#help-13
zenith sail
can you draw on this picture the length OE that you're looking for?
You don't actually need to find the angle
undone reef
zenith sail
awesome, notice that alpha is included in two right triangles
you can express sin alpha in two different ways, one of which including OE
zenith sail
you can express sin alpha in two different ways, one of which including OE
Do you see what I mean?
undone reef
is this what you mean?
zenith sail
and also
remember the 9/12/15 is also a right triangle
(I assume that's how you found the 9 in the first place)
zenith sail
Oh, that's basically just the pythagorean theorem
It works because the diagonals of a rhombus are perpendicular
9^2 + 12^2 = 15^2
so angle DOC is a right angle
using triangle DOC, you can express sin alpha in a second way
undone reef
Okay i found OE but now i need to find the volume of the pyramid
zenith sail
There's a formula you probably know for that
undone reef
zenith sail
,rotate
wraith daggerBOT
undone reef
There's a formula you probably know for that
I do but
undone reef
i do not understand why the angle for cos and for sin alpha is 53degree
zenith sail
don't worry about the angle
undone reef
Owh
zenith sail
so angle DOC is a right angle
from here
from triangle DOE, sin alpha = OE/9
from triangle DOC, sin alpha = 12/15
so OE/9 = 12/15
That is, they are similar triangles
undone reef
zenith sail
no problem 👍
undone reef
zenith sail
,rotate
wraith daggerBOT
zenith sail
yes 518,4 I agree
undone reef
Its ok that OE = H ?
undone reef
Ok, thanks, the last task for this is
find the whole area of the pyramid (i think thats how you say it in english)
So add the 4 side triangles with the base
zenith sail
It's usually called surface area in English
but yeah that shouldn't be too hard, you already have the base
undone reef
zenith sail
looks good 👍
undone reef
the task doesnt say anything about simplifying so do i leave the s=216+216*sqrt(2)
instead?
zenith sail
It's fine to have both
but 216+216sqrt2 is the exact form
as long as you have that in your work it's fine
undone reef
Ok thanks, if i have a different task do i reopen the help or post it here?
zenith sail
Probably best to close this and open a new one
cedar kilnBOT
cedar kilnBOT
Available help channel!
crimson sedge
hey
topaz saddle
apologies
crimson sedge
what's the sols (x, y, z) for $x^2+y^2\equiv z^2 \pmod{11}$
wraith daggerBOT
Mellow
cedar kilnBOT
what's the sols (x, y, z) for $x^2+y^2\equiv z^2 \pmod{11}$
The purpose of this server is to help you learn, not to hand out answers. Do not ask someone to give you the answer directly.
crimson sedge
**Mellow**
Like I found ( 1, 4, 5) (9, 5, 3) (1, 3, 4) (4, 5, 9) (9, 3, 1)
but those are (x^2,y^2,z^2) not (x,y,z)
dawn junco
yeah those are the different x^2, y^2, z^2 mod 11 that match (if you exclude the obvious cases like 0+1 = 1, etc...)
dawn junco
but those are (x^2,y^2,z^2) not (x,y,z)
indeed
it's not too hard to get the possible x's from that though
crimson sedge
hmm
crimson sedge
oh so for x^2 = 1 we have x=1,10 mod 11?
crimson sedge
pardon my shitty mouse-writing
haha thx
dawn junco
and you have that split for y and z also
crimson sedge
so if x^2 = 1 mod 11, then x=1 mod 11 or x=10 mod 11
lol we're thinking of the same thing
crimson sedge
and you have that split for y and z also
mhm
dawn junco
so each of these (x^2, y^2, z^2) situations gives you 8 solutions in the end
it's a pain
dawn junco
yeah those are the different x^2, y^2, z^2 mod 11 that match (if you exclude the...
are you told to exclude the obvious cases ?
otherwise you have to count them in also
crimson sedge
yea x,y,z \neq 0
dawn junco
alright
the last thing is you can swap x and y in a solution and you still have a solution
so should be 80 sols total
cedar kilnBOT
cedar kilnBOT
Available help channel!
grim kettle
How do I go about doing this line integral?
cedar kilnBOT
How do I go about doing this line integral?
dawn junco
well you know x+y=10 when you're on the line C
what happens to the force F in that situation ?
