help-10

[viral blade]

because i wanted to see what the horizontal asymptote would be

so I picked a really large value of x

that way it would be really close to the asymptote

[timid silo]

ok i understand that now what plugging in does what but how does that help solve the problem

[viral blade]

helps to find the horizontal asymptote

[timid silo]

How?

[viral blade]

the y-value we get should be really close to it

[timid silo]

Okay so what would be the next step in solving the problem

You plugged it in, whats next?

[viral blade]

this isn't really a formal way of finding the asymptote

the point is for you to guess at what you think the asymptote should be

[timid silo]

oh i see

okay i get that now

but now my main question is, how does finding the asymptote help solve the problem?

[viral blade]

the problem is a multiple choice problem

one of the answer choices starts "the horizontal asymptote of y=3.10"

a different answer choice starts "the horizontal asymptote of "y=0"

if we know the horizontal asymptote, we'll be able to get rid of one of those choices

[timid silo]

oh okay

[timid silo]

so whats next?

[viral blade]

i dont really know how to respond to that

you want to just skip this part of the problem because your math app could do it?

if you really want i will

[timid silo]

nono lol

i dont wanna skip it i just didnt wanna waste ur time since i wasnt getting it

[viral blade]

ah

fair enough

[timid silo]

yeah

[viral blade]

you should make a note to study horizontal and vertical asymptotes then

but anyways

[timid silo]

yeah ill watch a few yt vids on that tn

[viral blade]

2 of the answer choices can be eliminated based on giving wrong horizontal or vertical asymptotes

for the other 2

they go by the same format

[timid silo]

which 2 are those?

[viral blade]

"the average cost per unit will approach [value] as the number of units produced increases"

[viral blade]

middle 2

the 2nd one says the horizontal asymptote is y=0

it's actually y=3.1

the 3rd one says the vertical asymptote is x=3.1

it's actually x=0

[timid silo]

oh i see

[timid silo]

since the horizontal asyjmptote is y=3.1 it cant be B right?

[viral blade]

right

[timid silo]

and since the vertical asymptote is 0, it cant be C either

which leaves A and D

[viral blade]

right

[timid silo]

so how do you determine those then?

[viral blade]

both of them say

"the average cost per unit will approach [value] as the number of units produced increases"

does this sound more like it's describing behavior at a specific point, or end behavior?

[timid silo]

it sounds like its describing end behavior

[viral blade]

exactly

right

do you remember which asymptote corresponds to end behavior?

[timid silo]

Okay cool

i think the horizontal asymptote is the one that dedscribes end behavior

right?

[viral blade]

yeah

nice

[timid silo]

so that means A would be the answer?

[viral blade]

correct

[timid silo]

okay cool

so just to clarify so since i wanna make sure im understanding this

or wait, how do you know which is the horizontal asymptote and which is the vertical asymptote

since i really do wanna understand that part since this problem is from my finals practice thingy

[viral blade]

which of the two asymptotes?

[timid silo]

yes

[viral blade]

the horizontal asymptote is the one that's a horizontal line

if you have trouble remembering what that is, think of the "horizon"

[timid silo]

oh okay lol

[viral blade]

then vertical is the other one, the vertical line

[timid silo]

yes

i think all i have to do now is just watch a few videos on finding the actual numbers for the asymptotes? right?

[viral blade]

probably

[timid silo]

okay awesome! thanks for the help i was super confused on that 👍

[viral blade]

you're welcome!

[timid silo]

.close

[obtuse pebble]

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[restive ermine]

Hi! Can I have some help with simplifying a trig identity

[muted delta]

No

[twilit ledge]

i understand to separate the equation into to functions, f(t) = t^4 & g(t) = (t^6 + 8)^6

then taking the derivatives, i get f'(t) = 4t^3 and then using chain rule, i get g'(t) = 36t^5(t^6 + 8)^5

then i can apply these results to the product rule, getting 4t^3(t^6 + 8)^6 + t^4 [36t^5(t^6 + 8)^5]

is this correct thus far?

[crisp badge]

The rationale looks right

[twilit ledge]

this is where im hvaing my issues. i guess i cant figure out how to factor it right

[crisp badge]

I'm gonna preface this by saying I'm not the most experienced with derivatives

But if I had to guess, you might be able to factor with the (t^6+8)

You could also take out t^3 from both terms

[twilit ledge]

ill try that.

[crisp badge]

If that doesn't work then I got nothing

[twilit ledge]

so based on what youre saying, the factor would be t^3(t^6+8)^5 ?

[crisp badge]

If I am correct then yes

Which would limit the choices to 2 or 4

Once again, assuming I'm right

[twilit ledge]

this is what im getting

[crisp badge]

Imma be real I'm not sure I'm experienced enough at this to help you

[twilit ledge]

all good bro, is there someone who is that can help?

[crisp badge]

Maybe ping a helper

[twilit ledge]

<@&286206848099549185>

[crisp badge]

Ye they should be more experienced

[twilit ledge]

@crisp badge i appreciate ur efforts nonetheless

[dusk ruin]

This step is correct

[twilit ledge]

ok, so then my issue is once i set up the product rule

im not factoring correctly i presume

[dusk ruin]

Ok so

[dusk ruin]

You see your last line here where you say 40t^6(t^?+3)?

