or if the first term was (x+2)^2
#precalculus
lost cipher
lost cipher
you can probably make it a bit easier on yourself by factoring out 12 from the first two terms
simplifying it and then include the 9 at the end
viscid thistle
How can I find the value of x if y = 54
elfin night
viscid thistle
Ah yep t’y
fringe stream
what's the binomial expansion as a series?
fringe stream
what's $$(a + b)^n$$?
granite stirrupBOT
fringe stream
no, i'm asking you if you know the general binomial expansion
$$(a + b)^n = \sum_{k = 0}^n \binom{n}{k} a^k b^{n - k}$$
granite stirrupBOT
fringe stream
this should look familiar
solid reef
i never got taught that
I use the ones above the P(A or B)
im not really sure what the sigma stuff is for
granite stirrupBOT
solid reef
yea
i plugged it in
but i got a really low #
Ik I messed up tho
Obviously
Lmao
fringe stream
you need the coefficient of the term containing x^20
so for what value of k will the term reduce to an expression containing x^20?
solid reef
Oh
Shit
Wrong one
You would have to add 6
Like the exponent would have to go up 6
fringe stream
$$t_{k + 1} = \binom{14}{k} (2x)^{14 - k}(-x^4)^{k}$$
granite stirrupBOT
fringe stream
right?
solid reef
So k would = -6
fringe stream
choose a k for the above equation to get an x^20
solid reef
so 5?
granite stirrupBOT
solid reef
sorry i have no idea whats going on
im just gonna ask my teacher tmr
thanks for being patient and helping me out
fringe stream
try picking k = 2
viscid thistle
H
spring thunder
K
viscid thistle
How can I solve decimal quadratics by completing the square
atomic zodiac
,tex $-3x^2+4x+5$
obsidian monolithBOT
Gamedolf:
atomic zodiac
,tex $-3(x^2+\frac{4}{3}x)+5$
obsidian monolithBOT
Gamedolf:
atomic zodiac
,tex $-3(x+\frac{2}{3})^2+5-\frac{4}{9}$
obsidian monolithBOT
Gamedolf:
atomic zodiac
@viscid thistle
limpid plover
@atomic zodiac You can change your colour using ,tex --colour <insert colour>
obsidian monolithBOT
Please give me something to compile! See ,help or ,help tex for usage!
Unknown colour scheme. Known colours are default, white, transparent, black, dark and grey.
obsidian monolithBOT
Your colour scheme has been changed to transparent
atomic zodiac
ty@limpid plover
limpid plover
np
alpine portal
I need help this section is about composite functions...
I dont get how to start it.
do I just solve for 0.14-0.000002x < 10000 ?
or do I just compose the two functions as it is?
alpine portal
<@&286206848099549185>
atomic zodiac
revenue = price per item x number of items sold
number of items sold is just x
problem is "price per item" could mean a number of things
atomic zodiac
either the total profit per item, which would be 0.14 - 0.000002x - (0.096x - 0.0000005x^2,
or just the price you sell the items for, which would be 0.14 - 0.000002x,
or the price to make the items, which would be 0.096x - 0.0000005x^2
p sure the definition of revenue is the 2nd one
so you would have R(x) = (0.14 - 0.000002x)*x
0.000002 is so nasty to type 🙁
alpine portal
Is the second function irrelevant or something?
atomic zodiac
idk the question is presented really badly
i would guess there's a part b or something
alpine portal
Mane just have english and math seperated fock haha
You were correct it was R(x) = (0.14 - 0.000002x)*x
I hate useless info when i'm trying to learn something
alpine portal
Oh yeah and their wasn't a part b it was just that lol
atomic zodiac
lol
formal edge
delicate ravine
Trigonometric identities pre calc 12 level
solemn tiger
Consider expanding the right side in terms of sines and cosines.
viscid thistle
See that: $$ \frac{tan(\theta)}{cos(\theta)} = \frac{sin(\theta)}{cos^2(\theta)}$$ and $$sec^2(\theta) = \frac{1}{cos^2(\theta)}$$
granite stirrupBOT
viscid thistle
So: $$ \frac{1}{1 + sin(\theta)} = \frac{1}{cos^2(\theta)} - \frac{sin(\theta)}{cos^2(\theta)}$$
granite stirrupBOT
viscid thistle
Take reciprocal: $$ 1 + sin(\theta) = cos^2(\theta) - \frac{cos^2(\theta)}{sin(\theta)} $$
granite stirrupBOT
granite stirrupBOT
viscid thistle
$$ sin(\theta)(1 + sin(\theta)) = cos^2(\theta)(sin(\theta) - 1)$$
granite stirrupBOT
viscid thistle
$$\frac{2sin(\theta)}{sin(\theta) - 1} + 1 = cos^2(\theta) $$
granite stirrupBOT
delicate ravine
@viscid thistle my teacher wants us to simplify only the one side so that 1/1+sin(theta) = 1/1+sin(theta)
Proving the identity
viscid thistle
Hmm
fringe stream
yeah then just work on the right side
it should be easy to prove through some algebraic manipulation
solemn tiger
Express the RHS with sines and cosines. Get everything into one fraction, and it should be fairly easy to prove with a bit of manipulation.
