Ohhh I seee it now
#precalculus
opaque idol
quaint mason
after u substitute 4 in for m, u get t
opaque idol
And that will be the answer?
quaint mason
t=.4m^2
u know what m is already
substitute that in
and then solve for r by doing 150+4t
plug t in
and thats r
opaque idol
I got 182
quaint mason
mmm lemme see
opaque idol
Thank you I appreciate it
quaint mason
thats what i got
quaint mason
which
random cloud
You cant do difference of squares
opaque idol
It’s saying F of G
quaint mason
sorry gimme a sec
opaque idol
Plus I also gotta find if the function is even,odd and neither
Yeah it’s fine take ur time
opaque idol
I think you can say that
quaint mason
just havin problem solving for x or readin the graphs xD
opaque idol
Yeah lol
proud raven
same opposite always positive
quaint mason
jan, how do u solve for x from Jpiggy picture
opaque idol
If this helps on the left side on the bottom that line is g(x) and the top on is f(x)
random cloud
You cant do sum of squares tho
quaint mason
exponents adds
proud raven
i dont get the piggy questiqn what re you ask?ng
opaque idol
Is the function even,odd or neither?
quaint mason
from JPiggy ss, how do u solve for x again
proud raven
oh
random cloud
Exponent raised by exponent is multiplicative
quaint mason
yeah
opaque idol
Yeah
random cloud
Not additive
quaint mason
i thought it was additive vice versa for division and sub
proud raven
can always just expand and group to check
random cloud
Shortcut time 😎 😎
Yoooooo
I end up with
(s + 1)^4
I feel like I did something wrong
quaint mason
oof
random cloud
So wait
random cloud
u=s^3
random cloud
Cuz (s^3 + 1) = (s^2 - s + 1)(s + 1) which is just (s + 1)(s + 1) which is just (s + 1)^2
quaint mason
i cant remember how but its like jan said, somethin to do w the cubic
random cloud
I feel like I'm running in circles
random cloud
Where did you get that
proud raven
soap
quaint mason
ye
random cloud
S+1 is my divisor
quaint mason
yes
proud raven
,w factor x^9+1
obsidian monolithBOT
proud raven
:p
random cloud
But it's not completely simplified
And if you do continue with this
You get something weird
Why is that
random cloud
But why does that happen when we keep going
obsidian monolithBOT
obsidian monolithBOT
proud raven
?
most numbers arent nice
i guess
most numbers are irrational iirc
at least reals
or something idk analysis
random cloud
Noooo it happened again 😭
The far right parenthesis turns into (r^3 + 1) and it will go on forever
Wtf does that mean
,w graph x^6-1
obsidian monolithBOT
random cloud
This kinda annoys me wtf is going on
obsidian monolithBOT
random cloud
Am I the only one that sees the paradox
That it continues to go forever
Whyyyyyyy
And is there a rule that tells me to stop
When this happens
astral mantle
just expand out the equation
to 6x^5/x^4 - 6x^4/x^4 - 3x^3/x^4
then you can divide them all by x^4
so you get 6x - 6 - 3/x
and derive that
i think you did it correctly you just did signs wrong @terse ravine
astral mantle
what?
terse ravine
I'm confused
gritty axle
I still need help with this
terse ravine
f'(x)=6-3(-1)x^-2
terse ravine
f'(x)=6-(-3)x^-2
astral mantle
why do you just keep sending it over again]\
terse ravine
f'(x)=-3x^-2+6?
gritty axle
oops, im in the whole frong channel for this
terse ravine
nevermind I'll wait until I understand it completely.
too many are talking at the same time..
cloud prism
Well as a short summary: $$ (\frac{6x^5-6^4-3x^3}{x^4})' = (\frac {6x^5}{x^4} - \frac {6x^4}{x^4} - \frac {3x^3}{x^4})' = (6x)' -(6)' - (\frac 3 x)'$$
obsidian monolithBOT
Tobii:
terse ravine
cloud prism
Yes. -(3/x)' = -( -1 * 3/x^2) = 3/x^2
fathom root
hey could someone help me understand this answer
Determine the value that the function f approaches as the magnitude of x increases.
