2(0)² + 0 - 3
#help-19
lean yew
is g(0) = 0 though?
lean yew
i dun think g(0) was 3
jade trout
Oh.
lean yew
yup!
so given f(g(x)) and the original value of x, your job is simply to take the value of x, put it in g(x), get its value, then take the value of g(x) and do the same to f(x)
oops, phone
jade trout
Is -28/9 the answer??
lean yew
how did you get -28/9
wait wait
oh you're right, i'm sorry
mental calc fail
@jade trout yup you got it!
lean yew
so you can do your questions now, right?
odd edgeBOT
odd edgeBOT
✅
jade trout
.solved
odd edgeBOT
odd edgeBOT
Available help channel!
dull remnant
.
fast slate
A computer shop charges 20 dollars per hour
(or a fraction of an hour) for the first two hours
and an additional 10 dollars per hour for each
succeeding hour. Represent your computer rental
fee using the function R(t) where t is the
number of hours you spent on the computer.
tepid pelican
can R be piecewise?
tepid pelican
and would e.g. half a hour cost 10$ or full 20$?
steep mantle
ok piecewise makes so much more sense i qas thinking some absurd floor/ceil functions
tepid pelican
Okay so can you find R(t) that works for the first 2 hours?
tepid pelican
can you find a function R(t) which gives you the correct rental fee for t between 0 and 2
(meaning you dont need to worry about the change in price after 2 hours)
fast slate
uhhjh
tepid pelican
do you at least know what kind of function should R(t) be between 0 and 2?
fast slate
nope
tepid pelican
Will it be linear, quadratic, exponential, rational or what kind will it be?
fast slate
30?
fast slate
4?
clever fjordBOT
Result:
4
i multiplied 20 to 0.2
tepid pelican
perfect
How much would it cost for t hours (where t is no more than 2 hours)
how would you calculate that
(dont overthink it)
fast slate
20?
tepid pelican
not quite
If it's 1.5 hours, it costs 20*1.5$
if it's 0.2 hours, it costs 20*0.2$
if it's t hours, it costs ???
can you see the pattern?
fast slate
ohh
tepid pelican
do you know how piecewise functions work btw? Do you know how to write it?
fast slate
yes
tepid pelican
okay cool
so for your verification, the first part should look kinda like this
now we will need to determine the cost if t is more than 2
fast slate
yes
tepid pelican
how would you calculate the rental fee for e.g. 7 hours?
fast slate
20 x 7?
tepid pelican
not quite
A computer shop charges 20 dollars per hour
(or a fraction of an hour) for the first two hours
and an additional 10 dollars per hour for each
succeeding hour. Represent your computer rental
fee using the function R(t) where t is the
number of hours you spent on the computer.
let's re-read the question
it says that it costs only 10$ per hour for every additional hour after 2 hours
so what would the total cost be for e.g. 3 hours?
tepid pelican
Yeah, in the question they offer kind of a discount if you rent it for more than 2 hours
fast slate
90?
fast slate
30 x 3
tepid pelican
Why 30 and why x 3?
atomic marlin
Maybe you can think of such function $20[\min(t,2)]+10[\max(t-2,0)]$
clever fjordBOT
Emmaaaaa
tepid pelican
ill try to explain how it works
atomic marlin
Where [] takes the ceiling
tepid pelican
for the first hour, you pay 20$
for the second hour, you pay another 20$
for the third hour, you only pay 10$
tepid pelican
if you wanted to rent it for annother hour, you'd add another 10$
fast slate
qait where did 90 comef rom
tepid pelican
its incorrect, i thought you were answering the t=7 one
anyway, now that you know how it works, try calculating the cost for 7 hours
fast slate
is it 90 too
tepid pelican
It is 90, yes
atomic marlin
40+50 7 hours
tepid pelican
the 3 hour one would cost 50$, not 90$
tepid pelican
because the first hour costs 20, the second costs 20 and the third costs 10
fast slate
okk
atomic marlin
Write it piecewise or use min function to create a stop time
tepid pelican
okay so if it was something more, such as 12 hours, how would you calcuate the cost for that?
no need to compute the number, just say how
fast slate
first hour costs 20 then the second 20 and the third and so on costs 10
atomic marlin
Yes
tepid pelican
Yes, but instead of adding 12 numbers, you could perhaps utilize some multiplication
to make the process simpler
fast slate
How
tepid pelican
well, we could for example add the first 2 hours separately
that'd make 40$ for the first 2 hours
fast slate
40
atomic marlin
Another way is you see time interval completely independently
tepid pelican
once you account for the first 2 hours
fast slate
40 x 10?
fast slate
wtgh
tepid pelican
we already calculated the cost for first 2 hours, it was 40$
im asking how many hours remain to be accounted for?
of the total 12
atomic marlin
So 12 hours means the first 2 hours and 10 hours separated from first 2 hour
fast slate
10..?