viscid thistle
Saw it
delicate ravine
Okay I will try
viscid thistle
So: $$\frac{1}{ 1 + sin(\theta)} = \frac{1}{cos^2(\theta)} - \frac{sin(\theta)}{cos^2(\theta)}$$
fringe stream
?
granite stirrupBOT
viscid thistle
So: $$\frac{1}{ 1 + sin(\theta)} = \frac{1 - sin(\theta)}{cos^2(\theta)}
So: $$\frac{1}{ 1 + sin(\theta)} = \frac{1 - sin(\theta)}{cos^2(\theta)}$$
granite stirrupBOT
delicate ravine
Okay yeah I got that far^^
viscid thistle
$$ cos^2(\theta) = 1 - sin^2(\theta)$$
solemn tiger
Whenever you see a 1 + or 1 -
granite stirrupBOT
fringe stream
multiply the numerator and denominator by the conjugate of the numerator
solemn tiger
Always remember you can multiply by the conjugate.
viscid thistle
$$ cos^2(\theta) + sin^2(\theta) = 1 $$
granite stirrupBOT
viscid thistle
Pythagorean identify 
It's trivial to prove.
Just need unit circle.
So now just reverse the steps I just did and viola. Proof.
delicate ravine
Okay that's makes sense but our teacher wants us to do it like the right side of the equation (1/1+sin(theta) = sec^2(theta) -tan(theta)/cos(theta) so like simplify the right side to be equivalent to the left side
Hopefully that makes sense :/
@viscid thistle ^^
granite stirrupBOT
delicate ravine
Yep
fringe stream
$$\cos^2\theta = 1 - \sin^2\theta = (1 + \sin\theta)(1 - \sin\theta)$$
granite stirrupBOT
fringe stream
np
jolly steppe
What do I do for something along the lines of 2xy'y''=(y')^2+1
fringe plinth
You know something, I’ve been on this discord for a while now and read the questions asked in this channel, and coming from a UK student where we don’t have “pre calculus”, I really do not see where any of this is going to directly assist with learning calculus
We start learning calculus over here with basic derivatives and then integrals, moving on to area under curves and between curves
But this stuff?
I don’t see it
kind pewter
It's usually the thing you do before learning calc, in theory you need trig identities and stuff
It seems inefficient though
fringe plinth
Yeah but how does it help learn calculus
kind pewter
But then not more so than the rest of the school system
kind pewter
I didn't go through a school system formally myself, but seeing it as a tutor from outside it seems like utter madness
You learn techniques which you'll never use again, to do things which you'll never see again
And you take so damn long about it as well xD
Most people don't learn calc until what, late teens?
fringe plinth
The pre calculus questions that get asked in here seem more like further trigonometry 90% of the time
kind pewter
Yeah
gritty blaze
$$\int\limits_0^1 \sqrt{1-x^2},\mathrm{d}x$$.
granite stirrupBOT
fringe plinth
I’m a first year uni student and I’ve only ever needed to know the differentials and integrals of sin and cos to as well as the outcomes of those to do the calculus I need doing
kind pewter
There are some integrals which absolutely require trig tricks
fringe plinth
Differentiating tan is just sin over cos and use quotient rule lol
I’ll never understand this pre calculus shit
kind pewter
Like the one above probs
fringe plinth
The one above definitely doesn’t need trigonometry to integrate 🤔
kind pewter
Frankly, the early uni thing of forcing people to do annoying pointless integrations seems useless as well
gritty blaze
How would you do it ?
kind pewter
To get an exact result xD
kind pewter
You normally use a polar/trig sub for that right?
gritty blaze
You have to prove not 'realize' it.
obsidian monolithBOT
Puerøsola:
gritty blaze
@fringe plinth Now your silent is haunting.
fringe plinth
I’m silent because I have no idea what you guys are talking about
All I know is that I think pre calculus is not assisting with calculus
It’s further trig
gritty blaze
The Integral.