@grim kettle
grim kettle
I guess I am most confused about the line C
I would be able to do it with the line from P to Q
thats an easy integral of F with r(t) as the components doted with the displacement vector
dawn junco
I would be able to do it with the line from P to Q
C is the line from P to Q though
I don't understand your confusion here
grim kettle
I guess I am failing in applying this problem I did earlier to this one
dawn junco
yeah they don't want you to parameterize here
so you're not going to apply the previous problem
dawn junco
well you know **x+y**=10 when you're on the line C
and the force is F = (x+y) i + (3x+3y+4) j
so when you're on line C, the force F is ?
grim kettle
so when you're on line C, the force F is ?
F dot C right?
dawn junco
no
it's just replacing expressions here and there, no dot prodding yet
I even highlighted what to look at
grim kettle
I even highlighted what to look at
I'm not entirely sure
dawn junco
if x+y=10, what's 3x+3y ? let's do it that way
dawn junco
well 34 not 30 but yeah
grim kettle
yeah since the +4
dawn junco
so you're computing the work of a constant force pretty much
grim kettle
then I dot it with the displacement vector <-12,12>
and since F is a constant, it comes out of the integration?
@dawn junco
dawn junco
in a very hand-wavey way, yes
so that the total work ends up being F . d
@grim kettle
cedar kilnBOT
cedar kilnBOT
Available help channel!
honest torrent
cedar kilnBOT
weak otter
Do you get why it doesn’t work
honest torrent
Do you get why it doesn’t work
not really
because he is creating a new number that wont match to any of the corresponding ones which can conclude not countable
weak otter
Well that’s the goal
But the problem is that the new number doesn’t need to belong to the set
It could be 011 and so on
weak otter
Yeah lol
So
Do you get why if the number started with 011… it doesn’t belong to the set
Or just 11…
honest torrent
no 😭
weak otter
The way they construct numbers is in the following way
If n is in the set, the nth digit will be a 1, otherwise it’s a 0
So the number 1100000….. is just the set {1,2}
So it doesn’t belong
honest torrent
so number 1 is written in every even or odd pos
weak otter
If the number has 1s in only even or only odd spots, then the set it corresponds to belongs to the set that they care about
honest torrent
waikt
weak otter
Does that make sense
honest torrent
ok i get how 1 is supposed to be in the position of the set elements
but how do they map the set N with binary
weak otter
Wym
weak otter
im assumign youve seen cantors diagonal argument
the proof assumes that such an f exists, and then shows that it cant
honest torrent
so it is just random binary
honest torrent
im assumign youve seen cantors diagonal argument
i understand the argument to show that a set is uncountable
honest torrent
so what is exactly wrong with the proof
honest torrent
^
oh is it bc their could be another number that correclates to the set {1,2}
its not only 1100...
weak otter
no
thats the only number that correlates to the set {1,2}
the problem is that your whole argument hinges on the fact that {1,2} is supposed to be in the set
but its not
because 1 and 2 have different parities
weak otter
dawg 😭
i dont feel like explaining cantors argument over text sorry
just watch a video of it until you understand this part
the point is to prove that a bijection doesnt exist
cedar kilnBOT
@honest torrent Has your question been resolved?
uncut roost
help
uncut roost
full rover
help
so this is a function that appears to be exponential. what does that mean about its derivative?
uncut roost
the derivative will be in the positive section
full rover
right
uncut roost
but theres 3 😞
full rover
can we say anything about the original exponential?
uncut roost
it has a y-int at 1
full rover
we can also say that at x = 1, it equals 3
patent belfry
Hint: derivative of exponential is faster growing than exponential when base is greater than e
full rover
we can use this to get the idea that the derivative of the exponential is greater than the exponential, as 3 is greater than e
yeah
uncut roost
hmmm
patent belfry
So that rules out first option
full rover
because the derivation of a function b^x is ln(b)*b^x, if b is greater than e, then the derivative should be greater than b^x for ln(b) > 1, or b>e
patent belfry
And the fourth option
full rover
Bc d/dx a^x = ln(a)a^x
tbf the graph is too short to tell whether or not its already being multiplied by a constant
patent belfry
tbf the graph is too short to tell whether or not its already being multiplied b...
