precalculus

[uncut mulch]

write the denominator in terms of sin(x) and/or cos(x)

[viscid thistle]

So it would be 1/sin^2x -1

[uncut mulch]

what would be ^?

[viscid thistle]

2

[uncut mulch]

what's 2?

the denominator can be written as 1/sin^2(x) -1
combine into a single fraction and simplify

[viscid thistle]

I still dont get it

[uncut mulch]

simplify: $\frac{1}{\sin^2(x)} - 1$

[obsidian monolith]

ramonov:

[viscid thistle]

Would I have to multiply sin^2x to the one

[uncut mulch]

multiply by sin^2(x)/sin^2(x)

[viscid thistle]

Ok

[uncut mulch]

yes, that would be how you add/subtract fractions

[viscid thistle]

So it would be

-sin^2x/sin^2x

And can turn into

-1

[uncut mulch]

what?

[viscid thistle]

Because

They're both the same

Its like -3/3

[uncut mulch]

huh?

$\frac{1}{\sin^2(x)} - \frac{\sin^2(x)}{\sin^2(x)}$

[obsidian monolith]

ramonov:

[viscid thistle]

It would be -sin^2x/sin^2x right?

[uncut mulch]

no

[viscid thistle]

Oh oh

Wait sorry

1 - sin^2x

over sin^2x

[uncut mulch]

and 1- sin^2(x) simplfies to?

[viscid thistle]

cos^2x

[uncut mulch]

and now you have: $\frac{\cos^2(x)}{\frac{\cos^2(x)}{\sin^2(x)}}$

[obsidian monolith]

ramonov:

[viscid thistle]

Ok

And then I just multiply by the reciprocal

So it would be just sin^2x

[uncut mulch]

yes
get used to writing parentheses around the angle in plain text sin^2**(x)**

[viscid thistle]

Ok

Thanks so much

[opal swallow]

https://www.youtube.com/watch?v=QirtTPD0Unk

l;earningthis right now

[viscid thistle]

@viscid thistle what do u mean by that?

https://media.discordapp.net/attachments/363224154469826562/637121863776075781/IMG_3729.JPG

I need help with this

Im confused by the instructions

I dont need anyone to solve it for me, but rather, tell me how to

[uncut mulch]

how much do you know about functions
(Inputs/outputs)
have you done compositions before?
do you understand fog notation

@viscid thistle

[viscid thistle]

Oh haha, didnt know that was directed at me

@uncut mulch i know enough about functions, no to compositions, no to fog notation

[uncut mulch]

$(f \circ g)(x) = f (g(x))$

[obsidian monolith]

ramonov:

[uncut mulch]

does that clear things up?

if you know enough about functions, compositions shouldn't be that hard to understand

eg. for f(2), you'd replace x with 2
in compositions
for (fog)(x) = f(g(x)) you'd replace x with g(x)

[viscid thistle]

Hm so what do i have to do in the hw?

I literally dont understand the instruction

That’s my main problem

@uncut mulch

[uncut mulch]

$f(x) = -5x + 4 \ g(x) = \frac{x-4}{5}$

[obsidian monolith]

ramonov:

[uncut mulch]

what would f(g(x)) be?

[viscid thistle]

-5(x - 4\5) + 4 i assume

It’s the instruction of the hw btw, that i dont get

@uncut mulch

[uncut mulch]

for f(g(x)), you replace the x in f(x) with g(x). which gives you
f(g(x)) = -5 g(x) + 4

[viscid thistle]

Mhm i get it

So is the instructions basically telling me to combine the two equations on each number? @uncut mulch

[uncut mulch]

yeh. that's pretty much the gist of compositions

[viscid thistle]

Ah i see

Ight thanks for your time

Right one more thing, can you use that bot to solve (1/x)^2

@uncut mulch

This is me with another fog assignment

Waiiit that aint a calculator nvm

Sorry my brain isnt functioning well tonight

[quiet zodiac]

Does tanα = sinα / cosα ?

if so tanβ = sinβ / cosβ

then plug it into this formula

[patent beacon]

What's the question?

Yes, tan(x) = sin(x)/cos(x). What x actually "looks like" doesn't matter here

[quiet zodiac]

Ohh, that makes sense I just got caught up at that tan part

Thanks

[viscid thistle]

whats all the transformations on this thing

4^-x + 2

[viscid thistle]

Whats the horizontal or vertical stretch

bro this problem is killing me

[proud sparrow]

@viscid thistle where are your parentheses?

no parentheses?

[viscid thistle]

? no

Its translated over the y

its up two

How does the base effect it

vertical or horizontal

[proud sparrow]

The idea with horizontal stretch is that we want to make particular x behave like other x

[viscid thistle]

kk

[proud sparrow]

if you want to include all possible horizontal/vertical stretch, multiply x by a constant/multiply entire expression by a constant

[viscid thistle]

I was supposed to graph it with only the knowledge of ver hor shifts and ver and hor compress or stretch

I could not get it to work

[brisk frigate]

I'm having a bit of trouble understanding what this question is asking me to do, english is my second language so this doesnt make much sense to me, could anyone pls explain?

[proud sparrow]

ah

you might not want to choose e as your base

[viscid thistle]

oof

4

nvm

[proud sparrow]

@brisk frigate Okay so we have a 16ft by 16ft plot

[brisk frigate]

is plot just a rectangle?

[proud sparrow]

yeah

[brisk frigate]

or does it mean the garden

oh ok

[proud sparrow]

plot = garden

[prime prawn]

the area of shaded region = 64 ft^2

[brisk frigate]

ah i see, so it wants the width of the non-grayed out area right?

