precalculus

[lofty prism]

10

[finite wraith]

Fuck no

$f(x)=3x$

[obsidian monolith]

trece:

[lofty prism]

you are just going back . i guzss

a step backward

[finite wraith]

?? No

when you plugged (10) into g(x) you got 84 right?

[lofty prism]

ok sorry

[finite wraith]

Thats the OUTPUT that g(x) gave you

[lofty prism]

yes

[finite wraith]

now that OUPUT will act as an input for f(x)

[lofty prism]

84

[finite wraith]

so you have to do f(84)

[lofty prism]

not that OUPUT will act as an input for f(x)
@finite wraith thats where i must disagree with you

84 is an output
cant be an input

[past meadow]

Why not?

[finite wraith]

84 is a number

it doesnt have a tattoo on it saying "OUTPUT"

its literally just a number

[lofty prism]

it is already used by function g it cant be used by function f

idk if im clear

[finite wraith]

If you say so, then sure. (possible troll tbh guys)

[lofty prism]

?? im not a troll

[past meadow]

Do you think we just assign every number we can think of to some function and it cant be used as an input to any other function????

[lofty prism]

Do you think we just assign every number we can think of to some functuon and it cant be used as an input to any other function????
@past meadow at least in an exercise

idk sorry if im wrong guys ok

[past meadow]

Then you have some serious misconceptions.

[finite wraith]

you dont have to be sorry cus ur wrong, you have to be sorry for being ignorant

[lofty prism]

whats the difference

[finite wraith]

we say something, and your reply is "Nope, that cant be true"

[lofty prism]

ok sorry

for my behaviour

[finite wraith]

$f(g(x))$

[past meadow]

Can you just tell me where you got the idea that> @past meadow at least in an exercise
@lofty prism

[obsidian monolith]

trece:

[finite wraith]

this is what you had to calculate

[past meadow]

Oh it didnt quote the whole thing

[lofty prism]

i was told that nshool

school*

this is what you had to calculate
@finite wraith yes

g(10)=84

we need to calculate f(84). right

[finite wraith]

now plug 84 into f

to remind you, f(x) = 3x

[lofty prism]

f(x) = 3x
f(84) = 3*84 = 252
f(g(a))=252

[finite wraith]

yes it's 252

remember all functions do is take an input and play around with it, and then give you an output

[lofty prism]

Yes okay thank you

sorry for my behaviour

before

[finite wraith]

its ok

[lofty prism]

for the second part of th3 question i think we need to use perpendicular lines

product of their slopes if 1

is 1*

[junior sable]

when comparing g(x)=10^x to f(x)= x^10, in English we'd say that g(x) goes up by a power of 10 each time. What would we say for f(x)?

[lofty prism]

goes up by a power of x each time

[junior sable]

would you mind elaborating on that?

[lofty prism]

what is elaborating

[junior sable]

explaining more

[lofty prism]

i think goes up by tenth power is better

each time

[junior sable]

hmm. okay ty @lofty prism

[lofty prism]

Im Not sure

[patent beacon]

@junior sable
I think you're trying to relate f(n+1) to f(n). For 10^x, that's an obvious relation. You just multiply by 10.

"Goes up by" and "each time" are extremely vague, be careful there.

Now, you also asked about x^10. This case is very messy, there's no great way to relate f(x + 1) to f(x)

[junior sable]

gotcha ty kanye

[viscid thistle]

LOL.

[harsh cipher]

Hi everyone

I finished pre-calculus with 87%

Thanks to everyone in here who helped me through the way

Thanks @willow bear @uncut mulch and all others in honorable, helpers, and very cool ppl.

[remote veldt]

Congratulations! that's an awesome score

[viscid thistle]

I finished precalc with a 69.

[junior sable]

oh man Mirrion, my final is tomorrow. Hoping for the best. Congrats!

[past meadow]

Gl

You'll ace it

[junior sable]

Thanks! love mob psycho btw, huge inspiration.

[past meadow]

Yeah its sick

[junior sable]

Where can I drop a huge wall of text about how no one should take the online class I took?

[viscid thistle]

Here

doesnt drop it

@lofty prism your confusion may lie in intentionality vs extensionality of functions

the definition of a function completely ignores intentionality

it does not care how, why, or for what purpose the elements of the pairs the function consist of were chosen to be associated with each other

it only cares about what is associated with what

ugh I felt like I had a good tie in to the problem but I forgot it

[tiny sonnet]

I'm having trouble understanding this

Especially that last part

[pale bison]

take the interval (0, 1) for another example, 0 is the infimum (prove it), but 0 is not inside that interval

[tiny sonnet]

So you can get infinitely close to 0 but you can never hit it

[pale bison]

uh what are you trying to describe?

[tiny sonnet]

the interval (0,1)

Like you can go to 0.01, 0.001, 0.0001, and so on, yet you can never actually get to 0 right?

and 0 is smaller than all of those

So is that why it's the infimum?

[hexed ermine]

Lol pre-calc?

[pale bison]

infimum is the biggest number x, such that for all numbers in y in (0, 1), you have x <= y

well let's see what that number x can be:
if x is strictly positive, i.e. x > 0, then clearly, x/2 is also positive, and x/2 is in the set (0, 1), but x <= x/2 is not true
this means, x cannot be strictly positive

it could be negative, in fact, every negative number is smaller than any numbers in (0, 1)

but the biggest such x is 0

i butchered that sorry

[tiny sonnet]

wait

what is the set y?

wait so what does it mean by "if it exists"

You can have 2 supremims or infimums?

[pale bison]

no, it turns out that they're unique

(-inf, inf) for example, does not have a supremum or an infimum

[viscid thistle]

Why does wolfram tell me the domain of the following function is [-2,2)U(2,inf):

sqrt((x^2-4)/(x-2)).

How would I determine that algebraically? I arrived at the open interval (2,inf) because of the inequality under the radical, with the additional constraint it cannot equal zero as it's in the denominator.

Why can I pass a -2 into that bottom radicand? Sqrt(-2-2) is Sqrt(-4) and that doesn't give me a real output.