Yeah, but it looks like its going to hit some value close-ish to 9 at 2
uncut roost
patent belfry
Assume its just a drawing error
uncut roost
what if its just e^x = e^x
patent belfry
what if its just e^x = e^x
Its 3 at 1
full rover
what if its just e^x = e^x
then the graph should just be the same graph copy pasted
also it would be e at x = 1
little less than 3
patent belfry
Anyways we can rule out answer 1
full rover
wait it might actually be fuckin e^x
uncut roost
why
uncut roost
yay
patent belfry
ITS OPTION 4
uncut roost
i solved it 😍
patent belfry
Omfg biggest brain fart of the century
full rover
why
generally, any exponential with base close to e makes it so that the graph doesnt stray very far at all when you take its derivative
e is a goofy little number because it's just what we base exponential derivatives off of
uncut roost
e is so silly
full rover
if it's close to e (slightly above or slightly less) you're generally expecting the y value at 1 to be pretty close to what it was before you took its derivative
patent belfry
Fun fact, e wasnt actually named after the first letter in euler’s name, he just already had some thing for a,b,c, and d so he picked e
Fun math facts
full rover
because the natural log of any number close to e will always be pretty close to 1
uncut roost
wow
uncut roost
because the natural log of any number close to e will always be pretty close to ...
yes
okay wait i have another question
oh
patent belfry
Trick question
patent belfry
Think about it
full rover
wait no
uncut roost
2pi
patent belfry
Let him figure it out
full rover
:3
uncut roost
im a girl
patent belfry
Think about it
uncut roost
2 pi
uncut roost
2PI
full rover
what does that mean about the slope :3
full rover
yeah
uncut roost
pi is a number
uncut roost
1/lnpi2
full rover
do you have a graphing calculator on you?
full rover
if you can, write out f(x) = pi^2 for me
uncut roost
WAIT
full rover
onto the calculatr
uncut roost
😢
full rover
this is what f(x) = pi^2 looks like
uncut roost
okay one sec
patent belfry
okay one sec
Pi^2 is a number
uncut roost
its negitive
full rover
its negitive
wha
uncut roost
wait no
patent belfry
What is the derivative of y=2
uncut roost
it doesnt exist
uncut roost
0
patent belfry
Ok
uncut roost
patent belfry
Why?
uncut roost
because the derivative of 2 is nothing
uncut roost
yes
uncut roost
wait
full rover
because numbers dont have a rate of change
patent belfry
So what is the rate of change of pi/2
full rover
there is no relation to x, because x doesnt change y at all, bc y is constant
patent belfry
Unless our circles are slowly becoming ovals, pi doesnt change
And 2 also doesnt change
So pi^2 doesnt change
uncut roost
full rover
pi is just a very specific goofy little number, same as pi^2. when we take the derivative, we're (if any math nerd sees this please dont burn me at the stake) basically just taking the slope of the function. in the case of a linear function, the slope is constant, because the rate of change is always the slope. in the case of an exponential the slope itself is a function
full rover
nuh uh
warm crescent
what's the derivative of f(x)=9.86960440109
uncut roost
0
full rover
congrats, thats pi^2
warm crescent
ok and pi^2 = 9.86960440109
uncut roost
THATS SO SILLY
full rover
derivative rules only work when we're working with relations between two variables
we cant take the derivative of a constant because we're not changing it by anything
pi looks an awful lot like something that isnt a number tho tbh
warm crescent
keep track of what's the function variable, the derivative of f(x)=ax + b with RESPECT to x would be f(x) = a (for example)
uncut roost
ohhh because they are both numbers
full rover
ohhh because they are both numbers
yesssss
uncut roost
like 3^2
full rover
yepp
uncut roost
keep track of what's the function variable, the derivative of f(x)=ax + b with R...
i see
full rover
but y = x^2 has a non-zero derivative, because there is an actual change when we change the x
uncut roost
OK WAIT THERES MORE QUESTIONS IM STUCK ON
full rover
think of derivatives as just taking the slope as a function
uncut roost
ok what is this
warm crescent
lol
full rover
ok what is this
that looks
uncut roost
WHO MADE THIS QUESTION
uncut roost
LOL
full rover
just simplify it for me
uncut roost
okay
full rover
replace the variables with numbers rq
scarlet sand
what kind of abomination
full rover
okay so
this is actual hell but uhhhh
first we take the derivative of the outside function
for now we can temporarily replace ln of that monstrocity with
uncut roost
2ln(whatevers in here)
patent belfry
Chain rule galore
uncut roost
what
patent belfry
Better Chain rule: use wolfram alpha
uncut roost
whay cant it be 2ln
full rover
uhhhh
patent belfry
whay cant it be 2ln
2ln what
full rover
one sec
uncut roost
because the exponent
full rover
chain rule is
patent belfry
because the exponent
Because ln isnt a variable
You need to learn what the power rule actually represents
Have u done the proof of it?