It should be 40t^6 + 32

[twilit ledge]

how did you get 32?

[dusk ruin]

4*8

This is only the rightmost section fyi

[twilit ledge]

ok so factoring out t^3(t^6+8)^5 is correct

[twilit ledge]

yes

[dusk ruin]

Between the top and bottom circled you screw it up

as far as I can tell you did the rest right

Plus that matches an answer on your original problem

Just an error distributing ):

[twilit ledge]

im just confused as to where you multiply 8 and 4

bc when i factor out the t^3(t^6 + 8)^5

[dusk ruin]

4(t^6+8) + 36t^6 is the top of the circle yes?

Distribute the 4.

[dusk ruin]

Ignore this bit you factored it correctly

Only the stuff in the circle matters

[dusk ruin]

Top line circled is right, is this

Lower line is wrong.

Sorry about curtness btw on mobile so typing is hard

Make sense or-?

[twilit ledge]

im working it out now trying to get it

[dusk ruin]

kk

[twilit ledge]

this is what im getting

im not sure how you combine the 36 and the 4

[dusk ruin]

You dropped the square brackets by accident

[twilit ledge]

with the brackets thatll let me combine those terms?

[dusk ruin]

well yeah…? Order of operations, you add the stuff in parentheses or brackets before separating them

What you’re doing rn is like b(3+x) = 3b+x

[twilit ledge]

youre right.......

lol

[dusk ruin]

At last :D

[twilit ledge]

the parenthesis made me think there was still multiplication going on. lol

[dusk ruin]

Clarity

[twilit ledge]

awesome man youve been great help!

.close

[obtuse pebble]

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[dusk ruin]

it was my pleasure :)

[obtuse pebble]

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[timid silo]

How do I solve for x in this problemn?

[pliant breach]

you have to make the denominators the same

[timid silo]

oh yeah

so just multiple 20-x by 20+x on one side and vice versa right?

[pliant breach]

like this

[timid silo]

wait why cant you use the lcd

[twilit ledge]

cross multiply then solve for x

[pliant breach]

you can also do that too its 100x easier actually

[pliant breach]

wdym

[timid silo]

wait is this just for all fraction multiplication problems?

does this apply to all of them

[timid silo]

idk some random method i was taught in school

[twilit ledge]

if the same variable is on both ends of the equation u can do this to solve for it

[timid silo]

find the lowest common denominator and each denominator by it

[pliant breach]

it doesnt really work for variable cases like in your problem

[timid silo]

when you say variable are you referring to the x

[timid silo]

ohh okay

[twilit ledge]

yes

[timid silo]

awesome, thanks @pliant breach @twilit ledge!

.close

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[vocal kite]

how do i get the general solution?

[wooden cipher]

do you know about separation of variables?

[next reef]

@vocal kite

[vocal kite]

isit similar to rearranging the terms in dy/dx + P(x)y = Q(x) form?

[wooden cipher]

more like f(y)dy=g(x)dx

[next reef]

Those are linear differential equations.

Garlic asked about linear separability in DEs

[vocal kite]

yep

[wooden cipher]

if you factor, you can separate variables

[vocal kite]

ah ok

yepp

thank u 🙂

[obtuse pebble]

@vocal kite Has your question been resolved?

[trail cloak]

If you can't factor though, you'd have to find the potential function then find the constant of integration

[obtuse pebble]

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[primal tartan]

I’m bit confused why 15.43 must be true.

I was thinking of taking an x derivative of both sides of 15.43 but I’m not sure why the signs on my coefficients are changing.

[obtuse pebble]

@primal tartan Has your question been resolved?

[obtuse pebble]

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[icy cape]

Do I use Alternate Segment Theorem for this?

if so how so

[icy cape]

Actually I do but how?!

wait

The angle is 90 - a right?!

90 - a + 90 - a + 180 - 2a = 180

360 - 4a = 180

• 4a = -180
  a = 45 ?

[patent jetty]

Why not just use angle sum property

[icy cape]

What is that

[patent jetty]

ACB is an isosceles triangle ryt

[icy cape]

yes

[patent jetty]

So base angles u know

[patent jetty]

Ryt

(180-38)/2

@icy cape

[icy cape]

what is that

I mean nv

m

[icy cape]

How is it 38

how is a 38*]

OOPS nvm

[patent jetty]

AC=AB

[icy cape]

my brain is deflated atm

yea ik

[patent jetty]

Ok

[icy cape]

How is it 180 - 38

tho

[patent jetty]

Angle sum=180

[icy cape]

yes but why are u subtracting 38

[patent jetty]

x+x+38=180

Where x is one of the base angles

[icy cape]

bro how is 38 involved

how are they equal*

[patent jetty]

Cuz it's part of the triangle

[icy cape]

as in O and 38

[icy cape]

huh

[patent jetty]

Dude

[icy cape]

how is O equal to 38

[patent jetty]

A is

I'm talking about the big triangle

[icy cape]

yea ik but we're solving for a

not A

[patent jetty]

I know

[icy cape]

so why are u doing big trinagle

[patent jetty]

But it will still help

[icy cape]

triangle

ok

sure

[patent jetty]

Trust me

[icy cape]

ok

yes I see what u mean now

that u said big triangle

[patent jetty]

Ok so we find x

We can ryt

[icy cape]

yes

ofc

180-38 = 142

/2 = 71

[patent jetty]

Yup

[icy cape]

wait the tangent perpendicular to radius = 90 so 90 - 71 = a?