[blazing parrot]

$$\sqrt{\frac{x^2-4}{x-2}}$$

[obsidian monolith]

Not Chezstick:

[harsh smelt]

fraction is defined where denom is not zero

root is defined where expression under root is >= 0

so domain is the same as solutions to
$\frac {x^2-4}{x-2} \geq 0$

[obsidian monolith]

Commander Vimes:

[viscid thistle]

I understand the rational expression is defined when denom != 0 and the root requires an expression is greater or equal to 0. I think my error was to apply the quotient property sqrt(a/b) = sqrt(a)/sqrt(b) then focus on the denominator only.

Whereas obviously the numerator has the same condition >= 0

Thank you.

[alpine basin]

why are these no solution?

[uncut mulch]

what's the actual question

[alpine basin]

to "evaluate" them

[uncut mulch]

there are no real values x, such that 2^x is less than or equal to 0

[alpine basin]

ok

[uncut mulch]

consider the relation between exponents and radicals

[alpine basin]

ah right thanks

[alpine basin]

Why is it when I graph f(x)=2log(x) on desmos the line goes infinitely downard, but on my graphing calculator it stops at -2 and only goes on infinity horizontally

[remote veldt]

can you take a picture of your graphing calculator? desmos is correct

[alpine basin]

uh

yea lemme do that

[remote veldt]

try decreasing the x-window and see what happens

it might just be a display thing

[alpine basin]

its at the defaults im pretty sure

yeah -10 x min, 10 x max, same for y

cause the line goes off the screen horizontally

but the vertically it just stops so idk

[remote veldt]

I'm saying try changing the display window

to be, for example, x between -1 and 1

and see how it changes

[alpine basin]

nah still stops the same way

[remote veldt]

try graphing just ln(x)

not ln(-x)

[alpine basin]

yeah same exact thing, just not flipped

thats so weird

[remote veldt]

limitation of a graphing calculator ig

[alpine basin]

hmm

[remote veldt]

I guess a last thing to try is clearing calculator memory and trying it again

[alpine basin]

i guess its not that big of a deal

cause its still obvious it just goes down infinitely without actually touching the y axis

[autumn sphinx]

@alpine basin It is because of how quickly the function diverges. Graphing calculators tend to sample their function very sparsely, typically one sample per horizontal pixel. Because the final sample is infinite, it will basically return NaN or something equivalent and therefore the connecting segment to that infinitely-away-segment is not drawn. The result is that you get only the segment one pixel to the left, and at your limits, that happens to contact the vertical axis at a height of 2.

Desmos is able to sample much more finely than your graphing calculator (likely into the hundreds of thousands of samples), and so the point at which you get error-out will be much closer to the vertical axis, and in principle well off the bottom of your screen unless you set up some extremely wonky limits

Desmos may even have some tricks up its sleeve that allow it to bypass the limitation altogether, such as graphing the inverse of a function or doing parametric graphing, or variable-density sampling driven by nodes. I kind of doubt it, but it isn't impossible for tricks like that to be implemented cleanly

[pale bison]

@trim pecan

[viscid thistle]

@trim pecan Nerd.

[viscid thistle]

True or false: "The domain of f ◦ g consists of all values of x in the domain
of g for which g(x) != 0."

This is false, right? The condition g(x) != 0 may be relevant if the composed function is of the form of a rational expression with only g(x) in the denominator, or a log taking g(x) as an argument. But we could have a root expression (f o g) = sqrt(g(x))where the condition is g(x) => 0.

[compact pivot]

@viscid thistle
yes I think it is false

[rare zephyr]

help with no8

I tried 7! x 2 but the answer two that is false

i also dont get how to get around this "2 specific children want to sit on the same side" problem

Nvm i got it

[rare zephyr]

Help with no12

[blazing parrot]

You can treat each type as 1 object to group them together, then multiply by how the fruits of the type can be arranged

[rare zephyr]

ok got the answer

thx

[alpine basin]

Hi, this problem wants me to turn this into a single logarithm, and the answer is log3(7), but I was wondering how they got it

[viscid thistle]

log_a(1/x) = -log_a(x)

[alpine basin]

thats the problem

[viscid thistle]

use the thing i just sent to solve the problem

then figure out why it's true

(if you don't already know why)

[alpine basin]

so its the reciprocal kind of?

negative reciprocal

[uncut mulch]

power law

technically it's already expressed as a single log

[alpine basin]

okay thanks

[alpine basin]

How would I solve this exponential equation?

[uncut mulch]

consider the powers of 2

[alpine basin]

not sure what you mean

[uncut mulch]

1/2 = 2^?

8 = 2^?

[alpine basin]

8=2^3

1/2=2^-1

hmm ok

i think i got it

How do you know what base to use though?

[patent beacon]

Usually the smallest possible prime

[alpine basin]

I solved this problem and ended up getting x=5, x=2. But the correct answer is only x=5, so I was wondering why it wouldn't be both in this case

[uncut mulch]

logs of negatives aren't defined over the reals

[jade heron]

On the left hand side we have log(2)
On the right hand side we have log(6-10) - log(2-4)

[viscid thistle]

@alpine basin buckets, when x = 2, the values inside the logs become negative, and that can't happen

[pale bison]

||let's see how many times will people explain the exact same thing but differ slightly||

[viscid thistle]

Lmaoooooo

[hard hornet]

log(negative) = illegal

[remote veldt]

@alpine basin adding some new information, the reason that it shows up as a solution is that when you use

$$\log(a) - \log(b) = \log\left(\frac{a}{b}\right)$$

you're implicitly assuming that both $a$ and $b$ are greater than 0. In this case, when $x = 2$, both 3x - 10 and x - 4 are negative, so their quotient is positive. If the problem had been solve

$$\log(x) = \log\left(\frac{3x - 10}{x - 4}\right)$$

You would be correct! but the fact that the logs are split initially restricts the domain, and you need to respect that for the entire problem

[obsidian monolith]

Nicholas:

[viscid thistle]

$\xcancel{\xcancel{\xcancel{\xcancel{\xcancel{\xcancel{\xcancel{\xcancel{\log(-a)}}}}}}}} $

[obsidian monolith]

HoboSas:

[viscid thistle]

With a positive

[tawny nacelle]

hah new record 5 people explained the same thing but slightly different

[viscid thistle]

log(-) bad

[tawny nacelle]

hurr durr log no negative input

7 now

[viscid thistle]

i made a similar mistake at some point in highschool and i lost points for the question

proof by high school teacher

lost marks, therefore log(negative) making sense in R must be impossible

there, 6 people

[tawny nacelle]

but i was the 7th person to explain it

[viscid thistle]

i didnt count sorry

or maybe i cant count...