[proud sparrow]

yeah

the non grayed out area has a constant width

[brisk frigate]

ok, so the total area is 256, the flowers go in the 64ft square in the middle, and i need to figure out the width of the space left

so i take the 16ft total width and subtract sqrt(64) to it and get the leftover width? 16-8 = 8ft as width

ok its wrong rip

oh I then divide 8 by 2 and answer is 4

thanks guys

[viscid thistle]

Ive Been Bamboozled

[muted lichen]

Anyone familiar with calculus here

that can help me out

[rigid sun]

Sure

[muted lichen]

Uh

Are you really

[rigid sun]

😩

Ask ur question

Or put ur problem

[proud sparrow]

#calculus or #❓how-to-get-help please

this is precalc

[rigid sun]

Same thing

[muted lichen]

lmao

[rigid sun]

#calculus

[muted lichen]

by calculus I’m referring to pre calculus hence my level of comprehen

comprehension

[rigid sun]

Dude post the problem

[muted lichen]

DMs

[rigid sun]

No wtf

I can’t use textit in dm

@muted lichen come back u bot

[muted lichen]

It’s not a problem you not

It’s a question

Go to dms

[rigid sun]

Dude this is what the discord is for

Post question

@muted lichen

[hearty storm]

hi can someone help point me in the right direction for this

ahh ok

ty ty

[runic solstice]

Hello C:

Nice to meet everybody here, and I wish you a happy day

I've solved, I think, an exercise here, but I'm not sure if it's correct

[proud sparrow]

don't write =0/0

[runic solstice]

=0

[proud sparrow]

other than that the rest looks okay

[runic solstice]

Ok, thank you ^^

I know I have to evaluate first if the limit is undetermined

but since I knew it was 0/0 I didn't care so much

[proud sparrow]

maybe you can try using words

"Here, we cannot substitute in x=pi/4 directly as it would result in 0/0"

don't write =0/0

you can write "is of the form 0/0"

[runic solstice]

I see, I get what you're saying

Can we separate Sen^2x into Senx . Senx ?

or make Limit x→0 Sen^2x/x^2 equal to 1?

[proud sparrow]

wait

is that sin^2 x?

@runic solstice

[runic solstice]

Yeah

[proud sparrow]

idk where in the world people use Sen instead of sin

[runic solstice]

In spanish

but I did forget it

hahaha

or miss it

[proud sparrow]

https://es.wikipedia.org/wiki/Trigonometría
Ah I see, "seno".

yeah it should be okay because we define the notation as such

[runic solstice]

Nice, ty again

😄

[green zenith]

hello

i need some help with trig functions

what does pi - t means?

"the terminal point p determined by pi - t"

[proud sparrow]

@green zenith sounds like there's more context

[green zenith]

If the terminal point determined by t is P(a,b), then
(a) the terminal point P(x,y) determined by π−t is

x=? and y=?

[proud sparrow]

If the terminal point determined by t
?

Sounds like you have a parametric equation there

@green zenith

is that correct?

[green zenith]

i havent heard of that and there aren't anything else on the question

it is a point on the circle

[proud sparrow]

what circle?

[green zenith]

not circles

[proud sparrow]

show the entire question please

[green zenith]

that is the entire question

it is the point on the quadrants is what i meant

[proud sparrow]

...

There's a diagram, right?

[green zenith]

no. it is just the question and the x and y blanks

there are other part of the question, sorry i lied. i didnt think it would help

[proud sparrow]

whoops

[green zenith]

(b) the terminal point P(x,y) determined by −t is

(c) the terminal point P(x,y) determined by π+t is

[proud sparrow]

Okay, can you write the question in the order given?

If the terminal point determined by t is P(a,b), then
(a) the terminal point P(x,y) determined by π−t is
x=? and y=?
(b) the terminal point P(x,y) determined by −t is
(c) the terminal point P(x,y) determined by π+t is

Is this accurate?

any information about P?

[green zenith]

yes. with x=? and y=? in between a,b and c

[proud sparrow]

P as in point?

[green zenith]

yes it is a point

i assume both Ps are point

[proud sparrow]

absolutely no other context?

[green zenith]

yes

[proud sparrow]

terminal points must come from somewhere

if they have to end there

[green zenith]

can be the terminal point on the angle?

this is in trigonometry

[proud sparrow]

what angle?

did they draw a unit circle with an angle somewhere nearby?

[green zenith]

no

what am i saying

[proud sparrow]

maybe t is an angle

[green zenith]

well pi is an angle

right?

[proud sparrow]

pi is a number

angles can be measured

it just so happens that when we measure, we get a number, and that number is pi and pi represents an angle of 180 degrees

[green zenith]

ahhh

sorry, i had a lot of trig on my head

[proud sparrow]

but yeah, good chance they were talking about that

[green zenith]

and the four quadrants?

i guess the question does look weird without context

pi might have other uses other than angles and circles

[green zenith]

i need some help solving a log equation

it is log(x^4)=(logx)^2

my solutions ends up with no x's

[serene heath]

How so

Show ur working out

[green zenith]

so what i did was square root first sqrt(4logx)=sqrt((log(x))^2)

[serene heath]

Erm that doesn't look like it'll help much

Bring the terms to one side and factor

[green zenith]

okay

so then i will have 4=((log(x))^2)/(log(x))

will i have 4=(log(x))?

then x=10^4?

[serene heath]

Sure

But what if logx=0

[green zenith]

x=1?\

[serene heath]

Yes

[green zenith]

where can you find log(x)=0?

[serene heath]

If ur dividing by a variable u gotta account for when its 0

[green zenith]

why?

so that means the numerator should be equal zero if the fraction is equal to zero?

[serene heath]

Yea

U have this log(x)[-4+log(x)]=0

[green zenith]

is that multiplication?

[serene heath]

Ywa

[green zenith]

sorry but i am so confused

how did it turn to multiplication?

[serene heath]

I just factored out a log

[viscid thistle]

Help

[tardy crescent]

@viscid thistle, do you know the formula for an arithmetic sequence

[viscid thistle]

Yea

an=a1+(n-1)d

[tardy crescent]

Just look at the 5th term and 20rd term. Remember that an arithmetic sequence is where you add (or subtract) the same number to get to the next term in the sequence. So that means that the 5th term, 23, and the 20th term, 98, are separated by D * (23 - 5) = 15 * D, where D is some number that you add to each term to get to the next term

You took 15 equal-length steps to get from your 5th term of 23 to your 20th term of 98.