fast slate
ohh okk
tepid pelican
and how much is the rental fee for each of those 10 hours?
fast slate
140?
tepid pelican
no, not quite
the first 2 hours cost 20$ per hour
and then the remaining 10 cost how much per hour?
tepid pelican
the cost for the remaining 10 hours is 10$ per hour, so in total it would be 10 * 10$ which is 100$
fast slate
Ueu
tepid pelican
so the total cost for 12 hours would be
40$ for the first 2 hours
+
100$ for the remaining 10 hours
= 140$
just to check your understanding, can you do 16 hours now?
atomic marlin
Maybe I’m a bit awkward, Kim have you tried to write down $R(t)$ on a paper it might help!
clever fjordBOT
Emmaaaaa
fast slate
wait sorry im a bit retarded rn im learning scienca nd math at the same time
tepid pelican
Maybe I’m a bit awkward, Kim have you tried to write down $R(t)$ on a paper it m...
hmm, the whole point of the question is finding R(t), so we dont know what it is yet
atomic marlin
Try to list number on a paper might help I mean 😢
tepid pelican
wait sorry im a bit retarded rn im learning scienca nd math at the same time
like exactly at the same time? If so then it might be better to focus on one thing at time
fast slate
yeasorry
atomic marlin
Imagine you’re a greedy owner of computer shop, extracting money based on the rule
How to exactly make sure the rule is apply? A customer used the shop for one hour how much? 2 hours how much? How’s 3
List them on a paper
fleet tapir
list the cost in hour [2,3), [3, 4), [4,5) , ... what pattern do you see
oh is it that way, then you may get an even simpler expression than what i had in mind
atomic marlin
Fractional values won’t count so
tepid pelican
we are going for a piecewise func btw, not some absolute value shit (because piecewise is likely simpler and easier to understand)
atomic marlin
It’s always take the the ceiling of time so succeeding hour
tepid pelican
Fractional values won’t count so
it was said that 30mins would cost 10$, so i think they will count
sorry for that typo lol
atomic marlin
A computer shop charges 20 dollars per hour
(or a fraction of an hour) for the first two hours
and an additional 10 dollars per hour for each
succeeding hour. Represent your computer rental
fee using the function R(t) where t is the
number of hours you spent on the computer.
Per hour or a fraction of an hour
atomic marlin
The easiest representation will be $20\min(\ceil{t},2)+10\max(\ceil{t-2},0)$
clever fjordBOT
Emmaaaaa
atomic marlin
The function round up the time and take only positive value.. though I think it’s only beneficial to list number for study purposes
tepid pelican
The easiest representation will be $20\min(\ceil{t},2)+10\max(\ceil{t-2},0)$
except the OP prolly doesnt understand half of the symbols....
atomic marlin
That’s why it’s helpful he thinks as an owner themselves and list number
fast slate
how did you get this btw?
i miscounted
tepid pelican
so how'd you get 560?
1st hour costs 20$
2nd hour costs 20$
3rd hour costs 10$
4th hour costs 10$
5th hour costs 10$
...
out of the 16 hours, how many hours cost 20$ and how many cost just 10$
atomic marlin
Just add to the number helper listed for you
1 hour 20 + 20(second hour) +10 (third hour)+ 10(forth hour),…,10(sixteenth hour)
How many 10s and how many 20s?
fast slate
180
fast slate
I added
late sinew
tepid pelican
okay perfect
now remember that multiplication is just repeated addition
e.g. multiplying 4 by 5 is the same thing as adding four 5s
and it works in the other direction as well
adding fourteen 10s is the same thing as 14 * 10
and adding two 20s is the same thing as 2 * 20
fast slate
o
tepid pelican
so instead of adding so many numbers, you can simply multiply
fast slate
okok
fast slate
okok
tepid pelican
in t hours (where t is more than 2), how many hours will cost 20$ and how many hours will cost only 10$?
in 16 hours, it was 2hrs and 14hrs respectively
what will it be in t hours?
fast slate
2 hrs and 10 hrs?
tepid pelican
or are you?
fast slate
i am
tepid pelican
2 hrs and 10 hrs?
that'd be in 12 hours
the whole point of adding t is to make it more general
t can be anything
t could be 16, 12
or it could be 100
and you have to find something thatll work for all of them
Okay so in 16 hours, 2 of them cost 20$ and 14 cost 10$
in 12 hours, 2 of them ccost 20$ and 10 cost 10$
fast slate
yes
tepid pelican
we could also write it as in 16 hours, 2 of them cost 20$ and 16-2 of them cost 10$
In [anything] hours, 2 of them cost 20$ and [anything] - 2 of them cost 10$
as long as [anything] is more than 2
fast slate
I might kill myself bc of matk
fast slate
A computer shop charges 20 dollars per hour
(or a fraction of an hour) for the first two hours
and an additional 10 dollars per hour for each
succeeding hour. Represent your computer rental
fee using the function R(t) where t is the
number of hours you spent on the computer.