[tawny nacelle]

i assume the latter

[viscid thistle]

as would i

[willow bear]

this conversation is pointless

[viscid thistle]

wow

[tawny nacelle]

is it tho

[viscid thistle]

no fun 😔

[wide ocean]

help with no8
@rare zephyr what was the answer to number 8?

[rare zephyr]

325

[maiden pebble]

https://i.imgur.com/7CgVAfr.png

How are the limits 2+2 ?

shouldnt they both not exist?

[willow bear]

lim f(x) and lim g(x) each individually do not exist, yes

but lim (f(x) + g(x)) exists since the jump discontinuities in f and g cancel each other out perfectly once the functions are added

f jumps by -2, g jumps by +2

[maiden pebble]

oh, thats peculiar

[haughty cave]

Could anyone possibly help me with this? Idk if it's how the problem is worded but I'm not even exactly sure where to start

[willow bear]

$i^i = (e^{i \pi/2})^i$ is what you're expected to use, i guess

[obsidian monolith]

Ann:

[jade heron]

i^i is multivalued

Maybe try rewriting it in terms of exp( of something ) as ann said

[alpine basin]

How would I solve this problem? Help appreciated

[viscid thistle]

draw it out

[alpine basin]

wat

[viscid thistle]

draw it out

[alpine basin]

wat

[viscid thistle]

Draw it out

@alpine basin srsly, have you drawn it

draw it out

[alpine basin]

The problems similar to this had nothing to do with drawing it out so nah

Didnt think that was needed

[viscid thistle]

ALWAYS DRAW YOUR GEOMETRY PEOBLEMS

Its a way to help you fcking visualise it

First rule of geometry

^

[alpine basin]

i mean..

[viscid thistle]

It's like watching a movie without eyes

[fluid shore]

I've watched movies without eyes, fite me

[viscid thistle]

i mean..
@alpine basin you mean??

[alpine basin]

its not needed tho right?

[viscid thistle]

[alpine basin]

lol

[fluid shore]

Mission Impossible Fallout didn't have eyes, as far as I'm aware.

[viscid thistle]

Draw. It.

[alpine basin]

imma just get more confused tryna draw it when i have to do it on a test

[viscid thistle]

You won't understand it if you don't have a general idea of what you are doing

imma just get more confused tryna draw it when i have to do it on a test

imma just get more confused tryna draw it when i have to do it on a test

[alpine basin]

wut

[viscid thistle]

Okay

Its fine

[fluid shore]

There's not much point in helping someone who refuses to help themselves.

[viscid thistle]

We surrender

Go blindfolded through your problems

Good luck

Jokes apart, draw your geometry and eat your veggies

[alpine basin]

so converting the andle to radians and then multiplying it by the radius is not good enough, you think I should graph it?

[dusk mulch]

Quick question: Theta=5 just means 5degrees right?

[uncut mulch]

depends on context

[viscid thistle]

If there is no ° then its radians

[dusk mulch]

Makes sense

ty

[viscid thistle]

Well first off writing 5 alone to express an angle without units is ugh

^^

Radians don't have unit though

True i mean like a word after it

[viscid thistle]

Wow

[dusk mulch]

this is what I have

[viscid thistle]

My eyes

that mean theta equals 5

What's the problem?

Context

[dusk mulch]

What quadrant its in, but thats the easy part

Anyways, im good now ty

[viscid thistle]

np

stay blessed

It probably means degrees tbh

Why would it

5 degrees is a nice thing while 5 radians is weird

5rad is a lot tbh

But who knows

And this is probably something very introductory

What does the rest of the page look like @dusk mulch

no unit = radians

I know but not all math is written properly

Maybe the student hasn’t even been introduced to radians yet

[dusk mulch]

I have

I'll know in about a minute if its wrong or not, just have to input my answers

[viscid thistle]

Make your bets guys

[dusk mulch]

lol

[viscid thistle]

Everything on radians

If the book is wrong I won't lose anything

Everything on radians for me too

[dusk mulch]

For those who bet on radians

......

you are bringing home the money

[viscid thistle]

Yes

Nice

Ez

YES

Gottem

[dusk mulch]

Hoping someone can help me set up a framework to solve these

[viscid thistle]

What you got so far?

[white beacon]

What does central angle of 6 radians mean?

[dusk mulch]

I think that just means the perimeter or the circle is 65 cm

6 radians is an entire circle right?

[viscid thistle]

Vertex on center of circle

6 radians is an entire circle right?
Almost

[dusk mulch]

HAving trouble understanding that a central angle is

Sorry for the odd spelling guys, just started using a split keyboard

[white beacon]

Ah i see a radian is $1 rad = \frac{360^\circ}{2\pi}$

[obsidian monolith]

achilles199703:

[dusk mulch]

So 6 rad = aprox 344 deg?

[viscid thistle]

This is my work

I know it's beautiful you don't have to tell me

Nice drawing

[dusk mulch]

lol

[viscid thistle]

Thanks

[dusk mulch]

Your helping me with math, I wont judge

[white beacon]

does intercept mean something like intersect?

[viscid thistle]

The world of art has lost so much without you hobo

I know

Your helping me with math, I wont judge
Im mobile, that's the best I can do

Wait

Why did I draw a chord

Wait i dont even understand the question

It's weird

[white beacon]

Ah okay i think i get the question now:
We are looking for a radius of a circle which is big enough that the cut out of the last missing degrees to form the entire circle is exactly the arc with 65 cm or am i wrong

With cut out part i mean the angle of 6 radians only covers about 344° of the outer perimeter (no clue if you would call it that), so the last 16° are missing from the circle and the arc is supposed to go there

[viscid thistle]

How about this

[white beacon]

yay that was my thinking, but the question is worded so weird that i have a hard time understanding it, because a 1 to 1 translation of this is only garbage

Well you have to fill in the gaps but from this point forward it shouldn't be too hard to compute, i guess

[uncut mulch]

the intercepted arc would be the major arc

[dusk mulch]

If it clears anything up, there looking for a answer in CM

[white beacon]

the intercepted arc would be the major arc
@uncut mulch so it is the inverted picture then?