i see that the answer is 7 but im just a bit confused onto why that it is
moreover what the question is asking
cloud prism
So you're asking for $ \lim_{x\to\infty} 7 + \frac 1 {x-8}$ ?
obsidian monolithBOT
Tobii:
fathom root
yes
cloud prism
Well the first term doesnt depend on x so we can ignore that as it's constant. So we have 7 + $lim_{x\to\infty} \frac 1 {x-8}$
Well and that approaches 0
obsidian monolithBOT
Tobii:
fathom root
wait so i wanna ask first though is the question essentially asking for the horizontal asymptote of the function?
cloud prism
Yes
cloud prism
I didn't go over this with that rationale, I think: if x gets larger and larger 1/(x-8) get's smaller and smaller but never reaches 0
cloud prism
even if it would reach 0, it just never gets away from it again
fathom root
wait also
the second part of the question asks "Is f(x) greater than or less than this function value when x is positive and large in magnitude?:"
the answer is greater than but according to what you're saying, wouldnt the value of f(x) get smaller as x increases?
because the denominator is increasing, making the fraction smaller?
cloud prism
f(x) = 7 + a bit
so it is greater than 7 (the value just determined)
it gets as close to it as you want to though.
fathom root
wait so 7 would be the function value and the horizontal asymptote?
cloud prism
yes
well not the function value
the function value would be f(x) which is always a little greater than 7
But I guess they refer to the asymptote as "this function value"
Could be I'm completely mistaken :'D
Is there any more context?
fathom root
uhh i dont think so
im not too good at mathj
this is all it provides
as far as i can tell i dont see any other context
cloud prism
Well seems like I was not mistaken after all
fathom root
so are you saying like in a normal circumstance, the function value and f(x) are just the same thing?
fathom root
ohh ok
im native and i dont understand any of the language part
probably more than you tbh xd
ok as a final question, i jkust want to ask, when generally we say as x/f(x) approaches [some number], are we just describing when x/f(x) is just approaching an asymptote?
cloud prism
not really. That works as a picture in this case as we go to infinity, but you can also approach specific values, like points where the function is not defined
like 8 in your example f(8) = 7 + 1/0 which is not defined
but if we go very very close to f(8) from the right or left we can deduce some information about the function
cloud prism
but that is probably calculus stuff or comes later on
fathom root
oh wait wait actually last question my bad
so how could x go to infinity if the vertical asymptote is 8?
or is that just an expression for x increasing
cloud prism
your input value can be as large as you want
fathom root
so is it just a discontinuity at 8?
cloud prism
well we could figure that out by approaching f(8+e) and f(8-e) with e getting very small. If those match up there is literally just a hole there
otherwise the function might jump at that point
,wa f(x) = 7 + 1/(x-8)
fleet yew
Hole pole
thorn plank
viscid thistle
first of all read #❓how-to-get-help @thorn plank
secondly, its barely comprehensible
willow bear
what the actual fuck were you thinking trying to PING EVERYONE in a server of THOUSANDS, @thorn plank
viscid thistle
<@&268886789983436800>
seriously you're directed to #❓how-to-get-help when you join this server
willow bear
bruh
viscid thistle
my bad mods if this wasnt ping-worthy kindly forgive me for my terminal stupidity
quartz edge
derivatives are taught in high schools right? so early uni calculus wouldnt be the spot to post on for me rn
willow bear
it depends
quartz edge
is f'(40) = 800 on this graph?
quartz edge
what would f'(40) then be? 0
viscid thistle
yea
quartz edge
aah okay, thx
static thistle
logarithms are too exponents as inverse trigonometry functions are too __________
what would this be
lime bolt
Why do u care if he pings @everyone
wary stone
Oh nice it doesn’t work
viscid thistle
shut the fuck up
bitch
These were not acceptable
paper acorn
blazing parrot
okay for 1) try to write the trig functions they want (cos, tan, csc, cot) in terms of the ones u have the values for (sec, sin)
uncut mulch
drawing a triangle helps
then apply pythagorean identities and signs in quadrants of the unit circle
viscid thistle
"At a point 150 fett from the base of a building, the angle of elevation to the bottom of a tower on top of the building is 32 degrees. The angle of elevation to the top of the tower is 50 degrees. Find the height of the tower alone."