[patent jetty]

Ye

[icy cape]

Oh damn

[patent jetty]

19

[icy cape]

lets go

🙂

[patent jetty]

👍

[icy cape]

thank you very much sir

have a great day 🙂

.close

[obtuse pebble]

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[lament atlas]

is the composition of an increasing and decreasing function decreasing?

[royal basin]

do you know the definitions of "increasing function" and "decreasing function"?

if you do it's not hard to apply those definitions to verify your statement.

[lament atlas]

i think so

increasin is when f(x+1) >= f(x)

i don't know if this is the right way to write it

[royal basin]

incorrect

there exist functions f which satisfy f(x+1) ≥ f(x) but aren't increasing

[lament atlas]

and it has to be continous?

[royal basin]

there exist functions f which satisfy f(x+1) ≥ f(x), are continuous, yet fail to be increasing.

[lament atlas]

idk so

can you tell me the right definition please

nvm let me google it

if f(b)>=f(a) for all b>a,

this one right

[royal basin]

wording, but yes

a function f is (weakly) increasing if for all a and b in its domain, a < b implies f(a) ≤ f(b)

[lament atlas]

thank you

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[karmic scroll]

Q3... please help me to prove that with proper explanation

[royal basin]

,rccw

[stable rain]

well

use sum of angles on a line = 180

then find an equation for PQS and PRT

show those are equivalent

[thick oracle]

You can say that PQS=180-PQR

And PRT=180-PRQ

But you know PQR=PRQ

I'll let you continue from here

[karmic scroll]

Ty gusy

.close

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[bleak isle]

.help

[obtuse pebble]

Commands:
clopen: .close, .reopen, .solved, .unsolved
consensus: .poll
factoids: .tag
help: .help

Type .help <command name> for more info on a command.

[bleak isle]

.solved

[near jacinth]

How do I find the domain of this function?

Is it -inf to inf?

[meager shell]

yes R

[obtuse pebble]

@near jacinth Has your question been resolved?

[near jacinth]

Then why are they defining it from 0? 😭

It’s shown [0,2pi) why isn’t it (-inf, inf)

https://tenor.com/view/why-isnt-it-possible-christian-bale-patrick-bateman-american-psycho-why-is-it-impossible-gif-18161290

[obtuse pebble]

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[timid silo]

Why am i getting two values here?

[rain forge]

Because in the second he applies division first only with 41,5 and add 60

But in the first he add 60 plus 41,5 and divide them by 2

[timid silo]

That makes sense

Thx

.close

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[quick hazel]

.close

[obtuse pebble]

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[timid silo]

The problem I am trying to solve is finding the reflected pt of (2,2) over the line y=-0.5x+2

[timid silo]

This gave me a wrong result

[thick oracle]

[timid silo]

https://drive.google.com/file/d/10ifLcbOLtHNpu0nfWl61DXs87ipIK9hY/view?usp=drivesdk

[thick oracle]

[timid silo]

?

[thick oracle]

How do i know it's not a virus

[timid silo]

The drive one?

[thick oracle]

Both

[timid silo]

Well the drive one is not a download

ok i can tell you what i tried, so to find the pt i first applied a vector to make the line go through the origin, then i appled a rotation matrix to align with x axis, then a x axis reflection matrix and then i reversed the process.

to the vector 2,2 that is

[vital dew]

@timid silo do you know the equation for the reflected point?

[timid silo]

well i know the coordinates that i got for it

dont know abt eqn tho

[vital dew]

write the equation of the straight line in the form ax+by+c=0

[timid silo]

then that would be -0.5x-y+2=0

[vital dew]

take the co-ordinate of the reflected point as (alpha+ at , beta + bt)

t is a parameter

[timid silo]

oh wait.

im so sorry, i just realized i have to leave

my apologies

[vital dew]

to find t

t = [-2(a * alpha + b * beta + c)]/a^2 + b^2

no problem

[timid silo]

.close

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[primal idol]

Simple question on vectors.

Is an unit vector same as the direction?

The hat notation on the v means direction, right?

[royal shard]

i dont know the formal definition, but a direction vector should always be a unit vector so i would say so, yes

the hat means that it is normalized, meaning it has length 1

[primal idol]

I see.

That's an unit vector right?

Just double checking.

[royal shard]

oh scalar products, that has been half a year and i feel so rusty haha

[primal idol]

Yeah you recognize it!

There are notations proj and scal that you could easily recognize. Nvm lol.

[royal shard]

yeah i noticed the weird brackets

[rigid lintel]

$\frac{\mathbf{v}}{|\mathbf{v}|}=\left\langle\frac{3}{5}, \frac{4}{5}\right\rangle$

[warm shale]

heavy

[rigid lintel]

the right part is a vector actually

really dumb vector notation imo

since its easily confused with an inner product

but yes that is a unit vector since 3^2 + 4^2 = 25 and 25/25 = 1

[royal shard]

oh yeah, i was confused a bit
i thought it was the scalar product but it is indeed a vector

as i said, im rusty haha

[obtuse pebble]

@primal idol Has your question been resolved?