So intercepted would mean the area, which is coverd by the 6 radians?

[uncut mulch]

arc not area

[white beacon]

sorry my fault, meant that

If it clears anything up, there looking for a answer in CM
@dusk mulch you are looking for the radius r in cm i presume

[dusk mulch]

I think I may have found the answer using the formula S=R(Theta)

[white beacon]

what is s

[uncut mulch]

arc length

[white beacon]

length of segment?

ah ok

[viscid thistle]

My drawing was better

[uncut mulch]

you labelled the wrong arc though

[viscid thistle]

Not important

[white beacon]

Because he drew my thought, which was ultimatly flawed

[uncut mulch]

ic

[dusk mulch]

How the fuck do I work with miles? Do I just do the same thing but express my answer in a diff unit?

[uncut mulch]

pretty much yeh (also convert ° to radians)

[white beacon]

you can simply assume that there is no unit

in your formula the result for 6cm and 6miles are the same because regardless which you compute, you would just chuck in 6 in the formula and add the unit back later

Well thats what i would do if you don't have to convert from one unit to another

[alpine basin]

Why is the answer to this problem -4/5 and not 4/5? If its in quadrant 2 shouldnt both points be positive

[viscid thistle]

Points in 2nd quadrant have negative x

[alpine basin]

Oh oops

[dusk mulch]

When I start turning my deg to rads

Would I do 1/60(8) gives me 8/60 or is it 8/480?

[viscid thistle]

The 8/60 one.

@dusk mulch

$s=r\cdot \theta$ where $\theta$ is on radians

[obsidian monolith]

Al𝟛dium:

[dusk mulch]

I got this wrong and Im not sure why

1/60(8) = 8/60 deg = 0.002 RADS

3960 (0.002) = 7.92

Maybe I just didint understand the question correctly

[white beacon]

Maybe I just didint understand the question correctly
@dusk mulch Can't help you there, cause i am stuck at the word subtends, i thought my english was good

[uncut mulch]

rounding too early

[viscid thistle]

^

[uncut mulch]

,calc 8/60 * pi/180

[obsidian monolith]

Result:

0.0023271056693258

[uncut mulch]

,calc 8/60 * pi/180 * 3960

[obsidian monolith]

Result:

9.2153384505301

[viscid thistle]

(8/60)° is π/1350 rad

[white beacon]

still i do not understand the wording, what does rounding too early then refer to?

[viscid thistle]

Bc as the early you round, the accuracy of your result decreases

So its better to round the last/s steps

Like we did

[white beacon]

yes this is obvious, but how the question is phrased i don't understand to which part in the question the subtends then relates

[viscid thistle]

:?

The subtends then relates
?

[white beacon]

oh i see @uncut mulch didn't answer me when he was talking about the rounding too early part, so my problem lies still with the word subtends and its meaning

[viscid thistle]

So your problem is on the word "subtends"?

[white beacon]

Yes, not a native, never heard it before

[viscid thistle]

I mean i'm not native either but i can overlook at its meaning by the context

[dusk mulch]

9.26 was wrong

Unless if Im not supposed to be rounding at all?

[white beacon]

I thought i was integral in understanding the question

[dusk mulch]

omg i cant read

[viscid thistle]

Lmao

[dusk mulch]

its 9.22

[white beacon]

Lmao

[viscid thistle]

I thought i was integral in understanding the question
@white beacon just don't overthink it, it just states that the angle is located between those 2 lines

[white beacon]

yeah thanks, most of the times i cant solve a problem cause i overlooked something

[viscid thistle]

Dw

[dusk mulch]

,calc 8/60 * pi/180 * 3960

[obsidian monolith]

Result:

9.2153384505301

[dusk mulch]

So this is it?

After rounding its 9.22 right?

[viscid thistle]

I mean, yeah

[white beacon]

If you round it at the 2nd decimal, it should be

[viscid thistle]

But do you know if they ask you to round it

[dusk mulch]

Not explicitly

ok, so from now on I should only ever round my numbers at the very end?

[viscid thistle]

Are you allergic to fractions?

Yes.

[alpine basin]

How would I find the exact values of sin and cos for this angle?

[viscid thistle]

JEEZ THAT WAS QUICK

[white beacon]

every time you round you lose precision, so in the end you could be way of if you have to do multiple steps,

[viscid thistle]

^

@alpine basin lets move to #geometry-and-trigonometry , so we leave Corn for possible further questions

Let $P$ be the set of $42^{\text{nd}}$ roots of unity, and let $Q$ be the set of $70^{\text{th}}$ roots of unity. How many elements do $P$ and $Q$ have in common?

[obsidian monolith]

Disabled_Skooter:

[viscid thistle]

@dusk mulch any further doubt

may i get help if anyone is free?

[dusk mulch]

I got it

thx

working on another question now

[viscid thistle]

Good, np.

im lost lol

[white beacon]

may i get help if anyone is free?
@viscid thistle If I understand the question and wiki article right You have two sets

Set P contains all numbers for which the equation z^n = 1

[viscid thistle]

want a screenshot?

[white beacon]

want a screenshot?
@viscid thistle could help

[viscid thistle]

its problem 4 a

before we do that can we cover question 2 a and 2b?

[white beacon]

can look into it but will take a moment, have to look it up

[viscid thistle]

yea no problem

[white beacon]

Do you know how the root of unity works?

[viscid thistle]

not really

[white beacon]

Could try to explain it, care to switch to mathematics voice chat

[viscid thistle]

sure

(1-4i)

[white beacon]

$z= x +iy = r(cos \theta + i sin \theta)$

[obsidian monolith]

achilles199703:

[white beacon]

cos 72 + i sin 72

https://en.wikipedia.org/wiki/Root_of_unity#/media/File:One5Root.svg

[viscid thistle]

z^3 = -2 - 2i

1-i

The equation
[z^5 = i]has $5$ solutions. The unique solution in the third quadrant is $re^{i\theta}$, where $r > 0$ and $0 \leq \theta < 2\pi$. What is the ordered pair $(r, \theta)$?