How do I do this?
Like I am pretty lost with i
it*
uncut mulch
draw diagram
willow bear
have you made a diagram? @viscid thistle
viscid thistle
i made one rn but i only have it set as a right triangle, and i think the 150 would be the bottom part of it? like it is one of the sides that aren't the hypotenuse, and it isn't the height
it's the length part of it for me if that makes sense
so is the angle at the top 50 degrees? or is it the 30 degrees?
willow bear
try making a drawing of the actual setting
viscid thistle
this is what i have got
willow bear
where's the tower?
viscid thistle
the one thing with the door lol
viscid thistle
oh there are two different stuff?
minor pivot
Can square root of 181 over 9 be rationalized ?
willow bear
$\frac{\sqrt{181}}{9}$ is already rationalized
obsidian monolithBOT
Ann:
minor pivot
oh okay so there is nothing you can do with it?
minor pivot
hypotenuse over opposite
willow bear
no, what are you trying to do with this number?
minor pivot
181 sq is hypotenuse and the opposite would be 9
minor pivot
find the csc value
willow bear
i am asking you, what are you trying to do now that you've got this number: sqrt(181)/9?
what are you trying to do with the expression sqrt(181)/9
minor pivot
I'm wondering if that is my answer
willow bear
i don't know, you haven't posted the problem
so nobody can tell you whether or not sqrt(181)/9 is the answer to this mysterious problem, which it seems you expect people to magically know about
minor pivot
Use the Pythagorean Theorem to find the length of the missing side. Then find the trigonometric function of the given angle. Give an exact answer with a rational denominator. So I got a triangle the opposite side is 9 and the other side is 10. So I needed to find the hypotenuse which I did which is sq181
willow bear
you mean sqrt(181)
okay, so like
you're asked for csc(θ) where θ is the opposite angle to the side with length 10
yes your answer is correct now
gritty stratus
fervent abyss
it goes through 2, 5, so x = 2 and y = 5
substitute and evaulate
and then take the square root of the result
willow bear
@hazy furnace find the radius of your circle
fervent abyss
this is what they're trying to do, yes.
hazy furnace
idk how to do that
fervent abyss
I just explained it
uncut mulch
explaination was poor
fervent abyss
thanks, so am I
uncut mulch
apply the distance formula
hazy furnace
idk what that is
uncut mulch
look it up
hazy furnace
ok
fervent abyss
why are you making this more complicated than it needs to be
plug in 5 for x and 2 for y, evaluate the expression and take the square root
I'm not sure how that explanation is poor
hazy furnace
how i evalute experssion
uncut mulch
that works too I guess
obsidian monolithBOT
Result:
73
dont even need to take the sqrt
hazy furnace
yeah
uncut mulch
since you're not explicitly after the radius
willow bear
only to then square it immediately afterwards
fervent abyss
I didn't read the question properly, I just saw that they were asking for the radius
willow bear
hazy furnace
i dont understand how u get 2-5^2 + 5+3^2
willow bear
parentheses!!!
hazy furnace
idc
willow bear
hazy furnace
()()
fervent abyss
the circle goes through (2,5), so naturally, plugging those values in for x and y needs to result in an equation which equals the radius squared
fervent abyss
as the circle equation is the equation which all points on the circle have to satisfy
hazy furnace
,calc (1-4)^2+(5+3)^2
obsidian monolithBOT
Result:
73
,calc (-3+1)^2+(2+3/2)^2
obsidian monolithBOT
Result:
16.25
You can also use desmos :+1:
not sure which channel this belongs in, but what is the sum from k = 1 to n of k^4?