[viscid thistle]

Ok

Continue

[tardy crescent]

That should give you the common difference. Since you're at the 20th term = 98 and you want to find the 60th term, just take the common difference that you found, multiply it by 40 and add it to 98 to get the value of the 60th term

[viscid thistle]

What

Can I call u

So u can explain it verbally

[tardy crescent]

Sorry, my mic isn't on right now. To get to the 20th term from the 5th term, you added (98 - 23) = 75. And you know that each step along the way was the same length, and you took 15 "steps". So 75 / 15 = 5. That is how far you go with each step.

[viscid thistle]

Yea that’s d

I got that

[tardy crescent]

Cool

[viscid thistle]

What do I do now

[tardy crescent]

Then you can look at the fact that the 5th term = 23

Plug in 5 for d in your equation

[viscid thistle]

How do I get a1

[tardy crescent]

and 5 for n, since it's the 5th term

So now you have a1 + 5(5-1) = 23

whoops no I wrote somethin wrong there i think

no nvm that's right

So now you have a1 + 5(4) = 23

a1 = 3

[viscid thistle]

How do I do this too

[tardy crescent]

I can also post the original here: a1 + d(n-1) = an, where n = term number. So since a5 = 23, you can substitute 5 for n. And since you figured out that d = 5, you can substitute 5 for d. (It just happens that the common difference and term number here are equal, but it won't always be)

Ok, so it looks like you have a geometric sequence sum (also called a geometric series) in the denominator, and in the numerator you have the loan amount in dollars

[viscid thistle]

Yea

[tardy crescent]

They tell you that L = 10,000, and i in this case is 0.03 because of the 3% interest rate

So all you need to do is find that sum in the denominator, which is (1/1.03)^k

[viscid thistle]

Yea but I did it and it was wrong

[tardy crescent]

What formula did you use to do the sum?

[viscid thistle]

Calculator

[tardy crescent]

Alright, i'm just writing it down now to see how it works. Remember that the terms is in months, so 10 yrs = 120 months

[viscid thistle]

I did that

[tardy crescent]

Oh hang on, they said i was monthly interest rate, not annual

So i = 0.0025

[viscid thistle]

Ooh

Lol

[tardy crescent]

They're sneaky!

[viscid thistle]

:/

Ur a math teacher aren’t u

[tardy crescent]

No

[viscid thistle]

Ur smart tho

We friends now

[tardy crescent]

Thanks 🙂

[viscid thistle]

Bro we can help each other math

U can help me with mine and I can help u

[tardy crescent]

Sounds good!

[viscid thistle]

:))

[hybrid charm]

help me too 😊

[tidal rain]

Hey im having trouble understanding the steps my professor did here

Specifically the parts i boxed around

[latent tinsel]

Factored out two parts

a^2 – b^2 = (a + b)(a – b)
And 4

[acoustic laurel]

Your professor used difference of squares for x_1^2 - x_2^2 and factored out a negative 4 from -4x_1+4x_2

And after that, he or she factored (x_1-x_2)

from $(x_1-x_2)(x_1+x_2)-4(x_1-x_2)$

[obsidian monolith]

Chairman Rovic:

[acoustic laurel]

Imagine both the from $(x_1+x_2)$ and $-4$ as two terms that have one thing in common, $(x_1-x_2)$ is multiplied to both of them. That means, you can factor them from the two since distributing to both of them would mean the same thing. You can rewrite it as $(x_1-x_2)(x_1+x_2-4) as a result. You can get rid of the parenthesis in $(x_1+x_2)$ since multiplying $(x_1-x_2)$ to each $x_1$ and $x_2$ is the same as multiplying it by their sum.

Oof, looks like LaTeX has a limit

[tidal rain]

oh ok i get it now

thank you

[tame wedge]

I got this question which I'm sure is really simple and I'm probably stupid. Let z = r*cis(t), find any argument for conjugate(-z).

[blazing parrot]

if z = r*cis(t), what would Re(z) and Im(z) be?

[rare zephyr]

A graph of y = -x^2 + 8 is a represntation of a road tunnel

question, what is the maximum height of the tunnel?

It's not 8 somehow

Oh sht

Am i supposed to derive it

[viscid thistle]

Im stuck with how to figure out the denominator for this

(1- cos x)/(tan x) + (sin x)/(1 + cos x)

[rare zephyr]

@viscid thistle
Wouldn't the denom just be (tan x + sin x)

?

[viscid thistle]

I dont know how to get there

[rare zephyr]

as in?

[viscid thistle]

Isnt it

Well I got to

tanx - tanxcosx

[rare zephyr]

Since we know that tan x = sin x/cos x

tan x + tan x cos x = tan x + ((sin x/ cos x) × cos x)

@viscid thistle

[viscid thistle]

Ohh I get it now

So you dont convert the first tanx

Only the second one

[rare zephyr]

Yeah

[viscid thistle]

Ok thanks so much

I was stuck

[violet quail]

for what real values of t is

[frozen needle]

it telescopes

but it's hidden

[rare zephyr]

I'll just repeat

A graph of y = -x^2 + 8 is a represntation of a road tunnel
Question ; what is the maximum height of the road tunnel?

I used the fact that 0 is its axis symmetry as my working and input it into the equation to get 8 as the answer but its somehow wrong

The question did ask for the unit though, so I thought me missing the unit was the case but my working was marked as wrong too, what am I wrong about?

Me using the wrong method to get the answer or me forgetting to put the unit, m?

[empty fulcrum]

Wouldn't your answer just be the vertex

Do you know how to find the vertex?

Oh yeah it is just 8

[rare zephyr]

Here's the thing

On my paper 8 was marked as wrong

and I genuinely cant tell if its my "wrong" method or the inexistence of the unit it asked for

[hexed bolt]

What am I doing wrong here?