sour plinth
disagree, there's quite a lot of pre-calc stuff that can be applied in calculus
fringe plinth
Quite a lot of trigonometry maybe
But if we define pre calc as anything that might remotely assist with calculus
Then algebra is pre calc
Learning your times tables are pre calc
lol
sour plinth
well i dont actually know what precalc is, we dont have it here in australia
but i wouldve assumed it's whatever is right before calculus
kind pewter
Oh hey, a fellow Australian
earnest finch
I hate trig.
serene heath
ya it is a bit triggy
viscid thistle
How does one extract a equation from this
thick kayak
@viscid thistle imagine shifting the photo to the bottom left corner
limpid plover
If you have 15/2 as a root, it won't work as 15/2×2=15 which is greater than 12 which is impossible
So the answer is 3/2
viscid thistle
@limpid plover THANKS
flint bloom
can anyone help me convert a rectangular cord to a polar one
serene heath
post your question
viscid thistle
whats the difference between hyberbola and parabola in a conic section?
fallen cloud
hyperbola can be roughly approximated by a y=mx+b equation, a parabola cannot
axx - byy = c is hyperbola
axx - by = c is parabola
fringe stream
here should be fine
viscid thistle
ok i also nee help on the topic too
I tried learning this by myself and the equations are very confusing
fringe stream
what is confusing
viscid thistle
the equations and how to solve them
fringe stream
what part is confusing?
shell salmon
foggy silo
@winter spoke what i found via google search, not sure if it is what you want/need
better one
in your case this is needed
pagenumer 4/5 has them
viscid thistle
It's easier to do log stuff by looking at the antilog-- in other words, write everything in exponents.
Wait, use different letters :) Unless you mean a = A?
OK, do this: use different letters, that's going to get ugly fast
Yes, but ok... If x = log base a of A, then a^x = A as you said
It'll end up being exponential division
Not quite. Sorry, I just made a casual remark and sense we're getting too deep. You're looking at x/y though, right?
a^(x/y) = A^(1/y) may or may not be helpful
Because a^(x/y) is (a^x)^(1/y) by exponential multiplication rules
And a^x = A. I'm pretty sure the whole proof will fall out that way
hybrid hemlock
Hi
trail peak
patent beacon
== 120 + 360
granite stirrupBOT
480
granite stirrupBOT
-60
patent beacon
Note that -60 is the opposite angle. So if you flip the vector and rotate it to -60, it's the same
So note that
(5, 120) = (5, 480) = (-5, -60)
winter spoke
@foggy silo Thank you so much!
dim charm
Alternatively you can convert to rectangular and see which one is different
By using 5cos(120), 5sin(120)
sharp pagoda
Can anybody quickly help with this question, as I was sketching it can someone explain why h is a positive and does not become a negative and move left?
fringe stream
whats h?
sharp pagoda
Never mind figured it out, I realized I had to factor out the negative that's attached to x
viscid thistle
for the leibiniz derivative notation of dy/dx what is the meaning of the x and y's? Sometimes both show up, sometimes only x, im confused about htis
frozen needle
Leibniz notation is evil
sudden yarrow
is anyone good at precalcuus?
precalculus?*
this is urgent
and it is due tomorrow
devout pawn
Question: How is it possible to find the Vertex with only the Focus and Directrix? (I’m trying to solve one and it has “Focus (2,-3) and Directrix x=5”)
Oh wait, does Focus = (h + p, k) ?
sudden yarrow
guys dont forget my hw thats due tomorrow
devout pawn
Wait, isn’t what you did so far correct?
All you really have to do is put it into words
weary widget
is there any way to write the function x=lny+y as a function of x?
dull imp
@weary widget e^x = ye^y
weary widget
thank you!
viscid thistle
for the leibiniz derivative notation of dy/dx what is the meaning of the x and y's? Sometimes both show up, sometimes only x, im confused about htis
rocky bison
What do you mean?
As in what does dx
and dy mean?
Because those are largely smol figures
Comes more apparent if you look at definition from first principles
=tex f'(x)=\lim_{\delta x\to0}\left(\frac{f(x+\delta x)-f(x)}{\delta x}\right)
granite stirrupBOT
rocky bison
$f'(x)=\lim_{\delta x\to0}\left(\frac{f(x+\delta x)-f(x)}{\delta x}\right)$
obsidian monolithBOT
Pseudo:
solemn tiger
d/dx is the derivative operator. More specifically, you can apply it to a function: i.e. f(x) by writing that action as (d/dx)f(x) "the derivative of f(x) with respect to x". dy/dx is the derivative of y with respect to x, which can be rewritten as (d/dx)(y).