astral mantle
$\frac{1}{30}n(n+1)(2n+1)(3n^2+3n-1)$
obsidian monolithBOT
Star_:
terse ravine
Oh I forgot the 36x^2+48x+16
Then f'(2)=(10) / (36(2)^2+48(2)+16 = 5/128
Never mind, was a mistake in typing out the correct ans. Sorry, for pinging :c
I've been doing Math for 8 hours already x.x
chrome thorn
What are the extreme points of x/(2-sqrt(x)) ? I found x=16 as maximum but in the book it's says there is one more point which is x=0
willow bear
,w d/dx x/(2-sqrt(x))
obsidian monolithBOT
chrome thorn
But why? How can I find it algebraiclly
echo wagon
Extremum points occur where the derivative zero, or at the boundary points of the domain.
novel cargo
if a rational func has variables of even degree then it doesn't pass the horizontal line test and dosn't have an inverse
is this statement correct?
polar heart
use the fact that $e\approx 2.7$
obsidian monolithBOT
Anonymous:
halcyon granite
is there a way to find the extrema of a quartic instead of just plugging in numbers between roots
willow bear
take derivative and find zeros?
halcyon granite
without derivatives cuz i feel like my teacher wouldnt appreciate me using concepts we havent learned yet
halcyon granite
yeah he kinda just told us to graph a quartic function and describe it, and he always wants to know the extrema and on the answer sheet he has the extrema, but doesn't show how he got to them
viscid thistle
$\pi$
obsidian monolithBOT
boof:
viscid thistle
$e=\pi=3$
obsidian monolithBOT
boof:
viscid thistle
Yes this is cursed
halcyon granite
very cursed
shadow plaza
quaint mason
@polar heart why is e approximately 2.7?
lime bolt
because it is
tawdry python
quaint mason
i get that but can u show the work?
like how does that have anything to do w approximate values from a list of numbers
tawdry python
I cannot say that I can fully explain it to you, if you want a comprehensive answer check out Eddie Woo's video.
quaint mason
eddie woos?
tawdry python
it pops up in a lot of places and can usually be traced back to being related to exponential growth
quaint mason
he used a calculator, but the hw says not to, so is there a way not to use calculator or do u have to use calculator to solve for this
tawdry python
could I see the full question? I'm curious now
quaint mason
the one i posted above is the full explanation to the problem
they give u a list of numbers, and find e-1
echo wagon
Oh, they clearly just expect you to know that e is approximately 2.7
tawdry python
Thats what my first thought was too
I think that they're testing your knowledge of the approximate value of e
quaint mason
thats weird but ty yall
whats with the list of numbers tho?
like is it important in any way
tawdry python
I dont think so, it looks to be a set of options for you to choose from
echo wagon
Yes, they want to limit the correct answer to one. Otherwise someone who uses e = 2.7 and someone who uses e= 2.718 will enter different answers. Now you just have to choose the closest value in the list, so everyone has to choose the same one
tawdry python
It would be less confusing if they just asked
"What is the approximate value of [ e - 1 ], round to one decimal"
quaint mason
i see
night fiber
π=e=3
proud raven
so 2pi is a full rotation, yea?
and the negative means were starting at (1,0) and going anti clockwise
so were almost going a full rotation anticlockwise
youll land at a place where both the x and y coordinate are positive
so all you need to know is if the ratio of a positive number and a positive number is itself positive or negative @minor pivot
proud raven
yea
its 1 where the signs match
(of the x and y coordinates)
and -1 where they dont
minor pivot
oh so if the question was 7pi/4 it would be -1 right?
proud raven
yea 😄
minor pivot
thanks
ivory finch
It’s interesting looking at this channel. The US system is jarring for me- why do you wait till University to do some calculus aside from precalculus? The nature of the questions you get is also weird. Though perhaps it’s better- my country’s course infamously scars the mental health of most students and suicide isn’t uncommon.