[sharp quest]

well i got 2 for the first answer

and 6 for the next one

i think you're just not entering the numbers into your calculator right

@hexed bolt

[lethal oracle]

How do I find the area of a trapezoid circumscribed about a circle of a radius 12 inches

[violet granite]

Steps to solving?

Tag me please

[serene heath]

Just do it manually lol

Find all the terms first

Theres only 4

Then add them

[scenic musk]

can someone expalin why xsinx isnt sin^2x

[viscid thistle]

ok

so lets do a simple contradiction

[scenic musk]

ok

[viscid thistle]

i will plug in pi/4

pi/4 * sin(pi/4)

what is sin(pi/4)

[scenic musk]

uh its in between 0 and 1

[patent beacon]

xsin(x) isn't sin(x)sin(x)

[viscid thistle]

yes

mike what is sin

what is sin(x) specifically

[scenic musk]

a sinusodial function?

[viscid thistle]

yes that would be it

what is the definition

[scenic musk]

it is the opposite / hypotenuse of an angle

is it like saying

2x*f(x)

isnt

f(2x^2)

am i suppose to think of it like that

[viscid thistle]

that is not true

[patent beacon]

sin²(x) actually means [sin(x)]²

[scenic musk]

o

i just need to practice more

i can do derivatives simply but when i see trig

its like new language

[patent beacon]

Fair enough, feel free to ask if you need anything else

[scenic musk]

thank you very much

[patent beacon]

@scenic musk
This is an intro to trig, should be a review for anyone who can do calc. Make sure you know all of this before doing anything further
https://www.mathsisfun.com/geometry/unit-circle.html

[scenic musk]

oh awesome, thank you

[rare zephyr]

So where did I do wrong

[tame wedge]

Sorry to the person above me, I have this due in like 15min, I’ve asked before but the hint didn’t get me anywhere go figure eek. Let z=rcis(t), find any argument of conjugate(-z). I know that the conjugate of z is rcis(-t) so it would be -r*cis(-t), and I actually don’t know what to do, too many variables ;/

[proud sparrow]

what you want to do is move the minus sign into cis

@tame wedge

because you need the magnitude to be nonegative

[tame wedge]

Right, so would it be -rcos(t)+i*rsin(t)

Then the argument is arctan(rsin(t)/-rcos(t))

I’m getting confused because the Q asks for any argument

Find ‘an’ argument...

[proud sparrow]

well, arguments can differ mod 2pi

@tame wedge

[violet granite]

@serene heath gj for being arrantly useless and not answering my question

[proud sparrow]

@violet granite Okay, show me what you have so far

you want to find the value of that?

[violet granite]

I know you can plug it in because its only 4 terms, but what is the formula

If there was 1000 terms for example

[proud sparrow]

there isn't a known closed form

that's why they gave only up to 4

@violet granite

[violet granite]

ik there is though

[proud sparrow]

?

[violet granite]

Sn = (n/2)((2a1+ d(n+1))

Geometric series also have their formula’s

But yeah...

[proud sparrow]

here there isn't a known formula, don't worry

[rare zephyr]

still waiting for someone to answer my question...

[brisk frigate]

Could anyone tell me which one of these is wrong? And like why/how

[uncut mulch]

what's your definition of a rational function?

[proud sparrow]

@brisk frigate

^please respond to that

[rare zephyr]

.

[viscid thistle]

Guys I've been in pre calculus for almost 3 months now and I don't understand Most of the info covered cause the teacher is shit

Anyone have any good websites for precal that can actually teach and have practice questions

Ping me please

[rigid beacon]

@viscid thistle Professor Leonard on YouTube just started a precalc series Paul's Online Math Notes are good, and Khan Academy is also very good

[brisk frigate]

@uncut mulch @proud sparrow Sorry guys, it was late so I gave up and went to sleep

I see a rational function as a division of 2 polynomials and their exponents cannot be a fraction nor can they be negative

But I saw this video: https://m.youtube.com/watch?v=0zi1nzKuXtU and the guy said that 1/x is still a rational function so i supposed that even if you cant see all of the terms of x, you should assume they are just 0x^2, 0, etc

He also did this in the video:

Is that correct? Can he cancel those terms and then say that “2” is a rational function? Im lost tbh

[rigid beacon]

Well they aren't the same, f(x) would have a hole at x=-3

[empty fulcrum]

Rational functions can still have holes tho

[brisk frigate]

So I spoke to my teacher and aparently the only one I had wrong was “a”, which had an |x| does that mean that absolute values on either side mean that a function is no longer rational?

She just said it wasnt but didnt really explain

Because as far as I know, the only thing I had to look for was make sure the exponents of x were not negative or fraction and that there were polynomials

But which one of those does the |x| interfere with? Does the exponent change? Does it stop being polynomial? Or something else?

[viscid tree]

I’m not 100% certain, but I think absolute value means it’s not a polynomial anymore

[uncut mulch]

@brisk frigate |x| isn't a non-negative integer power of x

[upbeat prairie]

Hey, shouldn't it be

0 - 3 9

for the second row

I do not understand how it is 0 3 -9

[stuck lark]

@upbeat prairie the rref steps clearly say to add -2/3*R_1 to R_2

-2/3*R_1 = [-6, 2, -36]

[hoary valley]

Guys, is this function an odd even or neither ?

[serene heath]

What do u think

[hoary valley]

I chose neither, but apparently it's wrong... wtf

[serene heath]

Why did u say neither

Did u check for both even and odd cases

[hoary valley]

Cuz, the numerator is odd and the denominator is even.. so it's neither .

[serene heath]

Not quite how it works

If f(-x)=f(x) then its even

Is that the case here

[hoary valley]

It's even then

right?

negative cancels. so it becomes the the same f(x)

[serene heath]

How do the negatives cancel

[hoary valley]

nvm

they don't cancel actually.

It ends up like that.

It's not even.