tepid pelican
everyone struggles with variables till they get used to them
tepid pelican
In [anything] hours, 2 of them cost 20$ and [anything] - 2 of them cost 10$
can you understand this?
fast slate
so for your verification, the first part should look kinda like this
Wait sorrty are e doing the next part already
tepid pelican
Wait sorrty are e doing the next part already
Yeah, we are
fast slate
ob
wooden python
I might kill myself bc of matk
are you actually feeling suicidal right now or was this an exaggeration?
tepid pelican
we are now trying to find the rental fee if they rent it for more than 2 hours
fast slate
Uhhhhh
fast slate
we are now trying to find the rental fee if they rent it for more than 2 hours
2 hours and another 2 hours?
tepid pelican
2 hours and another 2 hours?
i mean that we are already focusing on the 2nd part (which is when t > 2, i.e. they rent it for more than 2 hours)
tepid pelican
we could also write it as in 16 hours, 2 of them cost 20$ and 16-2 of them cost ...
soo we ended here
is that part clear?
fast slate
nah can you rephrase that my bad
tepid pelican
Okay so in 16 hours, 2 of them cost 20$ and 14 cost 10$
and this was clear?
fast slate
yes
tepid pelican
yeah so the main point of what i was saying that the first 2 hours cost 20$ each and what remains is 16-2 hours, which cost 10$ each
the point is that the 14 was calculated as 16-2
fast slate
16-2 hours?
tepid pelican
16-2 hours?
yes, 16-2 hours is same as 14 hours
tepid pelican
1st hour costs 20$
2nd hour costs 20$
3rd hour costs 10$
4th hour costs 10$
5th hour costs 10$
...
t-th hour costs 10$
in general, the first 2 hours will cost 20$ each and what remains is t - 2 hours, which will cost 10$ each
fast slate
yea
tepid pelican
note that this is just generalization, its not anything super-new. We just replaced the 16 by t, because the process is quite general
okay so if the first 2 hours cost 20$ each and the remaining t-2 hours cost 10$ each, what will be the total cost for the t hours?
remember to use the multiplication trick
you can look back at how it was done with 16 hours, it will be very similar
1st hour costs 20$
2nd hour costs 20$
3rd hour costs 10$
4th hour costs 10$
5th hour costs 10$
...
t-th hour costs 10$
You are basically adding up this list, there are two 20s and t-2 10s
how could we simplify that with multiplication?
The result wont be a single number btw, it will be an expression containing the variable t
faint knot
butting in to say: think about what you would do to calculate this for 50 hours
youre not going to add up numbers all day to do it, youre going to take a shortcut using multiplication
the formula is just a way to write down this shortcut, with t standing in for the number you calculate
fast slate
t-2 x 10?
faint knot
what about the initial $20 and $20 for the 1st and 2nd hour
rn youve handled the 3rd hour through the t-th hour with (t - 2) x 10
tepid pelican
t-2 x 10?
This is just the cost for the remaining t-2 hours, what about the first 2 hrs?
fast slate
40
fast slate
oh mb
faint knot
1st hour costs 20$
2nd hour costs 20$
3rd hour costs 10$
4th hour costs 10$
5th ...
oh also $ signs are written to the left of the number
$5 = 5 dollars
theyre both read out loud as "5 dollars"
fast slate
40 (t-2) x 10??
tepid pelican
oh also $ signs are written to the left of the number
$5 = 5 dollars
theyre both...
oh, thanks, didnt know that
faint knot
40 (t-2) x 10??
presumably "together" means adding them...
40 + (t - 2) x 10, right?
if you wanted to figure out the 50th hour, that is what youd do
tepid pelican
Yeah,we have to add the (cost of) first 2 hours to the (cost of) remaining t-2 hours
fast slate
where the hehll did 50 cocme from 💔
faint knot
bro you gotta read what I just said
if you wanted to figure out the cost up to the 50th hour, that is what youd do
40 + (50 - 2) x 10
right?