Perhaps I should have said this in a different channel
dusty cape
anyone free here for a sec?
quaint mason
can someone explain why 10 is wrong
all i did was 4.67 divide by 4 because it is quarterly, then i got 1.1675. divide that by 100 turning it into decimal rather than percent and it becomes .011675. add 1 to that=1.011675. take that to power of 6 and multiply it all by 1000. where did i go wrong bruh?
to sum that all up
this.
willow bear
@quaint mason it's 6 months but 1.1675% is the quarterly interest rate, so you'll want to do this for 2 quarters, not 16.
quaint mason
wym i didnt do it for 16 quarters
willow bear
you say you raise it to the 6th power but then write 16 in the pic, which is a bit 
willow bear
quaint mason
^
willow bear
you're already writing it as a superscript, why insert a caret
quaint mason
idk
willow bear
...
willow bear
anyway the exponent should be 2
quaint mason
i actually
willow bear
for 2 quarters
willow bear
,calc 1000 * 1.011675^2
quaint mason
i caught the mistake
obsidian monolithBOT
Result:
1023.486305625
1023.49 is wrong?
quaint mason
oh wait wow
my calculation is wrong
not that
ah i found out what i did wrong
for some reason my mind kept thinkin it stays 1.1675 even tho ik im suppose to do it the way i described...
sorry thats my calculation error
thank you :)
thats right, ty :)
copper breach
Can someone please check my work and help me understand how to do question b.) and c.)
asap please cause i'm trying to review for my upcoming test
ty
fiery wren
really?
i thought it was asking me to find the angle of the coterminal
isnt the coterminal of -pi/4 = 7pi/4
and the angle of 7pi/4 is 315?
fiery wren
and -315?
fiery wren
yeah i understood dw lol
i'm either
overthinking or
doubting myself
so should i just leave it at 315 degrees
-315 degrees isn't coterminal with 7pi/4?
fiery wren
gotcha
and while i have you here
in the midst of my breakdown and overthinking crisis
this is okay?
quick mirage
Actually there are two answers here
austere void
+315 works too
quick mirage
When going clockwise, you go in the negative direction
austere void
ah equal
quick mirage
And that gives you -45
quick mirage
When going counterclockwise, you get the equivalent positive angle
I wish i can draw a diagram here
But im on mobile
fiery wren
i drew it out a couple of times to make sure im not going crazy lol
austere void
(the mathematicians and clockmakers definitely had some kind of dispute in there)
fiery wren
i think im going clockwise
quick mirage
I woukd say negative and postive direction but thats a bit counterintuitive and confusing
fiery wren
lemme post my diagram
oops
lemme flip it
okay
it has to be 315
since it's going counterclockwise
quick mirage
fiery wren
thank you guys
quick mirage
No problemo
fiery wren
yikes
not correct
it was only -45 degrees apparently, not 315 degrees
which doesnt make sense to me
quick mirage
Well, when not considering the range 2 pi, but in general, it could be illogical to say that -pi/4 = 7pi/4
So its not entirely confusing
quick mirage
But i guess they were looking for a specific answer
fiery wren
it's all good brother
quick mirage
@fiery wren just wanted to correct something i stated before, coterninal angles can be found only on 360n+theta
obsidian monolithBOT
kin:
smoky pagoda
same thing
smoky pagoda
by log rules
smoky pagoda
remember that $a\log{b} = \log{b^a}$
willow bear
and in particular log(1/x) = -log(x)
obsidian monolithBOT
Little Narwhal:
viscid thistle
👍
narrow peak
obsidian monolithBOT
Hmm:
obsidian monolithBOT
Hmm:
$\frac{A}{x+3}+\frac{B}{3x-1}$
Yeah, then solve for A and B
copper breach
Can someone please check my work and help me understand how to do question b.) and c.)
asap please cause i'm trying to review for my upcoming test
ty
I asked this question yesterday but again someone else asked a question right after ans no one replied to me wth
I would greatly appreciate if someone could help me
elder charm
what you did in a) is what you need to do for c)
elder charm
in a and b you just need to say that it's $64 e^{\frac{13\pi}{6} i}$ raised to the power $\frac{1}{3}$
obsidian monolithBOT
ConfusedReptile:
elder charm
didnt you forget to apply the 3rd-root to the e-term?