[obtuse pebble]

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[bleak skiff]

Hello, I have a quick question, what does it mean : R is a relation xRy when there is i in {1, 2, 3, 4, 5, 6} where x and y in Ei

??

[warm canopy]

Post the original question

[bleak skiff]

The ask me to to find the E6 set

But I don’t understand the relation

[warm canopy]

What set is the relation R defined on

[bleak skiff]

Real number

[warm canopy]

I don't know what you mean by find the E6 set

[bleak skiff]

They ask me to find E6 interval

[warm canopy]

Oh, is it an equivalence relation

[bleak skiff]

yes

What is E6 if we want R to be an equivalence relation

[warm canopy]

Then you just need to recall that the equivalence classes of an equivalence relation partition the set

And perhaps remind yourself what a partition is

[bleak skiff]

Ok wait

I don’t have my notes with me I guess that’s why I didn’t understand I’ll check that at home

.close

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[high raft]

hey I'm going through Epp book and I encountered this example that I didn't understand

[high raft]

this is their solution

I don't understand how p(k+1) is the highlighted statement
why not a sub k+1

this is section is about strong induction btw

[obtuse pebble]

@high raft Has your question been resolved?

[obtuse pebble]

@high raft Has your question been resolved?

[viral blade]

P(k+1) should be the sentence "a_k+1 is even"

the highlighted statement is not P(k+1), maybe it's a mistake in the book

[high raft]

yeah I believe it's a mistake, thanks

[obtuse pebble]

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[smoky tusk]

Could someone explain to me how my answer is incorrect? I feel really lost, it feels like I’ve done every step correctly…

[smoky tusk]

<@&286206848099549185>

[glossy basalt]

hello

[glossy basalt]

the final step seems incorrect

[smoky tusk]

Okay thank you I will look at that

[smoky tusk]

Thank you!!! 🙏 it was 1.5 x 10^-12

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[timid silo]

Please can someone guide me through the second line?

Its using the double angle formula Cos2x?

[brisk grove]

yes

like i dont see them using it yet but

its clearly written

cos(2x) = 1 - 2sin^2(x)

[timid silo]

So Cos2x = cos^2x + sin^2x

[brisk grove]

no

$\cos(2x) = \cos^2(x) - \sin^2(x) = 1 - 2\sin^2(x) = 2\cos^2(x) - 1$

[warm shale]

RedstonePlayz09

[timid silo]

1. Why is it cos^2x - sin^2x and not the cos^2x + sin^2x. 2) How does it get turned into 1-2sin^2x?

[brisk grove]

Are you asking how to derive it?

for ur second question, just use the fact that cos^2(x) = 1 - sin^2(x)

[timid silo]

Have you just added the -sin^2x to the other -sin^2x

Ah yeah I see

For the first question. Its just that in the formula book there is the COS(A+/-B) = COSACOSB -/+ SINASINB

[brisk grove]

yes

cos(2x) = cos(x + x)

and you can use the formula for cos(a + b) to derive it

[timid silo]

ahh okay, I see

[brisk grove]

so any other questions?

[timid silo]

Thats alright now I think cheers

.close

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[mental cosmos]

we roll a die 20 times, let $X$ be the number of times that an even result is received, let $Y$ be the number of times that the result "3" is received, find $\mathrm{E}(X+Y)$

[warm shale]

metnal

[mental cosmos]

any ideas?

[wooden cipher]

Since the dice rolls are independent, wouldnt it be 2/3*20

[mental cosmos]

i have no intuitive idea of what E is

all i know is that $\mathrm{E}(X)=\sum_{i} X_iP_i$

[warm shale]

metnal

[wooden cipher]

Whats the probability of getting an even number or a 3

[mental cosmos]

even number thats 1/2

a 3 thats 1/6

4/6

2/3

oh

hmmmmmm

but why multiply that by 20

20 trials

but why is the probability the same

because theyre independent

did you inexplicitly use this formula when finding that expression? @wooden cipher $\mathrm{E}(X+Y)=\mathrm{E}(X)+\mathrm{E}(Y)$

[warm shale]

metnal

[wooden cipher]

Not really

[mental cosmos]

oh thhe probabbility of X+Y itself is 2/3

or is it

[wooden cipher]

Eg if the problem said an even number or a number >=5, it would still be 2/3

[wooden cipher]

This pretty much yeah

[mental cosmos]

what about $\mathrm{Var}(X+Y)$

[warm shale]

metnal

[obtuse pebble]

@mental cosmos Has your question been resolved?

[gilded needle]

did you make any progress on this? X and Y are not independent, so Var(X+Y) is not simply Var(X) + Var(Y)

[obtuse pebble]

@mental cosmos Has your question been resolved?

[obtuse pebble]

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[strange fiber]

If there is 8 digit number made only from (1,2,3,4) and each number can appear maximum twice, how many options do we have to construct such a number?