faint knot
bruh
tepid pelican
we can verify that it works for the 16 hrs as well
fast slate
mb wasnt reading ur messaeg
tepid pelican
,calc 40 + (16 - 2) * 10
clever fjordBOT
Result:
180
and it does
fast slate
,calc 40 + (16 - 2) * 10
ohjh
tepid pelican
whatever t>2 we use, it will always give us the correct cost
faint knot
whatever t>2 we use, it will always give us the correct cost
and keep in mind there we need t > 2 for this to work
if you had t = 1, you wouldnt need to do the (t - 2) x 10 calculation
you know itd just be 20 dollars
tepid pelican
Yeah, you can now add this part to the piecewise fn R(t)
you can send a photo / screenshot here and we can verify it
fast slate
wait uh @tropic thunder -2 came from the 2 hours or
tepid pelican
wait uh <@580839136588464189> -2 came from the 2 hours or
there is total of t hours and the first 2 hours cost 20$
what remains is t-2 hours
fast slate
OK
tepid pelican
we can verify that (t-2) hours + 2 hours = t hours
fast slate
KK SO WJAT NOW
tepid pelican
KK SO WJAT NOW
well, now we know that the rental fee is 40 + (t-2) * 10 for t > 2
in other words, R(t) = 40 + (t-2) * 10 for t > 2
you can add that to your piecewise function
fast slate
also sorry what the hell is ceiling function
wooden python
you don't need to worry about that for your current problem
fast slate
o ok
fast slate
in other words, R(t) = 40 + (t-2) \* 10 for t > 2
Ok i thin k i understand
tepid pelican
if you wanted to, you could simplify it with some algebra btw
40 + (t-2) * 10 = 40 + 10(t-2) = 40 + 10t - 10*2 = 40 + 10t - 20 = 20 + 10t
but its not necessary
late sinew
Welcome to the server, ren 
tepid pelican
using () to denote a set 😭
lean yew
this might be a good first hint
tepid pelican
<@951190447185874994> last one what does this mean ion understand
a function has only one output for each input btw
tepid pelican
each pair is basically an input-output pair
so e.g. if you input 2, it gives 4, because there is (2, 4) in the set
if you input k, it gives 6, because there is (k, 6) in the set
and if you input 4, it gives k as an output, because there is (4, k) in the set
is this clear?
fast slate
yeah and
tepid pelican
okay now you need to ensure that one input cant lead to multiple outputs
otherwise it wouldnt be a function
tepid pelican
there are some numbers which when put for k result in a function, and other numbers that dont result in a function
e.g. if we put 1 for k
lean yew
think of ordered pairs as something like this
tepid pelican
we get
{(2, 4), (1, 6), (4, 1)}
lean yew
certain values of k will cause this to happen and this is a no-no
fast slate
we get
{(2, 4), (1, 6), (4, 1)}
I see
tepid pelican
we get
{(2, 4), (1, 6), (4, 1)}
this would be a valid function because each input has only one output
tepid pelican
certain values of k will cause this to happen and this is a no-no
and this is an example of something that is not a function
because the input 2 has both 4 and 6 as an output
what would k have to be in order for input 2 to have both 4 and 6 as an output?
fast slate
okkk
fast slate
what would k have to be in order for input 2 to have both 4 and 6 as an output?
wjts
what
Why is pre calculus easier than gen math
🙂
tepid pelican
we can also imagine the situation like this (notice that 2 -> 4, k -> 6 and 4 -> k)
now k is a variable so you can slide it around on the number line
tepid pelican
certain values of k will cause this to happen and this is a no-no
where would you have to slide it to, to get to the situation on this pic
i.e. two different arrows from the number 2
atomic marlin
a graph of a function is a map: $x \mapsto (x, f(x))$ such that$ x\in X $and $f(x)\in Y$ X is domain and Y is codomain
clever fjordBOT
Emmaaaaa
lean yew
we probably shouldn't bust out all the terms right now imo
atomic marlin
However it’s a bit more complicated to comment about function itself, function is assigning value from domain and under a certain rule to codomain
There is a bit different than the function itself and graph
fast slate
we can also imagine the situation like this (notice that 2 -> 4, k -> 6 and 4 ->...
oohh
tepid pelican
tepid pelican
https://www.desmos.com/calculator/dp3uebitjp
@fast slate you can try it out here
drag k around and see when it's a function and when it's not
atomic marlin
Isn’t this about the rate collected?
fast slate
Ok thank u iget it now
atomic marlin
Why are we at highly abstract function theory 🫣
lean yew
https://www.desmos.com/calculator/dp3uebitjp
did you make this yourself
fast slate
tjanks a lot @tepid pelican
tepid pelican
did you make this yourself
yep
tepid pelican
i like playing with desmos lol
odd edgeBOT
lean yew
i'm a geogebra person myself
tepid pelican
ic, geogebra is nice too
odd edgeBOT
Available help channel!
mystic saffron
odd edgeBOT
mystic saffron
This is the proof
for the radian to degree formula
I don't understand how you get from step 2 to step 3
mystic nova
Multiply both sides by theta
mystic nova
Hmm
mystic saffron
how would you know to do that to get to step 3
atomic marlin
Pi is not degree
mystic saffron
pi is radian
atomic marlin
So no that hallowed circle
mystic saffron
So no that hallowed circle
half circle is radian
atomic marlin
Really? I didn’t know ! Learned 🥰
mystic saffron
pretend we don't have step 3
.