They did divide 13/6 by 3.
cloud prism
oh right, I totally missed that
copper breach
I did apply the third roof
Roof
Root
So I got 13pi/18
I don’t understand what powder the complex number is raised to
1/3?
Or do I saw the 13pi/18
elder charm
Yes, 1/3.
gilded brook
How do you do this?
gilded brook
<@&286206848099549185>
gilded brook
Still need help for this one problem I really just don't know how it's done
First time seeing that symbol
echo wagon
Can you expand sin(x+φ) using the compound angle formula for sin?
Then compare what you get to what you have to rewrite
elder charm
No, e here is the Euler's constant, the base of a natural logarithm, approximately 2.7182818284590452353602874713527 😛
how do i solve for a and b?
use the fact that $e^{n m} = (e^{n})^{m}$
obsidian monolithBOT
ConfusedReptile:
obsidian monolithBOT
KO7S:
Compile Error! Click the 
reaction for details. (You may edit your message)
obsidian monolithBOT
KO7S:
elder charm
yes
vapid folio
my question is "solve the equation on the interval of 0 <= (theta) < 2pi."
the equation is cos(3theta) = 1
for some reason, the answer isnt 2pin/3
viscid thistle
Cuz theta is restricted to [0,2pi)
so n=0 is the solution
for some reason, the answer isnt 2pin/3
elder charm
$14.825 e^{-0.007t} \approx 14.825*0.99302^t$
obsidian monolithBOT
ConfusedReptile:
cloud prism
Well you could start by calculating the first 3 entries of the product... You should see where you are going from there
trim cave
wait
you could add all the entries into one row
then take that out
then you'd be left with ones
then you'd subtract every row from one another until you get just one in the row with the ones
then you take the determinant of that
cloud prism
Why do I think, that he just came here to get the solution to his homework from somebody?
willow bear
@stoic fox
stoic fox
yes?
willow bear
these are both 10 by 10 matrices, do you think their product could be undefined?
stoic fox
thats exactly the reason why i said "if it exists"
willow bear
have you ever multiplied two matrices before
stoic fox
yes sir
echo wagon
The product of 10 by 10 matrices always exist, so you don't need that qualifier. So that's exactly the reason you don't need to say that.
What makes you think someone named Ann is a sir?
willow bear
"sar" also yeah don't call me sir please
anyway multiplying two 10 by 10 matrices by hand is painful
echo wagon
And it might not exist
stoic fox
The villager way of saying "sir" since u guys didnt like it
viscid thistle
use wolfram alpha
stoic fox
no @viscid thistle stfu
willow bear
the issue isn't that we don't like the term "sir" it's that i'm not a man lol
echo wagon
LOL
willow bear
how's that relevant
stoic fox
well i am 23
viscid thistle
why are you doing precalc at the age of 23
willow bear
i'm 21 but again how's that relevant to my not being a man
stoic fox
why are you doing precalc at the age of 23
@viscid thistle What can i do sar
echo wagon
why are you doing precalc at the age of 23
Why not? Don't be rude
stoic fox
Why not? Don't be rude
@echo wagon thanku sar
echo wagon
Please stop calling people sar and sir. It's p rude to keep doing it after you were called out. You don't know who is male here.
willow bear
if you insist on using "sir" or "ma'am" for me i'd rather you call me ma'am
stoic fox
Ok madume
echo wagon
And I am male, but I don't like sir. And I'm younger than you, so it's extra weird
stoic fox
Ok madume undarstud
willow bear
...
stoic fox
...
willow bear
computing their product will literally take a thousand multiplications
echo wagon
checks how long he has been on this server because this has to be a troll post
echo wagon
Lol, you say you know how to multiply matrices, you're just too lazy to do it. So now you are asking us to do it. Ridiculous.