full rover
have you done a proof of the chain rule?
uncut roost
yes
full rover
okay good
so
ln(x) is a function
we cant just power rule it
it's not a variable
when you take the derivative of x^2 for example, you're applying the chain rule
uncut roost
ohhhhhhhhhh
full rover
it just doesn't show, because the derivative of x is one
full rover
yep
uncut roost
im so silly
uncut roost
but what about the exponent
full rover
you can pull down the exponent, that's not what you did wrong
you just need to remember to also multiply by the derivative of ln(x)
uncut roost
oh yes i didnt get to that part yet
full rover
that's the derivative we're going for
uncut roost
also there's no shot this shit is worth one point 😭
IK ITS SO FAKE
full rover
anwyays
patent belfry
Is this one of those shitty questions where “actually, using the limit form is easier”
I fuckin hate those
full rover
I fuckin hate those
no shot bc you'd need to factor out a cubic, split the sinx and split the cosx, and take the ln of that
okay so
we start by taking the derivative of a function f(x)^2
so we get
f'(x)*2x
so now we have
d/dx(monstrocity) * 2*monstrocity
uncut roost
warm crescent
you might liked to use ln(a^2) = 2ln|a| to avoid use another chainrule
full rover
(2 * ln(x^3sin(x)/cos(x)^3) * d/dx(lnx^3sin(x)/cos(x)^3
uncut roost
you might liked to use ln(a^2) = 2ln|a| to avoid use another chainrule
hey thats what i said
full rover
i might be dumb but
uncut roost
you are definitely not dumb 😭
full rover
not everything in the natural log is being cubed or smth
we cant just take out a power, or else we would get like
sin(x)^1/3 or smth
wait wait wait there is actually something we can do to make this less of a bullshit problem
uncut roost
you cant move it to the front i think
full rover
split the ln into two
uncut roost
how
patent belfry
split the ln into two
Thats a good idea
patent belfry
division = subtraction
Atleast we dont have to add quotient rule to this fucking mess
uncut roost
full rover
IT REMOVES HALF OF THE FUCKING SOLUTIONS
uncut roost
why did it send twice
uncut roost
FAKE
warm crescent
cuz the abs value
2ln(x) for x>0
ln(x^2) for x except at 0
so maybe you want to conserve the domain with ln|x^3 sinx| - ln|cos^3x|
uncut roost
so maybe you want to conserve the domain with ln|x^3 sinx| - ln|cos^3x|
i dont even think we learned that
warm crescent
ok btw
I think desmos is recognizing the exponents as part of the cos and sin arguments
uncut roost
maybe put it in the other mode
warm crescent
full rover
the problem is that uh
the square is OUTSIDE of the ln
wait IM FUCKING WRONG
HOLY SHIT
im such a clown
uncut roost
its okay you are not a clown
full rover
the square was inside of the ln not on the outside we're fine
warm crescent
no you're not wrong
full rover
you wrote it wrong T_T
uncut roost
oopsie…
uncut roost
IM SO SORRY
full rover
we can rewrite the monstrocity as:
$ 2\ln\left(\frac{x^{3}\sin\left(x\right)}{\cos\left(x\right)^{3}}\right) $
format bot pls
where
WHERE
$2\ln\left(\frac{x^{3}\sin\left(x\right)}{\cos\left(x\right)^{3}}\right)$
uncut roost
it broke from the monstrosity
wraith daggerBOT
Serphic
full rover
there we go
uncut roost
**Serphic**
yay
warm crescent
wellll... almost quite but
anyways, the derivative of ln|x| is 1/x so the abs is gone
uncut roost
ghe chakn rule
warm crescent
🤓 technically itwwdoudlb be $2\ln\left|\frac{x^{3}\sin\left(x\right)}{\cos\left(x\right)^{3}}\right|$
wraith daggerBOT
svc
patent belfry
ghe chakn rule
Im too tired i read this as genghis khan rule
full rover
🤓 technically itwwdoudlb be $2\ln\left|\frac{x^{3}\sin\left(x\right)}{\cos\left...