You usually see (d/dx) in the context "differentiate whatever is next to it with respect to x" whereas (dy/dx) specifically means "differentiate y with respect to x"
solemn tiger
x could be a function of anything 
You could have a function of time with respect to x for some reason
solemn tiger
In the end, they effectively mean the same thing
Take the derivative w.r.t. x
The top only starts mattering once you do implicit differentiation and partial derivatives
🤔
viscid thistle
so d/dx (x) is the same as f prime of x?
dull imp
@viscid thistle yea f'(x) is the same thing as saying dy/dx
if you wanna find the slope at a point, say 2, then its f'(2). or dy/dx | x=2
dx/dx is just...one
cause if you wanna take the derivative of something, you take it with respect to a variable. so say that y=x^2+1
so dy/dx is the same thing as d(x^2+1)/dx
or you can also write it as f'(x)=d(x^2+1)/dx
they all mean the same thing
split valley
Hey guys, question
if sign changes in a system of inequalites, do you use original inequality for test point or the new inequality
after solving the inequality for y
daring trellis
What do you mean?
When algebraically manipulating inequalities, it should hold true for every step.
viscid thistle
Is there a way without trial and error to find the GCF to simplify with?
Because to the power of 5 is kinda laborious to test a bunch of numbers for 5120
-(4^5)*5
solemn tiger
Why 5120?
The powers of s and t don't apply to the 160 out in front.
(160s)^5 is not the same as 160s^5
viscid thistle
Why 5120? Because 2^5*160=5120
I’m combining then simplifying off the combined product
solemn tiger
You already have the -2 outside the root, you're bringing it back in? 🤔
vale pewter
find the prime factorization
vale pewter
t!wiki prime factorization
brisk micaBOT
viscid thistle
Ty
viscid thistle
Do I need to understand the math behind why the derivative of sine is equal to cosine or should I just memorize it?
Probably easier to memorize it to be honest
patent beacon
@viscid thistle
Do you understand that the derivative comes from the definition of the derivative? That's all that's really important to understand. You also have to memorize derivatives
viscid thistle
@patent beacon Maybe, i think I do but i'd need to see an example to be sure I know exactly what your talking about. Like I get what a derivative is, but if you wanted an explanation of why the derivative of cos is -sin I could not tell you other than that the functions are obviously related in some way
patent beacon
Khan Academy walking you though the derivative of sin(x) @viscid thistle
Make sure you know what the definition of the derivative is, that is important
slender river
squez theroem
loud current
OKOKOK so anyone know much about polar and rectangular equations?
because I DONT and thats my big issue at the moment
I am smack dab in the middle of a quiz and for family reasons I missed both class sessions last week, so I'm completely lost
and out of town so i cant really ask for help from any classmates
so yeah I'm basically screwed unless I can get some major help
any help I can get I would much appreciated, if anyone who could help could dm me that would be swell
I'm desperate here
solemn tiger
Um...
I may be able to help with polar/rectangular eqns as long as it isn't an exam or something? 🤔
loud current
Not an exam, basically just a homework quiz on Pearson
I haven’t had an exam since high school, and also my prof gave me an extension so I should be fine
solemn tiger
Then ask your questions. 👍
frigid raven
Hello, Could someone please guide me through this problem? I have no idea what to do with this one. It is a sum and difference formula problem
lone rivet
Do you know what the sum formula for sin is? @frigid raven
frigid raven
Hey, So I just got help from another person in a different server. I now understand the problem and how to answer it @lone rivet Thank you!
lone rivet
Yeah, np
viscid thistle
So I multiply my numerator and denominator by my denominator, but why do I need to flip my second term in denominator?
Like for step one, why is it +root(13) and not -root(13)
spring thunder
you want to get rid of the sq roots in the denominator
and there's this identity pretty suited for it
$$(a-b)(a+b) = a^2 - b^2$$
obsidian monolithBOT
emeric75:
viscid thistle
So I flip because if I don’t the denominator will remain irrational
spring thunder
yus
viscid thistle
Kk ty
spring thunder
👌
serene heath
1/2a, a cant be 0
otherwise itd be 1/0
which is undefined
fourth if x is 0
then it'll just be 0 times sqrt0
which is just 0
and you can take the cube roots of negative numbers
neon vale
Need help with 1a and 1b
west holly
Yup
west holly
Square root is 1/2 power
Or u can do
So u did (6^x)^2
So that’s just
(6^x + 6^x )
= 6^2x
2x = 1
X = 1/2
neon vale
Thanks so much
thick raptor
yw
bitter ocean
I've got a question that relates to physics, but very basic.