[daring rock]

First thing to notice is that if each number can appear a maximum of twice, then each number must appear exactly twice

Since there are only four numbers

and eight positions

[strange fiber]

yeh

i think it is

4x4x4x4x3x2x1

[daring rock]

I see what you're thinking but that doesn't quite work, because you may still have 4 options by the time you get to the fifth position

For example, if you start
1234
then you still have all four options for the next spot

Think of it this way. This is the same as asking:

How many unique permutations are there of the string

11223344

Does that help at all? You might know a formula for permutations with repeated symbols

[obtuse pebble]

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[timid silo]

how do you even go about factoring this?

[timid silo]

just finding the gcf?

[dusk ruin]

yup

is there any part of it in specific you're having trouble with?

[timid silo]

oh sorry for not responding i didnt have discord open

[dusk ruin]

no worries lol

[timid silo]

but yeah im not really sure how to pull out the gcf in this problem

[dusk ruin]

you took like three minutes, that's 10x better than the average person I don't ping

[timid silo]

lol

[dusk ruin]

well really if you're struggling with factoring something it's best to split it up

ie turn xy^2=x*y*y

sometimes exponents make things too confusing

[timid silo]

one sec let me split it up

okay so it looks like i can only pull out one x and one y

[dusk ruin]

yup

[dusk ruin]

mmm that is wrong though

you only took one x or one y from each section

instead of taking one of each from both

[timid silo]

ohh

okay one sec

ohhh this is starting to look like one of those problems

[dusk ruin]

yup that looks better

and from there, you can factor it once more

though this time it's not taking out a common element (taking xy from both, for instance), but splitting one more complex term into two (or more) simpler ones

[timid silo]

awesome thanks!

i think thats the answer

[dusk ruin]

no problem!

that is correct :D

it was my pleasure to help

[timid silo]

thanks for clearing that up! : )

.close

[obtuse pebble]

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[celest glacier]

In the following, use The approximate function p with p(x) = -0.275x^2 + 4.4 and t with t(x) = 4.4 * cos((pi/8)*x) of another arc.

Confirm by calculation that the maximum difference of the function values of the approximate function p and t in the interval [-4; 4] is assumed to be x1 = 2.798 and x2=-2.798, and determine it.

[celest glacier]

How can I solve this i tried to get the first derivative of px - tx but I cant solve for x.

[obtuse pebble]

@celest glacier Has your question been resolved?

[celest glacier]

<@&286206848099549185> Pls Help I have no idea

[celest glacier]

Anyone?

[tardy epoch]

show your attempt

should be setting $p'(x) - t'(x)=0$ and solving for $x$ for $-4 \le x \le 4$

[warm shale]

riemann

[celest glacier]

x = 4.4*(pi/8)*sin((pi/8)*x)/0.55

This is what I get but no clue how to solve for x tbh

[tardy epoch]

show your entire work

picture is fine

[celest glacier]

My last steps

[tardy epoch]

there's a special value that satisfies both sides

ignoring all the slopes and period terms, do you know when $x = \sin(x)$?

[warm shale]

riemann

[celest glacier]

No not really

Sorry not that good when it comes to math...

[tardy epoch]

,w plot y=x and y=sin(x)

[warm shale]

Results provided by WolframAlpha

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Requested by riemann#2529

[tardy epoch]

can you see it from the graphs?

[celest glacier]

0

[tardy epoch]

[celest glacier]

But not sure how this helps me

[tardy epoch]

setting the derivative equal to 0 means you find where your difference is maximized or minimized

in this case you don't care if it's a min or max

[celest glacier]

-0.55x + 4.4*(pi/8)*sin((pi/8)*x) = 0

So this step right?

(This is the derivative)

[tardy epoch]

you've already found WHERE the derivative is 0

you want to know the value of the function where the derivative is zero

it just happens in this case that x=0

[celest glacier]

But How do I confirm it?

"Confirm by calculation that the maximum difference of the function values of the approximate function p and t in the interval [-4; 4] is assumed to be x1 = 2.798 and x2=-2.798, and determine it."

I thought I will get -+2,798 by calcuating it

[tardy epoch]

function where the derivative is zero means you plug in that value you found into your function

[celest glacier]

x = 4.4*(pi/8)*sin((pi/8)*x)/0.55

So i substiute 2,798 for x?

sorry the other way arround?

[tardy epoch]

function is p(x) - t(x), not the derivative

[celest glacier]

So I put the 2,798 in that?

Sorry for asking like an absolute idiot

[tardy epoch]

oh 0 was the local min

,w max -0.275x^2 - 4.4 * cos((pi/8)*x) for -4 < x < 4

[warm shale]

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Requested by riemann#2529

[celest glacier]

So this is the solution?