mystic saffron
how would you know to do that to get to step 3
.
mystic nova
1 degree is pi•1/180 radian so k degree equals pi•k/180 radian
mystic nova
1 degree is 1/180 of a half circle
k degree is k/180 of a half circle
And you said half a circle is pi, right?
mystic nova
Because we know half a circle is pi
mystic saffron
right
mystic nova
Yes
mystic nova
mystic saffron
1 degree is pi•1/180 radian so k degree equals pi•k/180 radian
but i still dont understand this
1 degree = pi/180 rad
mystic nova
180 degrees is half a circle and 1 degree is 1/180 of 180 degree
Similarly with k degrees
agile raven
<:catthumbsup:614540188747563008>
Sorry I’m probably wrong but isn’t half pi equal to 90 degrees?
mystic nova
Yes, half circle is pi
mystic saffron
Sorry I’m probably wrong but isn’t half pi equal to 90 degrees?
half circle is pi
half pi is 90
yes
since pi is 180
mystic saffron
180 degrees is half a circle and 1 degree is 1/180 of 180 degree
yeah but how
do we get to
the multiplication
of theta
if we dont know that step 3 existed how would we get to that?
mystic nova
Theta represents an angle
mystic saffron
.close
odd edgeBOT
odd edgeBOT
Available help channel!
tired estuary
im not sure how to do part ii
odd edgeBOT
im not sure how to do part ii
wooden python
draw the lines y=1 and y=-1
tired estuary
wait why?
wooden python
because those are the two y-values that stay in place when going from y=f(x) to y=1/f(x)
they are the solutions to y = 1/y
tired estuary
ooh i see
wooden python
everything above the line y=1 gets mirrored and squished down into the band 0<y<1, and vice versa -- everything in the band 0<y<1 gets mirrored and stretched out into the region y>1
and likewise symmetrically below the x-axis
tired estuary
i get the right side of the graph but idk how to get the left side if that makes sense
tired estuary
why does it look like that
wooden python
can you highlight which part(s) of it dont make sense to you
tired estuary
wooden python
ok so look at the part for -1<x<1/2
the original function decreases from infinity down to 0
so the reciprocal instead increases from 0 up to infinity
tired estuary
is the reciprocal always the opposite? like is the orignal is increasing to infinity, then its recipriol is decreasing from infinity?
also i dont really understand x<-1
wooden python
is the reciprocal always the opposite? like is the orignal is increasing to infi...
think about the behavior of the function 1/x
this is what all of this is based on
tired estuary
im so lost 😭
tired estuary
quick question: for ii, this is the product of 2 graphs y=x and y=|x| +1 right?
amber veldt
quick question: for ii, this is the product of 2 graphs y=x and y=|x| +1 right?
its the product of two functions but im not sure what you have in mind for the phrase "product of two graphs"
tired estuary
oh like when u sketch both them out but yeah function
tacit wasp
Huh?
amber veldt
what method are you using for this
calculus? plotting points with a table?
i recommend splitting this into two cases
x>=0, and x<0
tacit wasp
what method are you using for this
I think they mean plotting both x and |x| - 1 (for example, with different colours) and then multiply them pointwise
amber veldt
or if youd prefer 3 cases, x>0, x=0, x<0
tacit wasp
But I'm not sure though
tired estuary
idek its how i was taught like ignore the writing on the side but you take the x points and u see how far away it is from the x axis then you multiple the spaces by the distances if that makes sense
amber veldt
I think they mean plotting both x and |x| - 1 (for example, with different colou...
oooh... that doesnt sound so helpful
amber veldt
idek its how i was taught like ignore the writing on the side but you take the x...
aah. thats necessary if you only have a few points, but i wouldnt recommend that method here
when you have the full formula
tacit wasp
I think they mean plotting both x and |x| - 1 (for example, with different colou...
I believe this might be helpful when one of the functions is a constant
@tired estuary
tired estuary
aah. thats necessary if you only have a few points, but i wouldnt recommend that...
i was saying if you jsut have the graph without points or a formula u kinda have to like guess the values
tired estuary
how else can u do it?
amber veldt
or if youd prefer 3 cases, x>0, x=0, x<0
.
tired estuary
but here you have the full.formula
true but for like other questions where they just give u f(x) and g(x) and estimate the shape of the product of the functions anyways ill try learn another way to do it
amber veldt
whats the definition of absolute value? there's more than one definition
which do you know
tired estuary
the value must be 0 or positive
amber veldt
sure, okay
lets put that into a formula
if x>0, |x|=x
if x=0, |x|=0
if x<0, |x|=-x
agree?
amber veldt
if x=-5, what's -x?
tired estuary
5?
amber veldt
cool
now split the function youre graphing into 3 cases
x>0, x=0,x<0
that will be the graph for 3 parts of the picture
to the right of the y axis , on the y axis, to the left of the y axis
tired estuary
okk
so u can do this method when your given the fuction but can u do this with only points?