this is because we're taking out the 2, so we're only isolating for the positive answer right?
uncut roost
Im too tired i read this as genghis khan rule
LOL
warm crescent
yes for example ln(x^2) and 2ln(x) have different domains, but is the same "behaviour"
luckily, the derivative of ln|g(x)| is the same as ln( g(x) ) so just g'(x)/g(x) using chainrule
just different domain
full rover
yes for example ln(x^2) and 2ln(x) have different domains, but is the same "beha...
that's what i was gonna say 😭
actually it might not matter
bc
here
lets just go through with it
the first step of taking the derivative gets us
warm crescent
ok i hate latex i was typing but i gave up
full rover
for the shorthand im just going to call the inside function g(x) yeah?
uncut roost
o kay
full rover
ok i hate latex i was typing but i gave up
just use desmos/wolfram alpha and copy paste
and we ball
$\frac{2}{\frac{x^{3}\sin\left(x\right)}{\cos\left(x\right)^{3}}}\cdot\frac{d}{dx}\left(\frac{\left(x^{3}\sin\left(x\right)\right)}{\cos\left(x\right)^{3}}\right)$
warm crescent
it was a minus sign my bad
wraith daggerBOT
Serphic
uncut roost
where
full rover
on the left, we plug in g(x) as x, because derivative of ln(x) is 1/x
so we put it in down there, and multiply by 2
on the right, we're just taking the derivative of g(x)
full rover
it was a minus sign my bad
also yes i checked it has the same original domain dont ask why
warm crescent
full rover
you are
warm crescent
i keep forgetting the sign
uncut roost
dont give up! 
full rover
dont give up! <:catthumbsup:614540188747563008>
hey its ur problem too smh
full rover
that is
uncut roost
i understand the first step
uncut roost
**Serphic**
idk what to do after this
full rover
**Serphic**
apply chain rule
plug in g(x) for x in the derivative of ln(x)
then multiply by the derivative of g(x)
what is the derivative of ln(x)
uncut roost
1/x
full rover
plug monstrocity in as x
and you have the first half of the equation
second half is the derivative of the monstrocity
also dont forget there was a two there
so it basically ends up becoming $\frac{2}{\frac{x^{3}\sin\left(x\right)}{\cos\left(x\right)^{3}}}\cdot\frac{d}{dx}\left(\frac{\left(x^{3}\sin\left(x\right)\right)}{\cos\left(x\right)^{3}}\right)$
wraith daggerBOT
Serphic
full rover
where 2/x^3sin(x)/cos(x^3) is f'(g(x))
and d/dx(x^3sin(x))/cos(x^3) is g'(x)
we can simplify goofy fraction on the left to just $\frac{2\cos\left(x\right)^{3}}{x^{3}\sin\left(x\right)}$
wraith daggerBOT
Serphic
uncut roost
what
full rover
unfortunately
uncut roost
are you serious
full rover
yes 😭
patent belfry
1 point
uncut roost
patent belfry
Is there an easier way to do this?
full rover
Is there an easier way to do this?
surely
uncut roost
no my teacher is evil
patent belfry
Why are we given the a b and c things
uncut roost
yes
patent belfry
We arent supposed to brute force it computationally
full rover
its a cosecant function
uncut roost
first the teacher tricked us with the 2pi
full rover
a really janky cosecant
warm crescent
maybe this is easier to differentiate
full rover
maybe this is easier to differentiate
yeah you're right uhh we dont need hte left
you're right
that's probably the trick
we dont care about negatives we're plugging in a positive value
warm crescent
im dumb thats true
ok just remove the ||||||||||||||||||||||||||||||||||sssss
woops
patent belfry
ok just remove the ||||||||||||||||||||||||||||||||||sssss
Tf did you bring upon is
What are those spoiler tahs
uncut roost
LOL
warm crescent
ok hear me out
the derivative with abs and no abs is the same
but originally, which at this point is yapping cuz doesnt matter anymore, the abs is necessary
but yeah you don't need it for the derivative so you can kill them
full rover
but yeah you don't need it for the derivative so you can kill them
i am once again mistaken they are actually required
uncut roost
you can factor out 2
full rover
kind of
warm crescent
or differentiate each term
uncut roost
oh yeah
patent belfry
can someone ask wolfram alpha
patent belfry
I wanna see the answer to see how atrocious it is
uncut roost
6/x + 2/sinx -6/cosx
uncut roost
no
full rover
that's your answer but
warm crescent
6/x + 2/sinx -6/cosx
y forgot chain rule
uncut roost
warm crescent
( 2ln(sinx) )' = 2(sinx)' / sinx
full rover
y forgot chain rule
i do want to let you know when we expand out the natural log, half of the x values disappear
one of which, is guess what
17 😭
patent belfry
This would be faster if one person just raw dogged it
warm crescent
yes but is because of the abs we kill them
uncut roost
i do want to let you know when we expand out the natural log, half of the x valu...