[tardy epoch]

,w plot abs(-0.275x^2 - 4.4 * cos((pi/8)*x)) for -4 < x < 4

[warm shale]

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Requested by riemann#2529

[tardy epoch]

nevermind this was wrong

[tardy epoch]

@celest glacier can you confirm i input the difference between your two functions correctly

i might have missed a minus sign somewhere

[celest glacier]

Looks right to me

[celest glacier]

I have here another +4,4

so -0.275x^2 +4,4 - 4.4 * cos((pi/8)*x)

[tardy epoch]

oh okay then this was right after all

,w plot y= -0.275x^2 + 4.4 - 4.4 * cos((pi/8)*x) for -4 < x < 4

[warm shale]

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Requested by riemann#2529

[tardy epoch]

not sure how to find other solutions of the other two critical points

but yea it is indeed those two points

,w solve 0 = -0.55x + 4.4 * pi / 8 * sin((pi/8)*x) for -4 < x < 4

[warm shale]

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Requested by riemann#2529

[tardy epoch]

either Newton's method or some taylor series approximation

or maybe there's some other method i'm missing

give this a read for the general approach since you seemed to have some questions: https://tutorial.math.lamar.edu/Classes/CalcI/AbsExtrema.aspx

[celest glacier]

Thanks so much

@tardy epoch But still not sure how they get x=-+2,79813

So lets say x is -4 < x < 4. I say x = 1

I get something else ...

[tardy epoch]

And?

[celest glacier]

So how do they get the x=-+2,79813 lul

[tardy epoch]

Because you made up x=1

Don't make up values

[celest glacier]

But what is the calculation to get x=-+2,79813

I'm not understanding this part.

[tardy epoch]

.

[celest glacier]

Ah sry

[tardy epoch]

You absolutely need to read this

[obtuse pebble]

@celest glacier Has your question been resolved?

[obtuse pebble]

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[strange stag]

Oh it’s flipped :(

Sorry lol

[obtuse pebble]

Channel closed

Closed due to the original message being deleted

[strange stag]

Well

[nocturne minnow]

Fyi people could have rotated it for you

,rotate

[nocturne minnow]

Like that

[strange stag]

Yep I come into this server once every 3 months so I’m not really versed on the commands available xP

[nocturne minnow]

Anyways

This channel will close

So you need to open a new one

[strange stag]

its the cycle of life

[obtuse pebble]

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[strange stag]

thats it, im specially confused where am i gonna pull this constant vector from considering that r is a position vector. is it constant? doesnt make sense to me :(

this question is actually my eenglish translation of a training exercise my fluid dynamics teacher gave me xP

[obtuse pebble]

@strange stag Has your question been resolved?

[obtuse pebble]

@strange stag Has your question been resolved?

[strange stag]

I can clarify anything to help you help me :)

I’m supposing I just have to assume that gradient of P can be written as the gradient of phi by rearranging the terms below

But then who would a be?

[obtuse pebble]

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[shadow lava]

https://tenor.com/view/wrong-drumpf-trump-stupid-gif-6220235

Can someone explain why I’m not allowed to do this for my answer?

[gilded needle]

is there an actual question

ignoring denominators:

the LHS is -5 - 12sqrt(3)

the RHS is -(5 - 12sqrt(3)), which is -5 + 12sqrt(3)

i.e. the - sign in front of the fraction on the RHS applies to the entire numerator, not just to the 5

[shadow lava]

Or the - sign in front of a fraction can apply to the entire denominator.. if there was a long form polynomial in the denominator

[gilded needle]

yea, you can apply it to either the denom or the num

(not both)

but for comparison with the LHS it's more useful to apply it to the num

[shadow lava]

How do you know if you should apply negative sign to the numerator or denominator if you get a fraction like this?

[gilded needle]

you can apply it to either one

[shadow lava]

It feels weird.. numerator has 3 sign changes.. denominator only has 2 sign changes

Wouldn’t that alter the final answer to be a different sign?

Depending on which one you go with

[gilded needle]

no..

[shadow lava]

Interesting..

[shadow lava]

But what I have done is illegal, right?

[gilded needle]

the number of sign changes doesn't necessarily imply anything about the overall sign

[shadow lava]

Interesting..

[shadow lava]

But this is still wrong, yeah?

[gilded needle]

yes

[shadow lava]

I’ll try again with proper factoring of the - sign. That’s really what’s going on here

Like having -1 in front

[gilded needle]

if you assign the - to the numerator in both fractions, you get:

[shadow lava]

This looks weird but technically it’s correct?

[gilded needle]

$$-\frac{5}{26} - \frac{12\sqrt{3}}{26} = \frac{-5}{26} + \frac{-12\sqrt{3}}{26} = \frac{-5 - 12\sqrt{3}}{26}$$

[warm shale]

Bungo

[shadow lava]

I went with denominator instead just to see if I can do that

Keeping the numerator the same

So now I can choose where to distribute the negative.. numerator or denominator

It’s sloppy I know, but just as a test..

• sign in front can be -1/1 or 1/-1

Actually

I just realized something

I can’t have 5/-26 for the first fraction anyways

[next reef]

you mean, realized?

[shadow lava]

Both denominators must be the same

[shadow lava]

iPad autocomplete

[next reef]

You can just factor out -1, it's so easy

[shadow lava]

So if I wanna subtract these fractions, I need - in the numerator anyways

[shadow lava]

It is yes, but I was thinking distribution could lead to problems with - in front

Now I see it more clearly I think

If I see - in front of a rational, it depends .. addition or multiplication .. they handle it differently

In terms of what is allowed and not allowed with the - in front

• can lead to many silly errors in algebra if not careful …

I think because we assume it’s similar to addition.. which it is.. but for distribution you gotta put that - for every term in the argument

If you call brackets with terms in it for distribution the “argument”

Or maybe argument is a reserved word for functions only

https://tenor.com/view/going-crazy-willem-dafoe-grin-smile-gif-16959907

[obtuse pebble]

@shadow lava Has your question been resolved?