[pale kettle]

Are you sure that's what it becomes?

[hoary valley]

Yeah..

[pale kettle]

How did you get there?

[hoary valley]

I wanted to see if it's even, so I replaced (x) with (-x) to see if it ends up as the original f(x) . but It didn't so it's not even.

[pale kettle]

But are you sure that's what you get when you replace x with -x

[hoary valley]

I mean -x^2 will end up x^2 I think.

So I can write it x^2

Is that a thing?

[pale kettle]

Be careful about the order of operations here

Which are you doing first

the negative or the squaring

[hoary valley]

squaring first

I didn't think about that.

Ok so it will end up

[pale kettle]

You're sure it's squaring first?

You didn't change anything lmao

[hoary valley]

Yes, I think squaring is first. and then we add or subtract.

Can you help me pls.

[pale kettle]

But we're replacing x with -x

Does that mean we should do the negative first? Or is the squaring still first?

[hoary valley]

Ok so, -1 - 5^2 = -24

So we did the squaring first.

So yes we do the squaring first.

[pale kettle]

Sure, but are you sure it's supposed to be -x^2

and not (-x)^2?

[hoary valley]

If it's (-x)^2 then we do the negative first and then the squaring.

[pale kettle]

So which one do we want?

If we're replacing all x with -x

[hoary valley]

If it's (-x)^2 then it is x^2

[pale kettle]

Sure, but which one do we want here?

[hoary valley]

now it's not even.

What you mean "which one do we want here" ?

[pale kettle]

Well

Only one of these is f(-x)

Which one is it

[hoary valley]

the numerator?

[pale kettle]

what

[hoary valley]

I don't understand where you going. with " which one is it"

[pale kettle]

You've written two things down

[hoary valley]

here, this is it

[pale kettle]

Okay

[hoary valley]

It's not even.

[pale kettle]

Earlier you had -x^2 in the bottom

Why is that one wrong and this one right?

[hoary valley]

IT's not -x^2 because (-x)^2 = x^2

You're just wasting my time.

Bye.

[pale kettle]

I'm really not

I'm not sure you understand this

[serene heath]

[uncut mulch]

(twas double checking whether you understood which were the correct calculations)

[proud sparrow]

@brisk frigate actually E is also a rational function

try multiplying numerator and denominator by x^2

[kind moth]

Hi

I have a question about uniform motion

So to start this is the problem

https://gyazo.com/af40fb195ac7205e5e058357056f5d99

I have almost everything I need to solve, except for the rate of time with the current

It sais 9 hours less, so im thinking 9 - 72/x+2

[tardy crescent]

@kind moth, the time with the current is just 72 / x + 2, if x is your speed in still water. The 9 hours less allows you to write an equation using the time with the current (72/x+2) and the time against the current, so that Time With Current = Time Against Current - 9.

From there you can find common denominators, cancel out terms, and end up with a quadratic equation that you can solve for x

[pseudo sonnet]

how come the arithmetic partial sums formula doesnt work here

is it because the series isnt arithmetic in the first place

[heady jewel]

ye it isnt an AP

in AP theres an uniform increase

so the average thing works

[pseudo sonnet]

ah kk i see

is that correct

[willow bear]

is anything else known about the seq

beyond the first four terms

bc if not

[heady jewel]

1

3²

[willow bear]

,calc 2+10+18+26 + 19*56

[obsidian monolith]

Result:

1120

[willow bear]

[heady jewel]

@pseudo sonnet considering an AP

yes it is

yeet Ann

wish i had nitro

[pseudo sonnet]

how did u get that Ann

i got d = 8

then set my formula up and found a{60}

[willow bear]

are you GIVEN that this is an arithmetic sequence

[pseudo sonnet]

then i plugged a{1} and a{60} into partial sums formula

[willow bear]

are you GIVEN that this is an arithmetic sequence

[pseudo sonnet]

well no

but there is a clear common difference

[willow bear]

then why are you assuming it is

you cannot conclude just from the first four terms of a sequence that it is arithmetic

[pseudo sonnet]

a{k+1} - a{k}

[willow bear]

no, you CANNOT conclude that a sequence is arithmetic JUST FROM THE FIRST FOUR TERMS

there exist sequences that behave like arithmetic sequences for the first however many terms and then suddenly don't, yknow

and for all you know, your sequence could continue with all terms from the fifth onwards equal to 19

so please, post the problem in its entirety and exactly as it is stated.

[pseudo sonnet]

thats all we were given

it was a problem i revisited from a while ago

in class

[willow bear]

do you have the original problem, with its exact statement, and are you 100% certain that there is nothing you omitted or forgot from it?

[pseudo sonnet]

im sure ill just ask her tomorrow

ok

1 sec

here the sum is finite and has a geometric ratio

sequence*

[willow bear]

the sum is finite and all of its terms are given to you.

[pseudo sonnet]

yeah i agree

[willow bear]

there is nothing left unstated here.

[pseudo sonnet]

in this case

my steps are correct?

[willow bear]

yes sure

[pseudo sonnet]

i have a 2 hour exam tomorrow

i feel good just reviewing rn for the exam

[rare zephyr]

still waiting for someone to answer my question...

[willow bear]

what question

[velvet kelp]

Could i get help with this question

[willow bear]

what have you tried so far

[hybrid charm]

I mean volume is given so use formula for volume
😸

cotton stop bullying ppl

[velvet kelp]

i didn't know how to start it

it said find the actual dimensions i wasn't sure what to use at first

[willow bear]

well there's one unknown here

x

and the dimensions of your pool are given in terms of it

so if you find the value of x, then you will be able to find the dimensions too

does that make sense to you

[velvet kelp]

yes

[willow bear]

well

do you know, in general, how to find the volume of a box?

[velvet kelp]

yes it's L x W x H

[willow bear]

do not use x for multiplication especially when you have a variable called x

anyway yes length * width * height

so in terms of x, what is the volume of your pool?