its a trick
the answer is p
full rover
yes but is because of the abs we kill them
nope
removed the abs, its still gone
uncut roost
0
full rover
its a trick
i dont think so, because wolfram alpha says otherwise
patent belfry
What happens if you write “go to hell” in the answer box
patent belfry
Does it let you submit
uncut roost
yes
patent belfry
Do it
warm crescent
ok the derivative is 6/x +2cotx +6tanx that's it
uncut roost
i get one more try after this “practice quiz”
i get 3 tries total
i got 11/13 on the first one
full rover
ok the derivative is 6/x +2cotx +6tanx that's it
holy shit he didi t
uncut roost
he takes the mark of the highest one
full rover
that's right
full rover
honestly would've been faster if we just brute forced it but
laziness would normally pay off if this wasnt
such a
bullshit problem
uncut roost
and its worth 1 mark
full rover
can i pay you
uncut roost
how do you put cot in the calculator
full rover
hmmm
first one: derivative of ln(x) * 6, 6/x. second one: derivative of ln(x) which is 1/x, with sin(x) plugged into the bottom, times the derivative of sin(x)
full rover
how do you put cot in the calculator
tan(x)^(-1)
make sure the power is on the outside
or just
1/tan(x)
full rover
yes
warm crescent
I think yes
uncut roost
OMG I GOT ONE WRONG
warm crescent
which one
warm crescent
what
warm crescent
oh
uncut roost
thank you so much
warm crescent
is that the plataform powered by brightspace
my college uses the same plataform I hate it
cedar kilnBOT
@uncut roost Has your question been resolved?
cosmic steppe
Gonna post work a bit
cedar kilnBOT
Gonna post work a bit
cosmic steppe
so thats me tryna find z value
and idk how to even find the p value
okay nvm
if i reinput it it is fine
godi hate certiport
thank got 3.45 works but not 3.45
.close
cedar kilnBOT
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Available help channel!
icy mirage
Parametrics
cedar kilnBOT
Parametrics
winged stump
try plugging in $x$ and $y$ into $x^2+y^2=1$
wraith daggerBOT
ikesike
icy mirage
try plugging in $x$ and $y$ into $x^2+y^2=1$
am i meant to expand out LHS?
icy mirage
but leave it as a fraction
so i just did it, and it gave me exactly 1 is that meant to happen? Idk what point is missing
winged stump
how was the fraction before you reduced it to 1
icy mirage
how was the fraction before you reduced it to 1
$(t^4-2t^2+1+4t^2)/(t^4+2t^2+1)$
wraith daggerBOT
yes
winged stump
ok i might have misled you a bit, don't expand the denominator
we have $\frac{t^4+2t^2+1}{(t^2+1)^2}$
wraith daggerBOT
ikesike
winged stump
oh wait what level of math is this?
icy mirage
yr 11
winged stump
have you gone over imaginary numbers? am unfamiliar with year system
winged stump
ok then this is a trick question and there is no missing point
cedar kilnBOT
icy mirage
.reopen
cedar kilnBOT
✅
icy mirage
@winged stump so i just checked the answers and it says the point (1,0) is missing
vague rapids
note that x=(t²-1)/(t²+1)
where t and x both are real
what you should try is to solve for t² in terms of x
and then you'll see
@icy mirage
icy mirage
ok lemme try that
icy mirage
and then you'll see
so x cant equal to 1?
icy mirage
t^2=x+1/1-x
vague rapids
yes
now, the denom can never be zero
1-×≠0
and thus, x≠1
now, you can find the corresponding y coordinate
tepid wraith
tom
icy mirage
now, you can find the corresponding y coordinate
just making sure, i substitute x+1/1-x into the y equation right
cedar kilnBOT
icy mirage
.reopen
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✅
icy mirage
sorry ik this is like the exact same question format as the other one, but idk how to make t the subject in this
cedar kilnBOT
@icy mirage Has your question been resolved?