tired estuary
ohh thats so simple okay
amber veldt
what did you get for the 3 pieces?
btw this is the common notation for a function defined by pieces
$$y=\begin{cases} x \text{ if } x > 1 \ \cdots \ \end{cases}$$
clever fjordBOT
gfauxpas
tired estuary
im rlly slow hold on pls!
amber veldt
sure
tired estuary
amber veldt
good learning of notation, it's just y= instead of y on its own
,w plot y = x(|x|-1)
tired estuary
ook
clever fjordBOT
tired estuary
omg my graph
amber veldt
you got (1,0) correct
it's okay I was hoping you would ask me for help for the intermediate steps 😅
tired estuary
wait i have the one i used where i just looked at the points and it looks similar
amber veldt
I was just waiting for you to say
y=
it's okay your work is still good, let's find where you made your mistakes
tired estuary
😭
amber veldt
I'm going to add "0" as a seperate case , so we have
tired estuary
i think i drew the wrong shape in the first place like i drew the originalfunction wrong omg
amber veldt
$$y = \begin{cases} x^2 - x \quad \text{ if } x > 0 \ 0 \quad \quad \quad \text{ if } x = 0} \ -x^2-x \quad \text{ if } x < 0 \end{cases}$$
clever fjordBOT
gfauxpas
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
tired estuary
what's here, this is good
idek it was before when i looked at the graph and guessed where the points would be then plugged in values to see when it is positive or negative
amber veldt
idek it was before when i looked at the graph and guessed where the points would...
so that works IF you choose your "guessing interval" intelligently
let's refine your method so you can do that
for that to work, you want to find where the function has roots, AKA zeroes. in other words, where it touches the x-axis
or crosses
can you find where this function has roots?
tired estuary
x= 1 ?
tired estuary
wait what
amber veldt
if x= 0 , y=0
tired estuary
yeah wdym 2?
tired estuary
OH lmao okayy
amber veldt
any other roots?
tired estuary
x= -1
amber veldt
yeah
amber veldt
idek it was before when i looked at the graph and guessed where the points would...
so for your method to work
for polynomials at least
you need to check points
x < -1
-1 < x < 0
0 < x < 1
x > 1
tired estuary
into the orignal yeah? and see if the y values are positive ir negative to sketch it right
amber veldt
your teacher didn't teach you this? pfffftt
amber veldt
into the orignal yeah? and see if the y values are positive ir negative to sketc...
into the original or into the piecewise definition, it doesnt matter
same function, right?
so to graph polynomials, you should always chck to the left of, inbetween, and to the right of roots
tired estuary
your teacher didn't teach you this? pfffftt
stop violating my teacher hes the sweetestt
amber veldt
aw sorry
this will tell you where it's positive and where it's negative
it won't tell you shape of , say, a parabola
but if you see a function y=-2x^2 +1 you know it's a parabola anyway
tired estuary
rightt
amber veldt
btw for this one
you havent seen a case like this before so i'll tell you
this is two parabolas, connected to each other at x=0
two different parabolas
tired estuary
yuck
crude hollow
help
crude hollow
yeah
late sinew
Apply them then
late sinew
Show your work
crude hollow
kk
i did that then got kinda stuck
do i get derivative of sin2x then 1/cos3x and multiply?
north sparrow
,rccw
clever fjordBOT
late sinew
you didnt do chain
north sparrow
you forgot the 2 and 3 coming in front of the sin(2x) and cos(3x) when differentiating them
because of chain rule yeah
north sparrow
.close
odd edgeBOT
crude hollow
oh
north sparrow
.reopen
odd edgeBOT
✅
odd edgeBOT
crude hollow
thx
odd edgeBOT
Available help channel!
crude hollow
A cube is expanding in such a way that its edge is changing at a rate of 5cm/s. When its edge is 4cm
long determine the rate of change of its volume.
crude hollow
help
desert jolt
A cube is expanding in such a way that its edge is changing at a rate of 5cm/s. ...
!status
odd edgeBOT
A cube is expanding in such a way that its edge is changing at a rate of 5cm/s. ...
What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
that's the whole question? no other info? really?
crude hollow
how?
crude hollow
the edge is given when it began tho
amber veldt
the edge RATE is
desert jolt
because it was already that big when the problem started
I think we take it from 0
When it wasn't there
desert jolt
<a:thonktate:791272020985249793>
crude hollow
dy/dx=f'(x) and dx= 5 right or smth
twin plover
A cube is expanding in such a way that its edge is changing at a rate of 5cm/s. ...