[velvet kelp]

what do you mean by in terms of x? is it the given volume we already have?

[willow bear]

no, i am not asking you to say 2100

$l = 25x \ w = 10x+1 \ h = x \ l \cdot w \cdot h = , ?$

[obsidian monolith]

Ann:

[velvet kelp]

oh you meant the given dimensions we had

[willow bear]

answer my question.

[velvet kelp]

25x * 10x + 1 * x ? is that what you mean

[willow bear]

no, it is not, bc that is not equal to l*w*h.

mind your order of operations.

[velvet kelp]

then what do you mean? i'm stuck

[willow bear]

i mean that you are missing a pair of parentheses.

[velvet kelp]

why do I need brackets in the question?

[willow bear]

because $25x \cdot 10x + 1 \cdot x$ is not the product of $25x$, $10x+1$, and $x$.

[obsidian monolith]

Ann:

[willow bear]

explicitly parenthesized to make the order of operations painfully clear, $25x \cdot 10x + 1 \cdot x$ becomes $(25x \cdot 10x) + (1 \cdot x)$.

[obsidian monolith]

Ann:

[velvet kelp]

ohh okay (25x * 10x) + (1 * x)

I wasn't rly taught to do this thx

[willow bear]

taught to do what

and no (25x*10x)+(1*x) is NOT the thing you're after.

[velvet kelp]

then what should i do next?

[willow bear]

you should have written lwh = 25x * (10x+1) * x.

in accordance with the order of operations

which is to be overridden here with these parentheses so as to stay true to what needs to be conveyed

[velvet kelp]

okay

[willow bear]

...

i fear this might have fallen on deaf ears.

[velvet kelp]

no i get it because the width is it's own value and the brackets keep it from becoming separated

like it's one value

[willow bear]

the parentheses ensure the addition is done first yes

[velvet kelp]

yes, so what is done next?

[willow bear]

well

this is the volume

you also know the volume is 2100

from the problem

so

[velvet kelp]

do i just solve for x now?

[willow bear]

well, before you "solve for x", you've got to have an equation to solve, don't you think?

[velvet kelp]

ye my x value is 2

the equation was 25x * (10x + 1) * x = 2100

[willow bear]

,w 250x^3 + 25x^2 = 2100

[obsidian monolith]

Display results online and refine query

Requested by Ann#0413

[willow bear]

ok sounds reasonable

[velvet kelp]

answer should be 50m by 21m by 2m

[willow bear]

well there you have it

[velvet kelp]

okay thank you for helping me

[pseudo sonnet]

i know how to find the kth term and middle terms

but what about coefficients?

like what would be my K value here?

[willow bear]

what's a "K value"

[willow bear]

uh

that's needlessly complicated, and also relies on a specific order in which those terms are written

the binomial theorem applied to $(x+2)^8$ gives $(x+2)^8 = \sum_{k=0}^8 \binom8k x^k 2^{8-k}$

[obsidian monolith]

Ann:

[pseudo sonnet]

for example thats what i have been doing

[willow bear]

don't

[pseudo sonnet]

our teacher taught us that

i know how to fully expand it

[willow bear]

the binomial theorem applied to $(x+2)^8$ gives $$(x+2)^8 = \sum_{k=0}^8 \binom8k x^k 2^{8-k}.$$ you want the $x^5$ term, so of course you'll want the term in that sum that corresponds to $k=5$.

[obsidian monolith]

Ann:

[pseudo sonnet]

so i have to fully expand it out?

[willow bear]

no, you do not

you only want the x^5 term

[pseudo sonnet]

can i show you something

on my homework i did this

i tried using that for the x^5 term

but it didnt work

i got x^3 instead

[willow bear]

huh? what?

what do you mean, "tried using that"

[pseudo sonnet]

never mind

i figured it out

i started by giving a and b their powers

so they add up to n

then the combination is just

n choose the exponet im figuring out

can anyone help me with this

i have no idea how to comprehend this

[uncut mulch]

$x = 10^{100} \ \text{googolplex} = 10^x = 10^{(10^{100})} \ y = 10^{100!}$

[obsidian monolith]

ramonov:

[uncut mulch]

the hint when you asked this earlier was to use log

log is an increasing function
if a>b then
log(a) > log(b)

[pseudo sonnet]

ohhh

are you saying i take the logs of both

[willow bear]

you can compare the exponents

10^100 vs 100! instead of 10^(10^100) vs 10^(100!)

[uncut mulch]

forgot you could just do that.

[willow bear]

i mean that's what log being increasing boils down to

as well as the function $x \mapsto 10^x$

[obsidian monolith]

Ann:

[willow bear]

@pseudo sonnet compare $10^{100}$ and $100!$. whichever one is bigger, 10 raised to its power will be bigger too.

[obsidian monolith]

Ann:

[willow bear]

(do you understand why that is the case?)

...

[pseudo sonnet]

i was driving home sorry im home now

yes! that makes perfect sense that you compared the exponents because thats easier since they both have a base of 10 anyways

but honestly im not connecting the idea of logs to this

[willow bear]

no need

[pseudo sonnet]

there’s just one problem

[willow bear]

yeah no shit that's a sign that you SHOULDN'T BE USING A CALCULATOR FOR THIS

because those numbers are too large for your calculator to handle

[pseudo sonnet]

do i manipulate the 10^100 exponet

any chance this is what looking for?

since that has 24 zeroes

and a googol has 100 zeroes

therefore, 10^100>100!