----> [.] ===>
hit box move
I want to hit something and see how far it's moved
what do I need to google for this?
wild turret
coefficient of friction?
rocky bison
Well
Assuming there's no coefficient of friction
You're looking for conservation of momentum from the looks of things
@bitter ocean
bitter ocean
@rocky bison "conservation of momentum" and "coefficient of friction" seem reasonable, cheers
rocky bison
conservation of linear moment specifically
slender river
o k
floral tide
if in doubt
draw a triangle
and start from angle alpha
and by remembering that the opposite of the angle/hyp is sin
?
wtf just happend
did i get hacked
onyx tinsel
it must be my Wrath
my Wrath for people who use alpha instead of the proper notation for an angle, namely theta
nimble oxide
Whay are the standard equations for an ellipse when the major axis is vertical and when it's horizontal? <@&286206848099549185>
plain lake
in the future wait 15 mins after asking a question to ping helpers
it depends on which denominator has the larger value, if the larger value is under the part with x, it's horizontal, if the larger value is under the part with y, it's vertical
so where a>b (x-h)^2/a^2+(y-k)^2/b^2=1 is horizontal, and (x-h)^2/b^2+(y-k)/a^2=1 is vertical
for the major axis
nimble oxide
Alright, will do, I'll keep that in mind
And thanks
Wait, @plain lake in the vertical one is (y-k) supposed to be to the 2nd power?
plain lake
yeah just misstyped
nimble oxide
Ah alright,
And when dealing with an ellipse, isbthe algebraic definition of c^2 dealing with the Pythagorean theorem
bitter ocean
how to solve this?
dense zealot
so
use basic matrice multiplication
u get
ill turn it horizontal so its easier
<(c_1)(x) + (i_1)(y), (i_2)x + (c_2)y> = <k_1, k_2>
so just looking and matching terms
u can see the answer
bitter ocean
right - i think i should get
x= c1*k1 - i1*k2
y = k2*c1 - k1*i2
both of those divided by c1c2 - i1i2
but when I plug back into the system I'm not getting zeros, so I thought I must be doing something wrong
@dense zealot what you've done is expand, not solve for x,y
bitter ocean
sure - that's what i did
dense zealot
multiply both sides by identity matrix of the ci matrix
bitter ocean
multiply by the inverse of the coefficient matrix
bitter ocean
but I'm not getting zeros back, yeah idk :<
dense zealot
tbh just check in wolfram
bitter ocean
# these should both be zero for the fixed points
def f1(x,y,k1,c1,i1):
return(k1 - c1*x - i1*y)
def f2(x,y,k2,c2,i2):
return(k2 - c2*y - i2*x)
# just to assign values of x,y more easily
def xx(k1,k2,c1,c2,i1,i2):
return(( k1*c2 - i1*k2)/(c1*c2 - i1*i2))
def yy(k1,k2,c1,c2,i1,i2):
return((-k1*i2 + k2*c1)/(c1*c2 - i1*i2))
# some constants to test
k1 = 1
c1 = 2
i1 = 3
k2 = 5
c2 = 7
i2 = 10
x = xx(k1, k2, c1, c2, i1, i2)
y = yy(k1, k2, c1, c2, i1, i2)
# these should then be zero
print(f1(x, y, k1, c1, i1))
print(f2(y, y, k2, c2, i2))
how do I set this up in wolfram?
dense zealot
cuz u cant multiply a 2x1 by a 2v2
hot frost
hey guys, anyone wanna teach me log or know good sources? 😄
spring thunder
wot
bitter ocean
@dense zealot for AB you have to have the col space of A equal to the row space of B
spring thunder
in X=A^-1 B you're still multiplying 2x2 by 2x1 
bitter ocean
I know, I don't have a problem with doing that
spring thunder
no vorries bored
dense zealot
k got it
$$ \begin{pmatrix}\frac{c_2k_1-i_1k_2}{c_1c_2-i_1i_2}\ \frac{-i_2k_1+c_1k_2}{c_1c_2-i_1i_2}\end{pmatrix} $$
obsidian monolithBOT
NOT a pleb:
bitter ocean
right, that's what i've got, ack
bitter ocean
idk what i was messing up before
dense zealot
on csgo
spring thunder
i'm not even playing anymore smh
spring thunder
wot
dense zealot
its ok i have more than 2k+ hrs on it
bitter ocean
this isn't on topic
dense zealot
shh
dense zealot
lol
and @bitter ocean
im pretty sure u multiplied wrong
when i multiplied the answer just now with the other matrix i got k1,k2
@spring thunder no u
bitter ocean
the other matrix 'is got' ?
bitter ocean
@dense zealot no, that's what i have in my code
@dense zealot oh phuq, I had y,y instead of x,y in the code
😢
dense zealot
rip
bitter ocean
good job I wrote that code to check my math, I wouldn't have wasted half an hour else
molten ore
Need a comprehensive pre calculus book to precede Thomas' Calculus, any suggestions?
viscid thistle
How can we say the derivative of x is 1 when x can be anything? Surely we have to say that x cannot equal x^3?