willow bear
Why u so lazy then
you expect me, a random stranger on the internet, to sit down and do literally 1000 multiplications BY HAND for you?
echo wagon
Use an online calculator
willow bear
and i'm the one who's lazy?
willow bear
how were we meant to know
echo wagon
So your whole post is a troll post?
willow bear
we aren't telepaths, we can't read your mind
delicate rivet
delicate rivet
the function is y = 0.19cos(pi \7 x)+1.62
yea i used a calculator to find the derivative of function xbetween zero & 24
but on the answers, there are 2 sets of answers, one using only the max of the derivative graph and 1 using both the max and the minimum
which would be the correct one?
echo wagon
Do they give two different answers or two methods to get the same answer?
delicate rivet
yea, its the same method, 2 sets of answers
but one teacher uses both the min & max and one only uses the max
echo wagon
Show us?
willow bear
anyway @stoic fox if you still want that product
echo wagon
Pink is correct @delicate rivet
delicate rivet
okieee tysmm,
echo wagon
The sign of the derivative only indicates whether the tide is increasing or decreasing, not the speed at which it is doing it.
echo wagon
So you want the biggest magnitude of the derivative, without caring about the sign. So when it is + or -
delicate rivet
thank you again!
echo wagon
Np
obsidian monolithBOT
amy.ames.aims:
delicate rivet
nvm i figured it out
fast pawn
math sucks anyways
velvet blade
math sucks anyways
@WaidenWolf#6153 what is cool in your opinion?
shadow plaza
They left. Lol
opal rain
uncut mulch
product rule
worthy summit
Hi guys, I need help with difference quotients and rational expressions
More specifically I'm struggling with finding the difference quotient of rational expressions with square roots
viscid thistle
do you have an specific problem that you are stuck with?
worthy summit
Yes, f(x)= -sqrt of 8x-35
I know that f(x+h) is -sqrt of 8(x+h)-35
and I know how to set the equation up, but I get lost with the correct terms that need to be figured out
uncut mulch
what do you have atm
worthy summit
(-sqrt8x+8h -35 - -sqrt8x-35)/h
uncut mulch
uncut mulch
just to be clear:
$$f(x) = -\sqrt{8x} -35$$
right?
obsidian monolithBOT
ramonov:
uncut mulch
$\frac{f(x+h) - f(x)}{h} = \frac{ -\sqrt{8(x+h)} - 35 - ( -\sqrt{8x} -35)}{h}$
obsidian monolithBOT
ramonov:
sick seal
howdy yall, here on question b im struggling to find out how to implement the perimeter as an expression in terms of l.
bc i feel i somehow have to add (length2)+(width2)=335 somewhere in here
but g is asking for area...
fading token
area = length x width
sick seal
well yeah, but how do i show that when (length2)+(width2)=335
fading token
Note that you're essentially asking the question: "how do I separate $w$ when I have the equation $2l+2w=335$?"
obsidian monolithBOT
Rijinaru:
fading token
Does it help you when it's framed like this?
sick seal
to a degree, im just not sure how w fully disappears since it cannot be in the final expression.
fading token
Are you aware that $w= (335 - 2l)/2$?
obsidian monolithBOT
Rijinaru:
worthy summit
ramonov:
@obsidian monolith place the -35 under the radicand and then simplify it further
@uncut mulch
viscid thistle
-28
pallid geode
How would I go about this since i just got x=54 and other two x=0
viscid thistle
What?
viscid thistle
oh okay
heady linden
yes
i tried vietas already cause it is a similar problem but they didnt really work
viscid thistle
What did you do
heady linden
8?
heady linden
celest void
m = -2(-1/2 + 4) = -7
-2 = pq^2, 2 = 2pq + q^2
pq = -2/q sub into second equation get a pretty easy cubic
pretty hard precalc prob tbh
viscid thistle
Hard ?
heady linden
i am
pallid geode
Same
celest void
I do not expect school to give this type of prob
pallid geode
Its not school its extra curricular
celest void
celest void
welp
heady linden
my mistake was that i used an-1 subscripts from the wrong sides so i was using the wrong coeffs
so close yet so far :((
smh
steel venture
yes
unkempt burrow
yes
@steel venture so -(bp/k)+4?
steel venture
yes
unkempt burrow
thank you
latent fern
Could I have help for my practice test?