[obtuse pebble]

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[wide oracle]

do i keep this as -1(x+40)^2+1500 or (-x-40)^2+1500?

[wide oracle]

because its asking for y=a(x-h)^2 and im not sure if I want to keep (a)

[gleaming ridge]

a can be 1

[wide oracle]

but doesnt that change the parabola?

[gleaming ridge]

I said 1, not -1

[wide oracle]

let me take another example, I wouldnt be able to mulitply the 7 inside right?

[gleaming ridge]

true

[wide oracle]

.close

[obtuse pebble]

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[solar flower]

I need help on a question involving percentages. The question states that a chemist needs 6 liters of a %50 salt solution, but only has %20 salt solution and %70 salt solution, and how much of each to mix to get the desired amount and conentration.

[solar flower]

I can understand that 0.2x + 0.7y = 0.5*6.

So, 0.2x + 0.7y = 3 but I am stuck because there are two variables and I can't understand how to solve for one in this instance.

Nevermind, figured it out just now

.close

[obtuse pebble]

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[timid silo]

$A - 4B = -12$ and $-B - 4A = 18$
can someone solve this equation for me ,

[warm shale]

'🌌

[timid silo]

for a & b

[proud moon]

another way would be to substitue in the number

for instance make B=-18+4A

then replace the first equations B with -18+4A

so then A-4(-18+4A)=-12

A+72-16A=-12

-15A=-12-72

[timid silo]

is this supposed to equal -12

4.641666667 - 4*(17/30)

[proud moon]

15A=60

[proud moon]

nah i made a slight calculation error

so ignore my previous steps

ok i fixed it

@timid silo

you see how you could replace the B with A

right

[timid silo]

yea

[proud moon]

so make the second equation be B=-18-4A

right

since you have this B value

and the first equation also has A-4B=-12

then you could replace the B in the equation with -18-4A cause they are equal right

@timid silo

[timid silo]

that's a good way to do it thx

[proud moon]

this means that A-4(-18+4A)=-12 right?

[timid silo]

ig

[proud moon]

now what you could do is expand it out so A+72+16A=-12

so then 17A=-12-72

-17A=-84

[timid silo]

18+4*5.6 = B

[proud moon]

uh i made a slight error earlier

my head is not functioning atm

[timid silo]

okk it's alr

[proud moon]

A=84/17

ok now it's good

i accidentally forgot to multiply the 18 by -1 when i first simplified for B

basically what you wanna do in this case is isolate A or B and then substitute it in right?

after wards its alegra until you get one number which in this case A = 84/17

now you plug it in

so -84/17-4B=-12

-4B=-12+84/17

-4B = -204/17 +84/17

B=-120/17/-4

B= -30/17

[timid silo]

(-12 -(84/17))/-4 = B ?*

[proud moon]

nah it should be around 30/17

A= -84/17 and B=30/17

[timid silo]

084 = 84

alr ill plug them back in the original equation see if it works

[proud moon]

@timid silo

typo by accident

it was supposed to be -84/17

not 084

@timid silo

@timid silo

[timid silo]

ok

[proud moon]

plut in A=-84/17 and B = 30/17

also the mistake in the algebra earlier that made it hard to solve for B was that I accidentally forgot to write 84/17 as -84/17

that made it hella hard

step 1: isolate A or B

step 2: substitue in the value for A or B

step 3: solve the new equation

step 4: plug in the value back to solve for other variable

step 5: check your work

[timid silo]

ty it works

the things is that i did the first method yesterday but when i added -b + -16b , for some reason i wrote -15b

[proud moon]

ah ic

[timid silo]

ig my heads not functioning sometimes also

.close

[obtuse pebble]

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[obtuse pebble]

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[dark sonnet]

how do I know if these are augmented matrices ?

[obtuse pebble]

@dark sonnet Has your question been resolved?

[frosty spoke]

they're not

Nul A means the set of vectors v such that Av = 0

Col A means the set of vectors in the span of the columns

Row A means the set of vectors in the span of the rows

there's no augmenting done here

[gilded needle]

it wouldn't make much sense to talk about the null space, column space, and row space of an augmented matrix

i would assume that they are ordinary matrices

[obtuse pebble]

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[fathom mica]

I came across this and haven't still figured it out.

[grizzled shore]

Draw a diagram

[fathom mica]

Bro i won't work

Maybe tan 20°=x/35

[grizzled shore]

Try draw the information

Into a diagram

[fathom mica]

Hmmm

[obtuse pebble]

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[covert dagger]

The first ones the question the second one is my work

[covert dagger]

I'm confused on how to even approach this question after what I just did

[frosty spoke]

okay, so you know that r_2 = 3r_1

might make sense to say something like 3OA = OB

[timid silo]

r2 is the radius of larger circle, so r2 has to be larger

[covert dagger]

Ohhh yes

Ok so

Sooo what can I do after this?