vague rapids
sorry ik this is like the exact same question format as the other one, but idk h...
you may use the quadratic formula here to solve for t in terms of y
cedar kilnBOT
@icy mirage Has your question been resolved?
sonic socket
question 3, need help with the whole lot
cedar kilnBOT
question 3, need help with the whole lot
sonic socket
i understand like the link between displacement, velocity, acceleration and stuff
but not sure on my first step here
cosmic steppe
Displacement is just the difference in position, which is just the integral of velocity
cosmic steppe
Velocity is the rate position changes
In other words v = ds/dt
if you want to find displacement between a < t < b
then you integrate that
From a to b
sonic socket
so what do i do for my equation?
cosmic steppe
Write the equation for the velocity
sonic socket
v=ds/dt ?
cosmic steppe
You legit have the graph
You can legit represent v as a linear function
I'm just saying in a general case v = ds/dt but since you're given the graph, it's explicitly defined
cosmic steppe
why x =
cosmic steppe
the y axis is v
sonic socket
v = -3/5 t + 3
cosmic steppe
It does not say the graph shows displacement
sonic socket
then do i just differentiate that?
cosmic steppe
No. You have to integrate it
sonic socket
oh
cosmic steppe
Displacement is the area underneath the velocity curve
sonic socket
oh yeah because it’s -1
cosmic steppe
$\int_a^b v(t) \dd t = s(b) - s(a) = Δ_{(a,b)} s$
wraith daggerBOT
Peter Griffin
cosmic steppe
Fundamental theorem of calculus
sonic socket
-3/5t when you integrate that the n+1 goes on denominator or denominator of the entire thing make it go to the numerator?
cosmic steppe
-3/5 is a constant, so:
$$\int -\frac35 t \dd t = -\frac35\int t \dd t$$
wraith daggerBOT
Peter Griffin
sonic socket
oh okay
so the inside is t^2/2 + 3t
with -3/5 on the outside
-3/5((t^(2) / 2 )+ 3t)
cosmic steppe
Why are you multiplying 3t by -3/5
sonic socket
wait
cosmic steppe
There is no -3/5 in 3
cosmic steppe
$\int -\frac35 t + 3 \dd t = \int -\frac35 t \dd t + \int 3 \dd t$
wraith daggerBOT
Peter Griffin
cosmic steppe
Integrals are a linear operator
So you can just integrate each term and add them up
sonic socket
oh okay i see now
the way i do it is multiple n+1 with the denominator
-3t^2 / 10 +3t
cosmic steppe
Yeah
But now that's just the antideriavtive
You need bounds to get displacement
Look at the graph
What are your bounds
cosmic steppe
So $\Delta_{(0,5)}s = \int_0^5 -\frac35t + 3 \dd t$
wraith daggerBOT
Peter Griffin
cosmic steppe
Well the + C doesn't matter
sonic socket
why not?
cosmic steppe
You wanna do a definite integral
sonic socket
oh yeah
sonic socket
what’s FTC?
cosmic steppe
Fundamental theorem of calculus
sonic socket
oh okay
also
is what we are up to so far the answer for i) ?
since we found the equation
cosmic steppe
Well it wants an equation for any given time, t
So reallt let's say that we want T running from [0, t]
Then your displacement, x, would have to be:
$x(t) = \int_0^t v(T) \dd T$
wraith daggerBOT
Peter Griffin
cosmic steppe
Where T is a dummy variable
I mean think about it
For whatever t is
Assuming t > 0
Then you can find displacement underneath the velocity curve cut out from 0 to t
sonic socket
are you sure the question doesn’t want me to leave it how i have it?
ive never gone further and done dummy variables and stuff in class for anything
cosmic steppe
It's not about what you've done in class but how you're able to apply
Shits gonna appear outside on what you strictly do in class
cosmic steppe
I mean the dummy variable is legit just to avoid integrand-bound notation issues
Dummy variable could be anything but t
I just chose T
sonic socket
we can get marked down if we do maths/use methods outside our course is the thing
is it fine in that context to leave it as x = -3t^2/10 +3t ?
cosmic steppe
**Peter Griffin**
Anyways, this just simply means displacement is the area underneath the velocity from 0 to t
sonic socket
Anyways, this just simply means displacement is the area underneath the velocity...
yeah i get that
cosmic steppe
is it fine in that context to leave it as x = -3t^2/10 +3t ?