[obsidian monolith]

Disabled_Skooter:

[viscid thistle]

(1,6\pi/5)

[white beacon]

$4/5 \pi + 1/2 \pi = 13/10 \pi$

[obsidian monolith]

achilles199703:

[viscid thistle]

Let $P$ be the set of $42^{\text{nd}}$ roots of unity, and let $Q$ be the set of $70^{\text{th}}$ roots of unity. How many elements do $P$ and $Q$ have in common?

[obsidian monolith]

Disabled_Skooter:

[viscid thistle]

$e^{i(\frac{2\pi+2\pi k}{42})}= e^{i(\frac{2\pi+2\pi k}{70})}$

[obsidian monolith]

Disabled_Skooter:

[white beacon]

$e^{i(\frac{2\pi \times k}{42})}= e^{i(\frac{2\pi \times k}{70})}$

[obsidian monolith]

achilles199703:

[viscid thistle]

@fringe stream may you help me out please?

[white beacon]

https://en.wikipedia.org/wiki/Root_of_unity#General_definition

[wide ocean]

i thought the ans is C but it's "A"

i thought it was reflection on y axis, and horizontal compression by 5/9 ?

why is it expansion?

[willow bear]

it is horizontal compression by 5/9

it just happens to also look like a vertical stretch by sqrt(5/9) bc of this particular curve

[wide ocean]

OHH I see

Yeah compressing a root makes it bigger

I gotta remember that

@willow bear ty

[midnight lake]

pls help

this is killing me...

[willow bear]

not clear exactly how the division is supposed to happen

[midnight lake]

this is all that was given to me ;-;

was*

[willow bear]

ask your professor to clarify

[midnight lake]

oh

ok got it

[unique meadow]

@craggy dune infinity?

[craggy dune]

yes

do you understand why?

[unique meadow]

i think i do. so e raised to minus infinity would be 1/infinity?

[craggy dune]

yes

[unique meadow]

thanks!!

[alpine basin]

How would I get the exact value for this?

it says the answer is sqrt(2)

but I got something different

[craggy dune]

hmm

can you write sec another way?

something you might know the values of already?

[alpine basin]

nevermind I was simplifying 1/(sqrt2/2) incorrectly

I think I got it my bad

[craggy dune]

well if you got it its good no?

[alpine basin]

yeee

[finite wraith]

isnt sec(x) like 1/cos(x)

i suck at remembering trig identities

[viscid thistle]

Yes it is.

It's not even an identity... It's how sec is defined

[finite wraith]

idk dude my trig game sucks

the only thing i always remember is sin^2(x)+cos^2(x)=1

also tan = sinx/cosx lol

not much

[viscid thistle]

infinite / infinite + 5/4 =?

[finite wraith]

infinity lul

[viscid thistle]

how

[finite wraith]

infinite is not a number

some infinities are bigger some infinities are smaller

[viscid thistle]

i know

[finite wraith]

what do u think infinity/infinity is?

[viscid thistle]

1

[finite wraith]

u said u know what i said earlier

and u still make the same mistake

[viscid thistle]

:))

[finite wraith]

infinity over infinity is basically undefined

[viscid thistle]

i know a guy said infinite : infinite = 1 :))

if this true , 0: 0 = 1 , and this is not true

[alpine basin]

yo why is it saying to use the reference angle of these angles to find the exact values of them?

but then the answer for a for example is -sqrt(2).. which getting the reference angle of 135 wouldnt help with getting -sqrt(2)

[finite wraith]

a reference angle must be less than pi/2

135 is in the second quadrant right?

[viscid thistle]

wait i think 1 is solution....
infinite : infinite = 1 , infinite * 1 = infinite

[finite wraith]

so to find the referent angle you do

180 - 135

[alpine basin]

yeah it'd be 45

[finite wraith]

yes

so sec(45)

you have to find the value of that

[alpine basin]

I did it'd be sqrt(2) right?

[finite wraith]

,w sec(45)

[obsidian monolith]

Results provided by WolframAlpha

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

Requested by trece#6139

[finite wraith]

yes sir

[alpine basin]

but the answer for a on the key is -sqrt(2).. so what is the point of me getting the reference angle

[finite wraith]

210 is in third quadrant

so you do 210 - 180

so you get the point

for fourth qudrant u do 360 - x

[alpine basin]

ye I know how to get the reference angle, Im just sayin it seems pointless cause it deosnt help me get -sqrt(2)

[finite wraith]

second quadrant-> 180-x
third quadrant -> x-180
fourth qudrant -> 360-x```

hm

[alpine basin]

cause they already gave me 135

idk maybe the question is just weird

[finite wraith]

just do it like i showed u ?

[alpine basin]

wat

Yes I know how to get the reference angle

but in the question it says " And then use them to find the exact values of sec(135)" for example

how does getting the reference angle help with that.. when I just have to get the exact value of sec(135) and that'd be the answer is what Im tryna say

[finite wraith]

ok i see

what the question is asking now

ok so

for sec(135) we got that the referent angle is 45

and we got sqrt(2)

[alpine basin]

ye

[finite wraith]

135 is in the second quadrant

sec is positive or negative in second quadrant?

[alpine basin]

negative

[finite wraith]

so there you go

-sqrt(2)

its just flipped

do you understand?

[alpine basin]

hm yeah I guess its just a weird question

[finite wraith]

sec(45) is in the first quadrant

if u "flip" it

in the second quadrant its just negative

[alpine basin]

cause I could just solve for sec(135) and I get same thing

since they already give me it

[finite wraith]

i mean they just want u to use reference angles

[alpine basin]

ye

thanks for the help

[finite wraith]

np

[alpine basin]

How would i solve this problem?

[upbeat bone]

Do you know the definition of even and odd function?