V = a^3
Diff both sides , sub in values
desert jolt
What's volume of cube wrt side length
twin plover
dy/dx=f'(x) and dx= 5 right or smth
it's dt
amber veldt
unless you're approximating, don't set differentials equals to numbers like dx = 5, there should be a differential on both sides of the equation, like dy=5 dx (not saying this equation is correct in this context, im correcting your syntax)
twin plover
it's changing with time
twin plover
pls explain more
idk what you don't understand rn
twin plover
V = a^3
Diff both sides , sub in values
this is it
crude hollow
i think im getting it
amber veldt
I mean "a" isnt the regular choice of varible maybe that's why mayo is confused
mayo how did you learn the volume of a cube
twin plover
I mean "a" isnt the regular choice of varible maybe that's why mayo is confused
oh
a will be the side length
crude hollow
so dx/dt is 5 and we have to find dy/dt?
amber veldt
MAYO
crude hollow
yeah
amber veldt
you have 2 helpers asking you the same question
twin plover
so dx/dt is 5 and we have to find dy/dt?
Yep
desert jolt
amber veldt
okay im out
twin plover
Mhm
desert jolt
So now V = x^3
crude hollow
64
desert jolt
Differentiating this wrt time will give?
twin plover
mhm
desert jolt
Wrt t
twin plover
sorry pls bare with me
it's okay your doing great
crude hollow
3x^2 /5 right
twin plover
Not exactly
crude hollow
mb
twin plover
And what will the other side be
crude hollow
oh like that
twin plover
Yep
shut nymph
You’re missing a term.
here x is a function of time.
So d(x^3)/dt = (dx/dt) x (3x^2)
twin plover
And that's what you have to find
twin plover
You’re missing a term.
here x is a function of time.
So d(x^3)/dt = (dx/dt) x (3...
dx/dt is given
and so is x at that instant
twin plover
whar
shut nymph
dx^3/dt is not juste 3x^2
crude hollow
ans is 240 right
twin plover
I'm sorry I'm crashing out 💔
shut nymph
That’s not what he wrote tho
shut nymph
Ye
shut nymph
Yes
crude hollow
so thats it right
shut nymph
don’t forget units, but yes
twin plover
is this right?
Yep
odd edgeBOT
odd edgeBOT
Available help channel!
covert root
hi, was solving with gpt, think its hallucinating, i want to understand the problem
speed v of a body is linearly changing with the acceleration a of that body.
a) If its given that the speed of the body is 13m/s with an acceleration of 3m/s^2 and the speed of the body is 17m/s with acceleration of 5m/s^2, find the equation that will represent the speed of the body through acceleration.
b) By whay amount of acceleration will the speed be 3 times bigger than acceleration?
for the first one gpt solved it like this
v1=13m/s a1=3m/s^2, v2=17m/s a2=5m/s^2
plugging these values into this linear equation
a=kv+b
then into a system
{3=k13+b
{5=k17+b
then substracting the first from the second
5-3=k(17-13) ?
finally getting v=2a+7 for the relation
for part b we do the same but search for 3a?
odd edgeBOT
Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).
wooden python
but also this entire question is very weird. where do we get it from that acceleration and velocity should even follow a linear relationship?
!xy
odd edgeBOT
Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.
late sinew
but also this entire question is very weird. where do we get it from that accele...
speed v of a body is linearly changing with the acceleration a of that body.
given right
covert root
the problem is in another language im translating bar for bar, that relation also confuses me
the speed v of a body changes linearly with the acceleration a of that body.
wooden python
> speed v of a body is linearly changing with the acceleration a of that body.
oh gdi
mystic nova
How many body are there in the question a, one body can't have both acceleration of 3m/s^2 and 5m/s^2 if it's linarly changning speed
wooden python
the problem is in another language im translating bar for bar, that relation als...
what language is it in
shut nymph
How many body are there in the question a, one body can't have both acceleration...
I think just two different applications of the question
covert root
what language is it in
macedonian
wooden python
hm
covert root
think its talking about one body
wooden python
i speak bulgarian, can you send the original? i can probably figure most of it out.
(watch this turn out to be a bad idea)
shut nymph
can’t be one body, if ur given 2speeds/accelerations
wooden python
ok
your translation was basically correct but i read it too quickly at first and was slightly confused because of it
this looks like a physics problem but isn't
covert root
it is intentionally written in a confusing way imho
wooden python
yeah
cause it sounds like mechanics
but really v and a are just variables
so you found v=2a+7 right?
wooden python
b) asks you: what's the value of a for which v = 3a?
covert root
i assume b is the same thing as a but we plug in 3a instead of a
wooden python
which one? v=2a+7?
wooden python
well you found it yourself right
covert root
yes (gpt)
wooden python
v depends linearly on a => v = ka + c
where k and c are constants that we have to find
covert root
so by linearly depending we choose the basic linear form of y=mx+b?