No
x(t) is not the anti derivative itself
Again, it's displacement. Literally difference between two things. The anriderivtive doesn't show that
Only when it is definite does it show bevause of FTC
cosmic steppe
**Peter Griffin**
Evaluate this
sonic socket
i’m not sure how, it’s not apart of our course work
cosmic steppe
I guess if they really care, it's $x(t) = x(0) + \int_0^T v(T) \dd T$
wraith daggerBOT
Peter Griffin
cosmic steppe
They give you x(0) and want you to use that
cosmic steppe
i’m not sure how, it’s not apart of our course work
It's legit just the same as a definite integral
sonic socket
what was wrong with my answer then? it’s similar to what we’d leave it as in class
cosmic steppe
it's not a definite integral, that's what's wrong. You're erroneously assigning the displacement as the antiderivative itself. That doesn't show any change in position
The literal definition of displacement is change in position
What you shown is position actually
You want the difference in that? You need to show the anti derivative evaluated at some time, b, minus the anti derivative evaluated at another time, a
But that's legit just a definite integral, by FTC
sonic socket
i’m not doing some advanced calculus class so i don’t think that stuff is taught
this is an example from the textbook in what is kind of similar
cosmic steppe
It's an application. It's not advanced. It's legit just applying integrals to the definition of displacement
sonic socket
they didn’t do what you said to do
cosmic steppe
Different application. This deals with volume, not displacement
sonic socket
well i don’t agree with what you’re saying because we’ve never been told to do that stuff before
maybe at your level you’d do that, but i don’t think so at mine
cosmic steppe
How else would you do it. Volume is a scalar. Displacement isn't
You go find another way then
sonic socket
well we’ve never done anything similar to what you’re saying, and it doesn’t make sense to me what you’re saying so it’s new to me
why would we get revision of stuff we haven’t done before
<@&286206848099549185>
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
serene flower
cedar kilnBOT
serene flower
I cant even get started with this one
Are there any particular substitutions I need to do?
hollow osprey
Maybe try integration by parts
Then partial fractions
This problem is pretty long though idk why it’s multiple choice lol
hot crag
probably partial fractions, i think
cedar kilnBOT
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Available help channel!
crimson sedge
Where Can I find a big textbook, black and white, with everything I need to know about math, before doing the 12th year final exam. I woild like to have one that explains everything, and another white and black text book that have exercises.
hot crag
what...?
hot crag
i don't think that's a question you can ask here
#book-recommendations probably
or maybe the other channels
@crimson sedge
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
Rlly?
cedar kilnBOT
@crimson sedge Has your question been resolved?
cedar kilnBOT
@crimson sedge Has your question been resolved?
crimson sedge
Somone tell me
hollow basin
ok you just completely ignore what ren said
go to #book-recommendations, #precalculus, #calculus, #prealg-and-algebra , and/or #geometry-and-trigonometry
cedar kilnBOT
@crimson sedge Has your question been resolved?
hot cloak
cedar kilnBOT
hot cloak
could someone explain 3ai and 3aii
hot cloak
ok
crimson sedge
no
crimson sedge
Hmmm
cedar kilnBOT
@hot cloak Has your question been resolved?
fleet breach
The function f is doing stuff to elements in X, to become function values of Y. Because we don’t what is happening some of these elements might give all different values or some of the same (one to one and/or onto?). The f(A) I assume is a set of the function values of all the elements in A, Same with f(B) and B. 3ai) is about the set of all the function values in both A and B, which can be written in f(A U B) or f(A) U f(B). 3aii) Is about the set of function values from elements in both A and B being a superset of the function values from that are both in function values from elements in A and function values from elements in B. To prove These you would just do some let statements for general case of any element in A and any element in B with there respective function values and different cases of whether they would in the sets. I don’t know very well, hope this helps.
cedar kilnBOT
@hot cloak Has your question been resolved?
cedar kilnBOT
mild narwhal
Hello @frosty grail
frosty grail
Huh
mild narwhal
Yes
frosty grail
It's 90°
mild narwhal
Ty
frosty grail
Wanna know why?
mild narwhal
Yes I think I know i just looked it up
frosty grail
Okay
frosty grail
Yes