@alpine basin

[alpine basin]

Uh Im not too sure to be honest

[upbeat bone]

It's alright

Well,
A function $f$ is called even if $f(-x)=f(x)$ for all x, $\$
and $f$ is called odd if $f(-x)=-f(x)$ for all x

[obsidian monolith]

Wilston Lynx:

[upbeat bone]

So, to figure out your function is even, odd, or neither, all you have to do is to check it with those definitions

[craggy dune]

the question can even be simplified a bit by using a trig identity

[alpine basin]

Ah

wait which identity?

[upbeat bone]

$sin(2x)=2sin(x)cos(x)$

[obsidian monolith]

Wilston Lynx:

[upbeat bone]

Yeah, you can simplify the function with this identity

[alpine basin]

wait

How would I use it?

[upbeat bone]

I'll show you how to check whether $f(x)=x^2$ is even or odd. $\$
If you notice from the definition, actually all you have to do is to plug in $-x$ to the equation, so, $\ \$
$$f(-x)=(-x)^2=(-1)^2(x)^2=x^2=f(x) \$$ $\$
Because $f(-x)=f(x)$, therefore by definition, $f(x)=x^2$ is an even function.

[obsidian monolith]

Wilston Lynx:

[alpine basin]

hmm

[craggy dune]

now its your turn buckets

is the function f(x) = x^3 even or odd?

[alpine basin]

odd

right?

[upbeat bone]

How do you come up that f(x)=x^3 is odd?

[alpine basin]

cause -x^3 is -x

and -f(x) is odd

[upbeat bone]

I think you meant, $(-x)^3=(-1)^3x^3=-x^3$?

[obsidian monolith]

Wilston Lynx:

[upbeat bone]

But yeah, that's correct

[alpine basin]

o

[upbeat bone]

Well now I think you have the tools to solve your own problem

[alpine basin]

how would I plug in -x to the trig functions tho

[upbeat bone]

Just plug it in?

[alpine basin]

so f(-x) = 2sin(-x)cos(-x)

[upbeat bone]

Correct

[alpine basin]

uh

Im not sure how that gets me my answer

[upbeat bone]

Oh

[alpine basin]

my bad

[upbeat bone]

You might need to take a look at several trig identities

$sin(-x)=-sin(x)$ and $cos(-x)=cos(x)$

[obsidian monolith]

Wilston Lynx:

[craggy dune]

if you don't have that written down somewhere do so

you might need those again in the future

[alpine basin]

okay

[upbeat bone]

Yeah, I agree

[alpine basin]

how does this identity work tho, so my function would now be

(2-sinx)(cosx)?

[upbeat bone]

Emm that's not correct if you typed it that way

[alpine basin]

2-sinxcosx

[uncut mulch]

order of operations

[upbeat bone]

$2-sin(x) \neq 2(-sin(x))$

[obsidian monolith]

Wilston Lynx:

[alpine basin]

okay so 2(-sinx)(cosx)

[upbeat bone]

Okay, you're almost there

[alpine basin]

(-2sinx)(cosx)?

[upbeat bone]

Yeah, and?

What's 2sin(x)cos(x) again?

[alpine basin]

idk

sorry

[upbeat bone]

Look at your question again

[finite wraith]

$\sin(2x)=2\sin(x)\cos(x)$

[obsidian monolith]

trece:

[finite wraith]

(as a reminder)

[viscid thistle]

Bruh.

[upbeat bone]

Thanks but we're not really using that atm lol

[alpine basin]

so its -2sinx2cosx so its odd

or am i missing something

[upbeat bone]

-2sin(x)2cos(x)?

[alpine basin]

ye

[upbeat bone]

How come from (-2sinx)(cosx) you get -2sin(x)2cos(x)

[alpine basin]

well it was 2(-sinx)(cosx)

[uncut mulch]

the doesn't answer the question

$a(bc) = abc \not\equiv abac$

[obsidian monolith]

ramonov:

[upbeat bone]

The distribution property works like this $a(b+c)=ab+ac$, not $a(bc)=abac$

[obsidian monolith]

Wilston Lynx:

[alpine basin]

mkay

it is odd tho right?

wait thats what I did tho

I distributed 2 to -sinx and cosx

[upbeat bone]

I mean, a(bc)=abac is wrong

[alpine basin]

o wait i see now

Okay

[upbeat bone]

it is odd tho right?
@alpine basin Yeah, you should've write it like this, $\$
$(-2sinx)(cosx)=-f(x)$ $\$
by that way, you'll get that $f(-x)=f(x)$, or in other words, it's an odd function.

[obsidian monolith]

Wilston Lynx:

[alpine basin]

I was trying to solve b, which was

[upbeat bone]

The concepts are still the same as before

[alpine basin]

and i got f(-x) = -3(sinx)(cosx)(secx)

How is it neither tho? Shouldnt it be odd as well?

[upbeat bone]

and i got f(-x) = -3(sinx)(cosx)(secx)
@alpine basin This is wrong

[craggy dune]

take a look at f(x) = sec(x)

the same way you did with the other functions

is it odd or even or neither?

[alpine basin]

idk thats what im tryna answer

[craggy dune]

for that it might help to turn sec into a function you know more about

[alpine basin]

oh

so since its - but sec is included it cant be even and odd? so its neither?

[uncut mulch]

missing - sign in that tex

[alpine basin]

or

[upbeat bone]

Try changing sec(x) into another function

I mean another Trigonometry Function

What'll you get?

[alpine basin]

uh

1/cos?

[upbeat bone]

Yep

1/cos(-x)=...?

[alpine basin]

1/cos right?

since cos(-x) = cos(x)

[upbeat bone]

Yep

[alpine basin]

how does that prove its neither, not sure

[craggy dune]

look at the definition again

what does even mean and what is odd

and then look at what you have

[alpine basin]

Idk tbh i dont see how that'd matter

cause -2sinxcosx was odd

[upbeat bone]

Have you write down your work for that?

You'll realize that it's neither when you write it down

[alpine basin]

-3sin(x)cos(x)sec(x)

-3sin(x)cos(x)1/cos(x)

[upbeat bone]

$-3sin(x)cos(x)sec(x) \neq -3sin(x)cos(x)+sec(x)$

[obsidian monolith]

Wilston Lynx:

[upbeat bone]

Your question is asking for 3sin(x)cos(x)+sec(x), NOT for 3sin(x)cos(x)sec(x)

[alpine basin]

oh

so -3sinxcosx + 1/cosx

Hows that prove its neither tho

[upbeat bone]

so -3sinxcosx + 1/cosx
@alpine basin and that's the same as -3sin(x)cos(x)+sec(x) right?