We have to put some limits on x as a variable right? Do our laws of derivation assume x is a real number and not another collection of variables? Because if x=(x^4) that seems to violate the notion that the derivative of x is 1.
@dim sorrel
hexed ermine
If you have a problem with x it will be x
In a substitution manner, you can represent x to be something but you are going to have to differentiate that x anyways
thick raptor
@viscid thistle it matters what you're taking the derivative with respect to
viscid thistle
I'm trying to understand, but I think where I'm tripping up is fundamentally with the definition of x. So when we say d/dx (x)=1 we are assuming that x does not equal x^2, because by definition that would give us an answer. Well, I guess if I plugged in x^3 as the variable x to the function F(x)=x I would still get my slope of one and the derivative properties would still hold.
I think I just needed to type this out guys
thick raptor
@viscid thistle x does not have a value
When you say df/dx, you are taking the limit of the change in f over than the change in x
It's like saying that $\lim_{x\to a}x=a$
obsidian monolithBOT
Simple_Art:
thick raptor
You can't say "but what if x = 1?"
Essentially, when you take things like derivatives and limits, there is no value for x
It's what's called a "dummy variable"
It exists only for the purpose of some other calculation
viscid thistle
That's really interesting, I'm gonna think a little more about it and hopefully it becomes intuitive. I think I was just approaching the idea from two different, conflicting angles.
viscid thistle
What does it mean to take the derivative with respect to y? Does that mean we are taking the limit as we approach a certain y coordinate? I'm trying to better understand what the d/dx and dy/dx forms of derivative notation mean.
@thick raptor
thick raptor
$$\frac{df}{dg}=\lim_{\Delta g\to0}\frac{\Delta f}{\Delta g}$$
obsidian monolithBOT
Simple_Art:
viscid thistle
That makes a ton of sense! So is there an implied y in the numerator of d/dx?
Also would you mind showing me the derivative with respect to y, seeing it presented as a limit is super useful 😃
obsidian monolithBOT
Simple_Art:
thick raptor
The numerator is the value of x when x³ increases by h
note that x = ³√(x³)
@viscid thistle
viscid thistle
what method should I use to decide if this sequence diverges or converges?
fringe stream
limit comparison test
also, use #calculus or one of the help channels below
this is not exactly precalc
viscid thistle
oh ok, thx
naive sable
when im asked for the horizontal reflection of x^2 how do I write that?
cause any negatives reflect it vertically
serene heath
horizontal meaning about the y axis
which is f(-x)
which is just x^2
sine x^2 is symmetrical about the y axis
naive sable
why is horizontal on the y axis? I thought it was on x
I feel that this is really simple and im super over thinking it lmao
serene heath
yea youd think that at first, so did I
but think bout the graph is ''moving'' when reflected horizontally
naive sable
it looks the same
serene heath
horizontal reflections arent necessarily about the y axis btw
they could be about any vertical line
but i just assumed y axis since you didnt mention it
naive sable
this review is asking me to turn y=x^2 and write it down as it's horizontal reflection formula
so it's just y=x^2?
naive sable
hmm sorry let me try translate it better , its in spanish hahaha
just gives me the original equation being y=x^2
then asks me to write it down but reflected horizontally
serene heath
so it doesnt say about y=2 or y=-1 or anything?
naive sable
nothing on y
serene heath
perhaps theyre looking for a general formula then
the graph of x^2 reflected about y=a
hybrid coyote
what exactly am i doing wrong in this problem?
hybrid coyote
because there isnt a phase shift
this program doesnt tell you the correct answer :/
onyx tinsel
stupid program
chilly schooner
Wounding if I can get some help.
nimble oxide
Hey, so I'm working with circles and their equations, let's say my equation is 5x^2+5y^2=20
Would the radius be would it be the square root of 20?
chilly schooner
I'm trying to create an exponential function with two points given. The function form is y=AB^x. The points provided in the explanation is (3,5) and (6,2.5). I got B by finding out the different of the y-values are 1/2.
hexed ermine
@nimble oxide factor out a 5
nimble oxide
Oh it's my friend, PJS lol
chilly schooner
!Tea, yes it would
hexed ermine
Factor out a 5 from 20
nimble oxide
Oh you factor it from everything
nimble oxide
Oh, then you just take the square root of the number on the right of the equal sign?
chilly schooner
the circle formula is (x-h)^2 +(y-k)^2=r^2. the vertex is (h,k) and the radius is r. P.S the R in the fomula is squared and the radius is not squared.
nimble oxide
Alrighty thanks, serious GOAT
Trying to make 2 different equations with the same center but different radii
And I'm trying to make it as easy as possible lol
chilly schooner
Thank you PJS
lapis nimbus
I'm completely lost on Logarithmic equations
I'm not understanding how to graph them if I don't know what the equation is equal to
Like if f(x)=log(3)x+2
hexed ermine
log_3(x) you mean
solemn tiger
f(x) = log(3)x + 2 would be an affine function through (0, 2) that has a slope of log(3), did you mean log(3x)?