[uncut mulch]

uh no.
that seems to be the method for calculating trailing zeros and does not tell you how big the number actually is

[pseudo sonnet]

im not quiet sure then

[languid crane]

Think of the definitions

[willow bear]

10^100 and 100! are both products

[hybrid charm]

cotton don't bully ppl

[pseudo sonnet]

theyre both products that result in large numbers

[hybrid charm]

also 325 has no 0 but 100 has 2 😸

oic

100! and 10^100

😲

[pseudo sonnet]

what

[willow bear]

theyre both products that result in large numbers
but this does not mean you can't compare them

[pseudo sonnet]

well i cant compare them numerically

at least not with a calculator

[languid crane]

Why would I bully anyone

I’m not bullying anyone

[hybrid charm]

ok do whatever you want

100! is very large than 10^100

[pseudo sonnet]

but why

how

[languid crane]

100! = 100 * 99... 3 * 2 * 1

[hybrid charm]

just calculate their length

which can be done without calculator

[pseudo sonnet]

how do i do that

[hybrid charm]

also can use limit approach

and also algebraic manipulation

k bye

[undone pawn]

@pseudo sonnet

100! = 1×2×3×...×98×99×100

10^100 = 10×10×10×...×10×10×10

notice that both can be represented as the product of exactly 100 numbers

so you can do a term wise comparison for each expression

whichever has terms that contribute more to the value ends up being larger

and in this case it should be very obvious that one of them is much larger than the other

[heady jewel]

,w calculate 100!

[obsidian monolith]

Display results online and refine query

Requested by Lionel#5497

[heady jewel]

,w calculate 10^(100)

[obsidian monolith]

Display results online and refine query

Requested by Lionel#5497

[heady jewel]

so yeah 100!

[undone pawn]

XD

10^100
=100....000
=1×10^100

no shit wolfram

[heady jewel]

xd

[pale kettle]

Think about this

If you're still here

[willow bear]

@pseudo sonnet

[brisk frigate]

So I did the formula on #2 (highlighted in yellow) and put it on an online calc, so if any of the answers are wrong it means my formula must be wrong, anybody know why?

[willow bear]

you forgot parentheses

[brisk frigate]

rip

Maybe the division by 3 doesnt go there?

I assumed it would since its every 3 hours, but im unsure if thats how you would represent it

[dense oar]

It should be (1000)(2)^(t/3)

You just wrote it wrong

[brisk frigate]

oh

ill try

[dense oar]

So 1000 is the starting value and 2 is the multiplier

[brisk frigate]

oh you right

so the other values are also wrong

bc i plugged them into a calc

after making the formula

[dense oar]

Idk I don’t have a calculator with me lol sorry

[brisk frigate]

Yeah that was it, cant believe i was on that for so long and didnt realize it was just a typo

[pseudo sonnet]

@willow bear does this mean 100! will be greater because after @undone pawn expended i think 100! multiplies values greater than 10 where as 10^100 will only multiple by 10

100! increases faster

[willow bear]

100! doesn't "increase" at all nor does it "increase faster" than anything. it is just a number

and also, you need to be careful

only 91 of the 100 terms in the product that defines 100! are greater than 10

so if you only use that fact, then all you can say is that 100! > 10^91

which is not quite sufficient

not on its own anyway

however, a similar idea can be used to say that 100! is greater than 20^81, and it is possible to establish that 20^81 > 10^100

[pseudo sonnet]

how did you get to that conclusion

[willow bear]

what conclusion

that 100! > 20^81?

[pseudo sonnet]

20^81 > 10^100

[willow bear]

20^81 = 10^81 * 2^81

2^81 = 2 * (2^10)^8 > 2 * (10^3)^8

20^81 > 2 * 10^81 * 10^24 = 2 * 10^105 > 10^100

[pseudo sonnet]

how did you come up with the 20^81 value

what made you use that number compared to some other 20^x

[distant nova]

Hey guys,any tips to learn Precalc well?

[pseudo sonnet]

yeah practice

like any other subject

[willow bear]

@pseudo sonnet i could have picked values other than 20

20 is just somewhat straightforward as it is 2*10

but a similar comparison could have been attempted with 30 instead

[crude hemlock]

Is there any shortcut to finding the limit of a summation?

At infinity

[serene heath]

Not really

[willow bear]

not when you put it that generally

@crude hemlock is there a question you're looking at that led you to ask this

[pseudo sonnet]

is the vertical shift the midline for trig functions

[crude hemlock]

Well there's a rather large equation whose limit I already know but I'd like to figure out how it simplifies to said limit

I can post the equation once I can pull up a LaTeX cheat sheet

[formal iris]

How did he get from pic1 to pic2

Please @ me if someone gets it

[serene heath]

Multiply by 1/h/1/h

[crude hemlock]

Alright I got the latex figured out

$\text{f}(p, n, s) = \frac{\sum_{i=0}^p (s^{p-i}(\sum_{j=0}^n (-1)^j \cdot \text{g}(i, j) \cdot \text{g}(n-1-js, i-1))}{p^s}$

[obsidian monolith]

Kiako:

[crude hemlock]

$\text{g}(x, y) = \begin{cases} \frac{x\text{!}}{y\text{!}(x-y)\text{!}}&\text{if } 0 < y < x \ 0 &\text{else}\end{cases}$

[obsidian monolith]

Kiako:

[crude hemlock]

I found the limit (for this specific case) to be

$\lim_{(p, n)\to(\infty, p^{-})}f(p, n, s)=\frac{2}{s+1}$

[obsidian monolith]

Kiako:

[crude hemlock]

Excuse any syntax errors please

[crude hemlock]

Here’s a desmos of it

https://www.desmos.com/calculator/czvh2iryie
One that graphs

[visual crag]

This is a really dumb question but how do you find the domain of a composite function?? I know how to find the individual domains but I don’t get how to combine them to get the domain of the composition.

[rigid sun]

The domain of the inner function is where you start

Then after you’ve included the inner function, you find the domain of f•g, the new function you have created

The domain of the entire composite is where both domains overlap

Essentially, it is the domain of g and the function values in g that in the domain of f by itself

[patent beacon]

You'll want to find f(g(x)) first

I think it's pretty unlikely you'll find the domain without finding what the composite function actually is

[visual crag]

So it’s basically just where they overlap?

[eager python]

Question:
A can of soup has radius of 3cm and height of 10cm. The label on the can covers the curved surface of the can. What is the are of the label?