[alpine basin]

yes

[upbeat bone]

Hows that prove its neither tho
@alpine basin Look at the definition again

A function $f$ is called even if $f(-x)=f(x)$ for all x, $\$
and $f$ is called odd if $f(-x)=-f(x)$ for all x

[obsidian monolith]

Wilston Lynx:

[alpine basin]

oh

so for it to be odd it would have had to change to - sec(x)?

[upbeat bone]

so -3sinxcosx + 1/cosx
@alpine basin Now, can you rewrite this as -f(x) or f(x)?

so for it to be odd it would have had to change to - sec(x)?
@alpine basin Yeah, if it's -sec(x), the function would be odd

But here it's not

[alpine basin]

okay thanks

[upbeat bone]

You're welcome!

[alpine basin]

for the 3rd one, cos(-2x) would be cos(2x) right?

[upbeat bone]

?

You haven't posted the question yet

[still quarry]

Someone please help

[craggy dune]

another room

[upbeat bone]

This channel is still occupied @still quarry

[craggy dune]

buckets is here

[upbeat bone]

Please move to another question channel.

[craggy dune]

he's pretty violent

[alpine basin]

lmao

[upbeat bone]

lol

[alpine basin]

I got -sinx-2cos(2x), which would be neither as well right? Because the sign on -2cos(2x) didnt change to +2cos(2x) right? @upbeat bone

[upbeat bone]

for the 3rd one, cos(-2x) would be cos(2x) right?
@alpine basin Anyway, yeah

I got -sinx-2cos(2x), which would be neither as well right? Because the sign on -2cos(2x) didnt change to +2cos(2x) right? @upbeat bone
@alpine basin That's correct!

[alpine basin]

Okay great I think I got it down

[craggy dune]

[alpine basin]

thanks for all the help

[upbeat bone]

No problem!

[urban harness]

how would i do this

?

not sure since there is a y inside

[willow bear]

split into four cases, probably

[viscid thistle]

ok, @urban harness

Tell me what do you see?

[urban harness]

well its double absolute values

added together

idk what to separate or how to take the y out

[viscid thistle]

what does absolute value mean?

yea, what does it mean?

or, what is |n| equal to?

[urban harness]

well its positive?
n

[viscid thistle]

ok

[urban harness]

non negative

[viscid thistle]

|n| is not always n

[urban harness]

oh

[viscid thistle]

If n < 0

Then it wont = n

[urban harness]

ur right

[viscid thistle]

Say n = -1, does |-1| = -1

Ok good

[urban harness]

|-1| = -1 ?

[viscid thistle]

no

No it doesnt

[urban harness]

it equals 1

[viscid thistle]

|-1|=1

[urban harness]

yes

[viscid thistle]

but anyways

what does abs val mean for your problem?

how does know this improve your understanding?

and are the two abs values added together, the only thing you see?

[urban harness]

well added together to be less than or equal to 12?

do all the signs just become positive?

2x+y-3

2x+y+3*

[viscid thistle]

no

[urban harness]

hm

[viscid thistle]

what can you do?

that is what are you allowed to do right now, given your limited understanding?

your first idea was to seperate the variables?

right?>

[urban harness]

yes

[viscid thistle]

so, if you think you can't, what else could you do?

[urban harness]

somehow take out the absolute signs?

[viscid thistle]

Is that something you understand to do?

[urban harness]

no:(

[viscid thistle]

Then, what do you know to do?

As a tutor, my primary mission is to further your understanding from what you know.

So, I really won't tell you anything.

But I will work through your thoughts with you

[urban harness]

im not sure what i CAN do, i tried looking for videos and examples but apparently there isnt anywhere where there is x and y and double absolute values anywhere all together

so im not sure how to start

[viscid thistle]

Ok, so you see these two abs values less than a number.

[urban harness]

yes

[viscid thistle]

what do you see in the abs values?

[urban harness]

the x intercept and the y

[viscid thistle]

really?

you do?

[urban harness]

well the variables

only

[viscid thistle]

ok

what are variables?

[urban harness]

x and y

not sure what numbers they r yet

[viscid thistle]

what do variables mean?

what does it mean for something to vary?

[urban harness]

well it carries a value

well can it have different values

[viscid thistle]

yes

[urban harness]

yes

[viscid thistle]

so a variable can have different value; it's value varies

right?

[urban harness]

yes

it can vary

[viscid thistle]

so how do we know what values are ok for the variables?

we know that there are values that belong there, but what ones?

[urban harness]

well all together it has to equal less than 12

[viscid thistle]

YAS

so, now that we reviewed our understanding of the problem

what is something different we can do to further our understanding rather than separating the variables

?

(separating the variables from the abs values that is, because we dont know how that works)

variables are what again?

they hold the place of a number

what could you do?

[urban harness]

can we use substitution?

[viscid thistle]

what do you mean by substitution?

what is there to substitute?

[urban harness]

i mean cant we move the y to the other side

[viscid thistle]

I don't know where your understanding is

with the word substitution

[urban harness]

no no forget that substitution

not for this question

sorry

[viscid thistle]

did you figure it out?

[urban harness]

do we maybe take the derivative...?

[viscid thistle]

are you in calc or precalc?

and are we still in that abs val problem?

lol

[urban harness]

KEO GO AWAY

u dont know it either

[viscid thistle]

try random numbers for x and y

what's the point in that?

I'm trying to further may's understanding from their point of view.

Just to get a feel for what seems right.

And, after trying out somethings that we can* do, working backwords and understanding the problem further to come up with a clearer systematic way.

hmm

I don't think this problem is all that easy to reverse engineer if you don't understand absolute value even if you know the answer

[urban harness]

im in calc but he gave us this problem saying its precalc related but i never did this in precalc either

so im confused

[viscid thistle]

you don't need any calc

you need the definition of absolute value

disagree, trying out some values in the ineq lets the person get a feel for the abs value

in a simpler case maybe, but this has too much going on in it

botn, pm me

ok

@urban harness you still here?