Or log base 3 of x?
hexed ermine
Oh okay
lapis nimbus
My bad
lapis nimbus
Move the graph up 1?
solemn tiger
log(x - h) + k
h is the horizontal translation, k is the vertical translation.
lapis nimbus
Yup I'm making stuff up now I meant 2
hexed ermine
If you add 2 to the argument, that means the function shifts to the LEFT 2
lapis nimbus
Because (x+2)=0 means x=-2?
solemn tiger
The logarithmic function is defined for (0, infinity).
Since we have log(x+2), we can plug in any value on the domain (-2, infinity) for x.
As it won't make the stuff inside the log 0 or negative.
lapis nimbus
So from there I'll just plug values in for x and graph that out
Thanks for the help guys, I appreciate it
nimble oxide
How do I find the measure of the transverse and conjugate axis
I know how to find them on a graph, i just dont know how to write down their proper measurement
hexed ermine
When you have your hyperbola in standard form it's just 2a and 2b for your transverse and conjugate axis
fringe copper
Is anyone around
hexed ermine
Sure
onyx tinsel
yeah we dont do that in math
hexed ermine
So 8 needs to be x
onyx tinsel
"I want the answer to be that and not this"
fringe copper
Hmmm
hexed ermine
log_2(16)=4
fringe copper
In 50 can’t I say x=2^2y
hexed ermine
2^y=2x
fringe copper
I mean 2x=2y
0h yeah
I see what I did wrong
So if x is 4
Y is 2
Right?
No
Hold up how will this work then
hexed ermine
Not quite
But closer
Plug in 1/2 for x
You get log_2(1)
2^0=1
So y is 0 when x is 1/2
fringe copper
I got it lol
low tide
A. Average Speed = 14.5 Seconds per Feet (Not sure if my units are correct)
B. I got up to d(t)=16(3+h)^2 >> 16h^2+96h+144 and d(t)=16(3)^2 >> 144, but now I'm not sure what to do next
C. I can't remember if there is a formula I should be using here. I'm not sure how to use h for this question
Also if there's any questions about the points on the side, this is a practice test she made for us to use as practice
Could someone help me solve this?
I'm unsure what the next step I should do for B is.
For this one I'm also unsure of the formula for the function I should be making. Some ideas I've had are P(t) = P-1000(t)
rare zephyr
<@&286206848099549185>
serene heath
dont understand which bit?
serene heath
because its a constant
if you sketch y=a
it'll just be a horizontal line
the gradient is 0
pine rampart
a constant function changes 0 amount if you change x by any amount
so the derivative is 0
deft umbra
guys, where do i start solving this ?
do i use this : sin(x − y) = sin x cos y − cos x sin y ?
deft umbra
i need to get Zf and Df
i think its called range and domain in english
i solved it via https://www.wolframalpha.com/input/?i=f(x)%3Darcsin(2-x^2)
but i dont understand how to solve it to get x = sqrt(2) and x = -sqrt(2)
native panther
Learning some shit let’s go this is whack
gritty blaze
Easy.
solemn tiger
It's trig, where math was still fun!
onyx tinsel
HOLD
native panther
Ok quantic some of us are learning this for the first time
onyx tinsel
HOLD
what do you mean "math was still fun"
are you implying math is no longer fun
this had better be a misunderstanding
or I will lose my shit
native panther
Lul nerd
limpid plover
Don't forget to wipe hard disk if you decide to actually do it
pine rampart
trig isn't even real math
higher math (i.e. real math) is way more fun
get it right next time, nerd
onyx tinsel
excuse me?