[pastel quarry]

you know nothing about the label’s height, how is that even possible

[uncut mulch]

height of 10cm

[vague yew]

its cylinder

[uncut mulch]

it's basically asking for the area of the curved surface of a cylinder

[opaque thunder]

4(sin^6y+cos^6y) simplify

[harsh cipher]

Hi guys

and girls 😛

right part of the graph. (2.35,-10.61). Wouldn't that be absolute minimum?

I'm not sure why the teacher explains that as relative minimum.

[last linden]

its not absolute because on the left side of your graph it can still go lower towards -infinity

[harsh cipher]

thank you.

[neon trench]

hello

im just chilling doing homework and i ran into this problem

10^(2.2x-1)+3=34

not really sure how to do it

[sonic jay]

ur solving for

x?

well i mean prolly yeah

well to bring the exponent down u have to take log

first I would take

3 to the other side

so it's

[neon trench]

yep

10^(2.2x-1)=31

[sonic jay]

10^(2.2x-1) = 31

now i'd take the log of both side

log(10^2.2x−1)=log(31)

=

(2.2x−1)*(log(10))=log(31)

see if u can solve it now

[neon trench]

so lemme get this straight

you take the log of the thing with the variable in the exponent, the variable moves down to the front?

[sonic jay]

Correct that is the main use of log

[neon trench]

ohhhhh

[sonic jay]

so say for example

U had 3 ^ (5x)

if you took the log u'd get

5x log(3)

[neon trench]

Gotchaaaaas

so in the previous problem I have to solve it algebraically now?

[sonic jay]

exactly

I mean

the log is also

algebraically done

u are allowed to use a calculator right?

[neon trench]

so log10 is just 1 right?

yeeeeeee

trying not to though 😛

[sonic jay]

yep

[neon trench]

so now i have 2.2x-1 = log31

[sonic jay]

right

[neon trench]

its implied that its log sub 10 right?

[sonic jay]

im confused

what is log sub 10?

you got rid of log(10) in previous step

[neon trench]

nani

[sonic jay]

when u equated it to 1

[neon trench]

so what do i do with log31?

[sonic jay]

im pretty sure u can only use a calculator for that part

[neon trench]

oof

[sonic jay]

Or you could write in simplified terms

*unsimplified

bad typo

[neon trench]

so it would be x-1 = log31/2.2

that got me x - 1 = .67789

and the move over the one

answer is 1.67789?

[sonic jay]

sec

i dont think thats it

[neon trench]

yeah me neither lmao

[sonic jay]

so the problem with that is

you have to move the 1 first

[neon trench]

gotcha

[sonic jay]

so it'd be (log(31) +1 )/2.2

[neon trench]

ayeeee

so in that situation do addition/subtraction and then multiplication/division

[sonic jay]

I wish I could explain it better but i'm also a student not a professional. However it's the precedence of algebraic operations

[neon trench]

you did a great job haha

[sonic jay]

Right so if u keep practicing similar problems u should be more comfortable at it

[neon trench]

i have a whole worksheet of these and theres like 30 of em 😛

[sonic jay]

thats good for u.

I have classes where my professors don't give us practice problems and we have to learn our own. haha those don't go very well

[neon trench]

oh no, i usually fall asleep in class (not good) and then the day before the quiz I cram and learn all of it in one night (today lol)

today was hard though since i had no idea what we were talking about and didnt have my textbook home with me

[sonic jay]

u in high school or college?

[neon trench]

highschool

senior year :))

[sonic jay]

LMAO i took pre calc in senior year of HS as well didnt learn enough to pass the entry exam to calc

so had to retake precalc and for the best

[neon trench]

oh jeeeez, im in precal dual enrollment so its ROUGH

[hexed bolt]

Hello I need help on this

[neon trench]

lmao cant help you, im not even learning trig yet kek

[uncut mulch]

for a)
your curve is bounded by [-2pi,2pi]
you should have 4 values separated by commas

[hexed bolt]

I tried that on my previous guess

Does it have to be in order from least to greatest?

[sonic jay]

unfortunately that depends on the program

but for the actual answer

the order doesn't matter

[uncut mulch]

what did you enter?

[hexed bolt]

I did the pi/2 and -pi/2 and then did 3pi/2 and then -3pi/2

[sonic jay]

pi/2 and - pi/2 look correct

actually

[uncut mulch]

clarify what you meant by "and"

[sonic jay]

they all look correct to me

[uncut mulch]

as in did you put
-pi/2, pi/2
and then
-3pi/2, 3pi/2
in a separate attempt?

[hexed bolt]

No in the same attempt

I'll try in order

[uncut mulch]

mmm strange

[sonic jay]

sometimes its just the terrible software

[hexed bolt]

How would I do the other 3

or 4

[uncut mulch]

there are two intervals when its decreasing
there are two intervals when its increasing

[hexed bolt]

Oh ok

The first interval would be decreasing right?

[sonic jay]

maybe this helps?

[hexed bolt]

Okay thanks

So the decreasing intervals are -2pi to -pi and 0 to pi

[sonic jay]

that looks correct to me at least

[hexed bolt]

Would i put a union sign between them

[sonic jay]

uh

I don't know

I dont remem having to ever use union in precalc

lmao but it depends on ur professor really not a general thing im sure

[hexed bolt]

ok

[sonic jay]

theoretically it makes sense but idk if that's how u can answer the question and have the program process it

[hexed bolt]

How do I find the relative max and min

[sonic jay]

there seem to be 3 relative maxs and 2 relative mins from that graph

maybe @uncut mulch can help?

I have a general idea but i havent done stuff like this

in a while

[hexed bolt]

Damn ok

[neon trench]

hi uh okay

im back

and

confused again

36^(x)=216^(1-x)

i took the log of both sides and got
(x)(log(36)) = (1-x)(log(216))

this is right no?

[sonic jay]

this what it looks like

[neon trench]

yeeeeeee

[sonic jay]

also I think ur first step is correct