[urban harness]

yes

[viscid thistle]

ok, what's up

how's it going?

[urban harness]

bruh

math b hard

[viscid thistle]

hahaha\

did you try some random numbers?

yes/no @urban harness

[urban harness]

put a random # in for BOTH X AND Y

well

[viscid thistle]

yea, why not?

[urban harness]

when i put x=1 and y=2

its true

the statement is true

[viscid thistle]

ok

[urban harness]

its lessthan 12

[viscid thistle]

that's one number

[urban harness]

yes

[viscid thistle]

err

that's one point, two numbers

you should try a lot of numbers

like maybe 6 or 8 pairs of (x,y) points

[urban harness]

thats part of the solving process?

[viscid thistle]

first of all

you have math anxiety

and I need to get you to feel safe around math

by getting into the motion of trying everything you can do

[urban harness]

true

[viscid thistle]

which right now, is testing as many points as possible to get the feel of the problem

and once you do at least 6

we talk some more

and re-evaluate understandings

[urban harness]

OKAY BRO

i shall come back to u

latur

[viscid thistle]

LOL

yes

hurry da f up

[urban harness]

wait dude its like past my bedtime i trying

[viscid thistle]

k

@urban harness if you're still doing points, stop and tell me what you learned

[daring yarrow]

@viscid thistle wanna keep explaining to me? im interested

[fleet yew]

@daring yarrow explain what

[daring yarrow]

bruh nvm

[willow bear]

is there a problem you're stuck on?

[sweet wedge]

I've tried everything I knew
The square of terms sequence isn't an A.P (common difference varies)
And it's not a telescoping series
That's all I am aware of.

You guys should check my statements for yourself. Never know when I might make a silly algebraic error

[willow bear]

it feels to me as if this question has no answer

yeah, no, this question is fucked up actually

it is possible to give examples of arithmetic progressions with the same values of a and n but different sums of squares

taking a = 1/2 and n = 5 as an example, the APs 0, 1, 2, 3, 4 and -4, -1, 2, 5, 8 both sum to an(n-1) = 10, but the sums of their squares are 30 and 110 respectively

@sweet wedge

[sweet wedge]

Hmmm

Oh well

[willow bear]

what i'm saying is

[sweet wedge]

No I understand

[willow bear]

you should either skip the question or bring it up with your teacher

[sweet wedge]

Yeah, I'll tell them

Oh well, thanks for your time 🙂

[rare zephyr]

If theres 2 objects and 4 spaces how do you calculate the total possible arrangements for it?

[barren sapphire]

Can you distinguish the two objects?

[viscid thistle]

@rare zephyr

[muted granite]

Can this be a true statement? It has to be false, right?

matrices.

[remote veldt]

I'm pretty sure that holds for all invertible matrices with an invertible product

[patent beacon]

It also happens to be true that AB is invertible iff A and B are invertible

[muted granite]

matrix A and B are all different variables. I did the math and it came out false. I just want to make sure there is not something tricky going on.

A=A,B,C,D and B=E,F,G,H 2x2

[patent beacon]

So yes, that is true for all invertible A and B

[muted granite]

Ok, to be clear. The above statement is false?

[jagged glade]

It's true.

[remote veldt]

the statement is true

for any two invertible matrices A and B

[muted granite]

How? When I do the math A does not = B?

[remote veldt]

then there's an error in your algebra

[patent beacon]

Why does A have to equal B?

[jagged glade]

I guess it's an error when you compute the inverse.

[remote veldt]

oh wait lmao yes that's a bigger problem

[muted granite]

Thats what the problem is asking me to do.

[remote veldt]

why do you think you need A = B

no?

it's asking you if (AB)^(-1) = B^(-1)A^(-1)

[muted granite]

Yes

[remote veldt]

at no point does that say A = B

[muted granite]

It says show that (AB)^(-1) = B^(-1)A^(-1)

[remote veldt]

yes

why are you saying that A = B

the equality of A and B is irrelevant

[patent beacon]

Oof that's quite the computation haha

[remote veldt]

expand all the denominators, factor out negatives

those should end up being the same

[muted granite]

oh, factor them out

hrmm

you can't bc on the top problem its + and -. you can't cancel out

also, there is nothing to cancel out.

[patent beacon]

-(a + b) / x = (-a - b) / x

[granite inlet]

Which link

To invite someone here?

[patent beacon]

That's how you get the negatives to match

[muted granite]

I see what I have to do. geez. what a pain.

they do equal.

[granite inlet]

https://discord.com/invite/BacbVax

[muted granite]

thanks

[granite inlet]

Join that server please.

xD

[muted granite]

if I factor the denominators they will match

[patent beacon]

Now, there's a few problems with this method.

• This is only a proof for a 2×2. If I asked for a 4×4 you'd be screwed
• It's a pain. That's too much computation.

[muted granite]

lol

[patent beacon]

So let's do this the easy way, using algebraic properties of a matrix

[patent beacon]

@muted granite
Sorry I got busy. Want to talk over this more?

[muted granite]

@patent beacon I think I get it. Now that I realize that there is the additional step of factoring. If I run into trouble I will @ you. Thanks.

[patent beacon]

Nah fam you don't want to actually multiply matricies together

Unless the question is specifically asking for a 2×2?

[muted granite]

No, the denominators need to be factored to make A=B

[glass nacelle]

Sorry for a super dumb question but my brain is fried why does

[still meadow]

You multiply both the numerator and denominator by the conjugate.

@glass nacelle

[glass nacelle]

I got (-6i+2)/(-6i - 8)

[still meadow]

Recall that i^2 = -1.

What's the conjugate of -3i + 1?

(or 1 - 3i?)

[glass nacelle]

I think that's my mistake. Trying it by the conjugate.

3i+1 right?

[still meadow]

Yup.

[glass nacelle]

So I got (6i+2)/10 = (3i+1)/5. Just messed up the conjugate. Thanks.

[still meadow]

You're welcome. :D

[alpine basin]

How would i show the asymptote of this equation?

I graphed the line and got the domain and range correctly, but not sure about the asymptote

[viscid thistle]

do you know what the asymptote should be?

[alpine basin]

its 4 I think right?