<@&268886789983436800> ban tbh
come look at this fucking limpertoper
"trig isnt real math" he says
your mum isnt real math 😂 😂
pine rampart
improper use of the moderators tag
serene heath
rip
versed ravine
Someone help me out with this?
viscid thistle
Sum and difference formulas?
versed ravine
But how?
hexed ermine
You can find the formulas online
viscid thistle
Well, you should be able to apply them directly then. Just "plug and chug"
deft umbra
i did f o g but i'm stuck at g o f
can somebody help me out ?
do I multiply 1*(x-1)^2 + 1 when i'm inserting in g(x) ?
solar abyss
@deft umbra i think ur correct for g o f, just that for x<0, it should be 4x^2 not 2x^2
deft umbra
thank you very much ! 
rocky girder
how do i express sin60 + sin20 simplified
stark copper
I’m with dill on asking this question, I can send my half finished attempt if you can use it to spot an error
rocky girder
how do i express sin(pi/3) + sin(pi/9) @fallen cloud
fallen cloud
pi/9.... ew
rocky girder
ik
stark copper
fallen cloud
$$ cos(\frac{\pi}{9})=\frac{(\frac{1+3i}{2})^{\frac{1}{3}}}{2}+\frac{1}{2(\frac{1+3i}{2})^{\frac{1}{3}}}
obsidian monolithBOT
Yeat:
fallen cloud
sin(60)+sin(20)...
solemn tiger
Wew upside down 
hexed ermine
Make a reference triangle and label your cosines and sines
angle alpha
make a triangle in Q1
you have cosine of alpha being adjacent over hypotenuse
so you can find the opposite side
hybrid sentinel
ahhhh hi
wise umbra
lol
hexed ermine
Hint, when you have a negative power that implies discontinuity ie asymptote
viscid thistle
More hints pls @hexed ermine
viscid thistle
Are we playing hide and seek that you are just giving me hints? @hexed ermine
And not explaining things.
Any helpful links?
viscid thistle
Well, I have already solved it using GeoGebra graphing calculator.
I just want to have a grasp of the graphs of those functions in a more intuitive way. @hexed ermine
west holly
just graph them and learn
serene heath
how did you go about it?
stark copper
serene heath
hmm messy
serene heath
try this instead $\cos(2x)=1-2\sin^{2}(x)$
obsidian monolithBOT
lemon catto:
serene heath
i meant the working out was messy not your handwriting
stark copper
Oh well the steps I was doing too aren’t as efficient as I want
serene heath
try the double angle formula and see what you get
stark copper
That is the section I’ve just been doing addition formula so much I’ve gotten used to it 😓
serene heath
nice
stark copper
I’m not sure how to format this
serene heath
wdym
stark copper
I’ll show you just gimme a sec
stark copper
^
Okay cause cos Pi/2 is just 0
But sin of Pi/2 is 1
So it wouldn’t work with the equation staying as sin
serene heath
alright
stark copper
But I understand that it’s the cosine double angle
serene heath
you have $1-\sin^{2}\bigg(\frac{\pi}{4}-\frac{x}{2}\bigg)$ right
obsidian monolithBOT
lemon catto:
stark copper
The answer is just sinx though
Yeah no I understand kinda but like the process is foggy
serene heath
why did you turn the -x into +x tho
serene heath
no it doesnt
stark copper
Ik it does in the addition
serene heath
its just double whats inside
stark copper
Ooo
serene heath
so you end up with $\cos(\frac{\pi}{2}-x)$ correct?
obsidian monolithBOT
lemon catto:
stark copper
Yeah
serene heath
but $\sin(x)=\cos(\frac{\pi}{2}-x)$
obsidian monolithBOT
lemon catto:
serene heath
and vice versa
serene heath
more to do with the fact the sin graph is just the cos graph shifted pi/2 unites to the left
you prove that result to be true by using angle sum formula to expand $\cos(\frac{\pi}{2}-x)$
obsidian monolithBOT
lemon catto:
stark copper
So then would cos -x technically not be incorrect?
serene heath
wdym
serene heath
not sure why you replaced the pi/2 with 0
serene heath
yes but thats not how you evalute the value cos(pi/2-x)
stark copper
Is there a way to do it algebraically?
serene heath
what you essentially did is that $\cos(\frac{\pi}{2}-x)=\cos(\cos(\frac{\pi}{2})-x)$
which isnt true
obsidian monolithBOT
lemon catto:
stark copper
The question is what I treated as the right side and I substituted the Pi/4 value into the left side which are the steps I carried out though?
I’m sorry I’m clearly confused on form lmao
neon vale
For 3a how am I supposed to know that 16^1/4 is 2 without a calculator??? Help??
solemn tiger
16^(1/4) is the same as saying the 4th root of 16.
A number times itself 4 times, yielding 16.
gaunt gate
that would be -3=3
neon vale
How
gaunt gate
oh shit potatos you're right
obsidian monolithBOT
omar23:
isn't radical 9 $ \pm 3 $
Idk anymore I’m confused
neon vale
I’ll just put it into the original equation ig
glacial maple
I really don't think 2 is extraneous
obsidian monolithBOT
omar23:
neon vale
Ugh
neon vale
No just says solve and check for extraneous sol
gaunt gate
the book makes mistakes sometimes
write it down and ask your teacher about it tomorrow
gaunt gate
np fam