense 💀

[wraith hinge]

I think they want you to use reciprocals to simplify some of these

[grand aspen]

i did that with all of them

and it's really slow

[wraith hinge]

like for example, $csc(x) = \frac{1}{sin(x)}$

and see what cancels

[grand aspen]

yup

[solid kiln]

pulse

[grand aspen]

you think I should do that to all of them?

get them all to cos and sin

[wraith hinge]

looks like you can also factor some variables

[grand aspen]

ok bare with me

a little messy but

Got anything?

[trim jolt]

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[grand aspen]

.close

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[subtle iron]

I need help with determinants

[subtle iron]

I don't know where to start off, so instruct me as much as you can

[wraith hinge]

what are you confused about

[delicate jasper]

why determinants

[eager comet]

(as in, this question doesnt seem to have anything to do with them, lol)

[subtle iron]

Oh? I thought it was mb

[eager comet]

the notation for det is a straight line

[subtle iron]

Uh I just don't know how to get values for them

the whole concept I dont get

[silent canyon]

I prefer det []

[eager comet]

these are just two 2x2 matrices

[delicate jasper]

-5 needs to be equal to w

x needs to be equal to what?

[subtle iron]

? Why w?

[delicate jasper]

why not

[subtle iron]

I need to know lmao

[nova spire]

Two matrices are equal <=> each of their coefficients are equal

[subtle iron]

it sounds random to me

[eager comet]

Would you say this is true

[subtle iron]

Um sure

[silent canyon]

Literally the row and column numbers match

[eager comet]

so if i asked you to solve for x?

[silent canyon]

How obvious does this have to be 😂

[delicate jasper]

maybe their first time seeing matrices

[eager comet]

(what we are doing here is fundamentally the same thing)

[subtle iron]

I'm assuming the x is supposed to be ?

the same as the sc u showed me?

[silent canyon]

Someone said determinant 🤔

[nova spire]

Can you find x, knowing...

[nova spire]

This?

[eager comet]

here you see the 2x2 matrix ( 1 2 3 4 ) is equal to itself right

it is not equal to any other combination of numbers in the same form

i.e

[nova spire]

.

[eager comet]

this is only true if
w=a
x=b
y=c
z=d

there is no other possibility

if you understand and can apply this fact, you should be able to solve your question

[subtle iron]

oh

[eager comet]

do you see now why, for instance, w = -5?

[subtle iron]

Therefore for my question the answer would be w=-5

[eager comet]

Yes

similarly you should be able to find the other variables

[subtle iron]

x is 6, y is 5, and z is -6

Ok that was fault for overthinking it

[nova spire]

Yes!

[nova spire]

No problem

[subtle iron]

Last time I saw this, I literally assumed determinants lmao thank you guys.

[eager comet]

nw, hope this helped

[subtle iron]

@eager comet One more question lets say its between a 2 and m/4 on the other side

would I do the opposite

and multiply it

m=8

and if its like 3x 6

I would divide

[eager comet]

if 2 and m/4 are in the same position in the equal matrices

then 2 = m/4

m = 2*4 = 8

[subtle iron]

yep

thx

again

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[brittle lance]

Can someone help with number 23? It needs to be in the form y-k=a(x-h)^2

[brittle lance]

Nvm

.close

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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

[last junco]

i need help

[visual garnet]

.close

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[last junco]

if xy=9, x+y=14 find the value of x^4+y^4

who can help me

;-;

[trim jolt]

Please read #❓how-to-get-help

[visual garnet]

did u try elimination

idk

[tepid rock]

find the value of x^2 + y^2 by using (x+y)^2
Then find the value of x^4 + y^4 using (x^2+y^2)^2

@last junco

And if you don't get it, open another channel.

[last junco]

it is

if xy=9, x+y=14 find the value of x^4+y^4

^4

ohhhh got you

[tepid rock]

I know the question, I just told you how to solve.

[last junco]

thanks

[trim jolt]

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[last junco]

i got the final anwser

[last junco]

it was 2417 and

31522

but my teacher said 31522 is wrong

why?

<@&286206848099549185>

[tepid rock]

Show your work.

[last junco]

actually

the question is

x+y+xy=23

x^2y+xy^2=126

and i solve and get

xy=9 x+y=14

or

xy=14, x+y=9

[last junco]

2417

[last junco]

31522

[last junco]

do u know why its wrong

31522

<@&286206848099549185>

[tepid rock]

#❓how-to-get-help

Don't repeatedly ping helpers.

And definitely read that.

[last junco]

ok im srry

but can u tell me why

;-;

[tepid rock]

Also, you didn't post the original question earlier.

,w x + 126/x = 23

You got xy = 9 you say?

xy = 14 works fine as well?

Okay that's what you said.

,w x + 14/x = 9

,w x + 9/x = 14

Unless there's something else the question says about x and y. I think there's no way to deny either of the solutions.

Does it say anything else?

@last junco

[last junco]

yes