So then I could ace the math test I have tomorrow
uncut mulch
did you already attempt it?
latent fern
I have attempted partial of it but parts I am stuck on
uncut mulch
go through the whole thing, preferably in a test environment first
and we can guide you on what you missed / need to work on
uncut mulch
sure
latent fern
That’s the first one
uncut mulch
not really pre-calc
latent fern
....
quick mirage
When you want to isolate for a term like b, all you need to do is do the backwards operations of PEDMAS
or BEDMAS
or whatever it is in your educational system
latent fern
Yes PEMDAS
uncut mulch
but where did you get stuck?
latent fern
On the adding... of -2 lol
uncut mulch
consider adding 2 to both sides
latent fern
Okay I did that but after that is what I got stuck on
uncut mulch
$\frac b4 - 2 \red{+ 2 } = -1 \red{+2}$
obsidian monolithBOT
ramonov:
uncut mulch
what do you have after that
quick mirage
Think of it this way
$+2-1$
obsidian monolithBOT
AbooZinho:
quick mirage
You're left with $b/4 = 1$
obsidian monolithBOT
AbooZinho:
latent fern
B=4?
uncut mulch
lowercase b
latent fern
Well yeah... sorry I’m dumb
uncut mulch
to get from b/4 to b, you could multiply by 4,
so you could multiply both sides of the equation by that
latent fern
THANKS
Okay thats actually sooo helpful
I know im not too bright..
I think I know how to Ace this test tomorrow thanks!
slow geode
obsidian monolithBOT
timour:
willow bear
x = 2e^y - e^{-y}, solve for y
somber yew
I saw a proof for the associativity of function composition, can someone explain the reasoning behind the steps marked with (?)
somber yew
This is how Tao wrote them 
willow bear
weird
somber yew
Should I quote the definitions too?
willow bear
brhu
somber yew
Nope, none of these lines is mentioned in the errata(although another line from the same proof is).
Aight one screw up on my end 😅
Sowwy
somber yew
This just looks like we assume what we want to prove
How does the third step move to the fourth?
f(g(y)) = (f o g)(y) where y = h(x)
Hmmmm this makes more sense.
But I'm not yet entirely convinced about how this argument is working, I know it should be true but this symbol pushing feels weird.
Is there an alternate way to prove it? Perhaps by using some arbitrary elements?
willow bear
it should be obvious that applying (h, then g), then f and applying h, then (g, then f) should give the same result tbh
somber yew
Oh, okay. Thanks!
unkempt magnet
im not sure if i understand this
does this just mean that if 0 < |x-5| < delta = epsilon then 0 < epsilon because |f(x)-7| = |7-7| = 0 so |f(x) - 7| < epsilon ???
shell isle
Does anyone know how to do the integral of cos^6 x sin^3 x dx ?
blissful ridge
Have you tried something?
worn anvil
viscid thistle
consider trying to identify the parent function by it's looking and then apply their function transformations
shell isle
I got it, I messed up on a trig identity
misty ocean
subtle mist
@misty ocean arccos(-sqrt(3)/2) = 5 pi/6 =/= 7pi/6 hence the first statement is true and the second is false. This is from the fact that cos(x) is not injective as several inputs corresponds to the same output, i.e cos(7pi/6) and cos(5pi/6) is both equal to -sqrt(3)/2
being injective means that for all x y in some domain is a set S, then f(x) = f(y) => x = y
sick seal
why cant t <0?
patent beacon
Then t = √[x/21]
And you don't need to worry about the negative sqrt
lime bolt
it is just x-3
sick seal
this is stupid. why tf is that question here.
confusing me by taking me back to 3rd grade
istg
uncut mulch
no
lusty falcon
gritty meteor