[obtuse pebble]

@covert dagger Has your question been resolved?

[covert dagger]

Umm

[obtuse pebble]

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[timid silo]

Yo

[timid silo]

How did they simplify this

Whats the reasoning I dont get it

[grizzled shore]

Is there a picture coming

[grizzled shore]

f(x:y) >= 0

[timid silo]

Yeah

I meant the second line mb

Whats the thinking process to solve this

[grizzled shore]

Can you factorise 2k² - 3k + 1

[obtuse pebble]

@timid silo Has your question been resolved?

[timid silo]

Yeah

[grizzled shore]

Do it

[velvet shard]

help here

[grizzled shore]

#❓how-to-get-help

[timid silo]

We remove the 2 from m^2 and do everything else /2

Then sum-product

[grizzled shore]

Write it out

[timid silo]

Wait is it the same reasoning there

[grizzled shore]

Yes

xD

[timid silo]

Im dumb as fuck

[grizzled shore]

You got this!

[timid silo]

No I mean i get it now lmao

Didnt realize it

Thanks 🙏🏻🙏🏻

[grizzled shore]

👍

[timid silo]

!close

.close

[obtuse pebble]

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[real pike]

Our lecturer isn't very helpful and didn't go through this topic very well. We're meant to turn ds into dx I assume then turn it into polar coordinates, but I'm really not sure how to do it.

[obtuse pebble]

@real pike Has your question been resolved?

[warped fulcrum]

I think you have to get a parametrization of the circle first

[real pike]

How do I do that

[warped fulcrum]

Well a circle is really just (cos(t), sin(t))

But that is the unit circle

Can you then figure out how a circle with radius 4 would look like?

[real pike]

Is it 4cost 4sint then

[warped fulcrum]

Not quite

Oh yes sorry

I was thinking about something else lol

[real pike]

No worries

[warped fulcrum]

So you then have a parametrization of the circle

[real pike]

Right so what do I do with ds?

[real pike]

And how do I use that

[warped fulcrum]

Well the following then holds

You can read up more no it here https://tutorial.math.lamar.edu/classes/calciii/lineintegralspti.aspx

[real pike]

Ah OK so I can find dx/dt etc and get rid of ds

Ok

Thank you

[obtuse pebble]

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[obtuse pebble]

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[dusk garden]

I just want to make sure

this is equivalent right?

[glossy basalt]

nah

[knotty crow]

what's base of the log on the RHS?

[dusk garden]

ohh

[wise talon]

you might have gotten this confused with log a^b = b log a

[dusk garden]

if I want to use a calculator for log

how would I convert it?

[wise talon]

ah

logc(a) = logb(a)/logc(b)

where b and c are the bases

[wooden cipher]

...

U sure bout that one?

[dusk garden]

yeah im kinda confused

[wooden cipher]

Look up "log change of base"

logc(a)=logb(a)/logb(c)

You can use ln for logb because thats the case wheb b=e

[dusk garden]

ah I see

I think I'm good now

[wise talon]

oh my bad

I think I need sleep

[wise talon]

absolutely not

[dusk garden]

.close

[obtuse pebble]

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[stone raptor]

can someone explain why this is true?

[stone raptor]

is it like two vectors only have two cross product vectors (v) and -(v) or something

[viral blade]

a•(b-c) = 0 and a×(b-c) = 0

[stone raptor]

ok what does that mean lol

like significance of that

[viral blade]

what's a•(b-c) in terms of magnitudes and angle

[fleet knoll]

. and x is equal, no?

[viral blade]

The exception being if a=0

[stone raptor]

ok im not following

[viral blade]

what's the dot product of two vectors, in terms of their magnitudes and angles

[stone raptor]

|a||b|costheta

[viral blade]

so if the dot product is 0, what's the angle between them

[stone raptor]

pi/2

90 degrees

[viral blade]

right

now what about the magnitude of the cross product

there's a similar formula for that too

[stone raptor]

|a||b|sintheta

[viral blade]

right, so if that's 0, what can theta be

[stone raptor]

0

[viral blade]

indeed

or pi

so if the dot product and cross product of two vectors is 0, then their angle must be pi/2 and either 0 or pi at the same time

[stone raptor]

ok...

[viral blade]

the only way it's possible then is when one of the vectors is 0, and the whole notion of angles between vectors doesn't really work the same

[stone raptor]

so the angles cant be equivalent then one of vectors is 0

[viral blade]

yeah

so either a or b-c is 0

[stone raptor]

alright

thanks

[viral blade]

np

[obtuse pebble]

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[formal echo]

How would I start question 3a

[wooden cipher]

Find the tangent line

By taking the derivative

[formal echo]

Ok thanks

Then do I sub in 1 into the differentiated equation to find the gradient or do I not need to do that

[tardy epoch]

,rotate

[tardy epoch]

try both ways

[obtuse pebble]

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[timid silo]

what are they asking me to do with |AB|

i was under the impression that meant the distance

[high lily]

well yeah

they want the distance between points A and B

[timid silo]

yea i dont understand why i got it wrong the first time thank you

.close

[obtuse pebble]

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[viral quail]

The topic is simultaneous equations. Step by step how can I solve it using substitution?