wooden python
yes, that's what they meant with "se menuva linearno"
there's not much else to say about this
covert root
yes, that's what they meant with "se menuva linearno"
ok thats actually very helpfull to me thanks
no that is all i needed
i was lost as to where the equation form comes from
thanks a lot
.close
odd edgeBOT
odd edgeBOT
Available help channel!
sick pollen
Comment on the relationship between acceleration and net force in Experiment 1. How is this related to the slope of the line of best fit?
sick pollen
I don't understand how to figure this out
there are a bunch of questions like this in the lab and I can do the calculations and the expiriments but I always get stuck on these questions
quasi sparrow
think of F = ma as y = slope * x
sick pollen
think of F = ma as y = slope * x
the slope is mass times acceleration? I don't get it
ohh slope*x
ohhh slope is the mass?
quasi sparrow
no slope is not both mass and acceleration
sick pollen
no slope is not both mass and acceleration
its just mass?
graceful viper
ohhh slope is the mass?
what is the unit of the slope?
sick pollen
what is the unit of the slope?
I don't know that ive been trying to figure that out
quasi sparrow
y = vertical axis usually
graceful viper
I don't know that ive been trying to figure that out
mathematically, what is the formula of the slope?
silk kindle
the slope is acceleration over force which rearranging f=ma gives 1/m = a/f so the slope is 1 over the mass
sick pollen
mathematically, what is the formula of the slope?
y2-y1/x2-x1
oak crown
the slope is acceleration over force which rearranging f=ma gives 1/m = a/f so t...
Could you not brainfeed other people, it isn't really helping if you don't let them do the crucial things
sick pollen
yeah I got more confused
silk kindle
Could you not brainfeed other people, it isn't really helping if you don't let t...
ok sure, sorry im new i assumed that just answering it and explaining the answer is what the help channel is for
sick pollen
For each trial in Experiment 2, calculate the reciprocal of the wagon’s mass (one divided by the wagon’s mass). Using graph paper or computer software, referring to Experiment 2’s data including this new value, create a scatter plot of acceleration (on the vertical axis) versus the reciprocal of the wagon’s mass (on the horizontal axis).
Comment on the relationship between acceleration and the reciprocal of mass in Experiment 2. How is this related to the slope of the line of best fit?
Im having trouble with all these questions
am I just not taking into account enough of the information from the course?
oak crown
yeah I got more confused
You have a linear function of force and acceleration, F=ma, so as per riemann's example you'd have the y being acceleration and x being force
oak crown
think of F = ma as y = slope * x
So you need to rearrange the formula to get it in this form
silk kindle
So you need to rearrange the formula to get it in this form
how is this different to my brainfeeding, your telling him the most crucial part
sick pollen
im still confused give me a second to read
oak crown
how is this different to my brainfeeding, your telling him the most crucial part
Because I'm not doing the crucial part for them
silk kindle
Because I'm not *doing* the crucial part for them
the crucial part is knowing what to do not doing it, its not difficult to rearrange its difficult to know that rearranging is what you need to do to solve it
thats absurd to disagree with that
quasi sparrow
the crucial part is knowing what to do not doing it, its not difficult to rearra...
stop spamming noah's channel
noah's getting confused enough already without your arguing
silk kindle
is he getting notified?
sick pollen
whenever im stuck on this stuff I get a migraine
I really wish this server had a voice chat
silk kindle
where is the vc
sick pollen
most helpers don't want to do voice chats
where I don't see any
silk kindle
says no access for me
sick pollen
https://discord.com/channels/268882317391429632/520310614988685312
it says no access
quasi sparrow
oof nevermind
quasi sparrow
You have a linear function of force and acceleration, F=ma, so as per riemann's ...
yea go back to this and do it on paper
silk kindle
noah's getting confused enough already without your arguing
can we take it somewhere else then
steep mantle
https://discord.com/channels/268882317391429632/520310614988685312
secret club
late sinew
U can go to dms if you both are willing
silk kindle
the crucial part is knowing what to do not doing it, its not difficult to rearra...
can any of the people who disagreed with this give me an explaination as to why because i really dont see your perspective and just thumbs downs dont help
and go to dms or smwhere else just to not clutter here
sick pollen
so to start when I'm reporting to slope, what unit should I use for it
modern ingot
the crucial part is knowing what to do not doing it, its not difficult to rearra...
i think whats most important is how you approach solving new problems
How to solve it, by George Pólya goes over these concepts really well (imo)
silk kindle
How to solve it, by George Pólya goes over these concepts really well (imo)
does the overarching message give more importance to how to solve something or solving it
timid solar
so to start when I'm reporting to slope, what unit should I use for it
well, we have a graph. a line's equation is y=mx. we know y's unit and x's unit.
odd edgeBOT
This channel is only for on-topic discussion. Please take casual conversation to #discussion or #chill.
quasi sparrow
so to start when I'm reporting to slope, what unit should I use for it
you're thinking backwards. find the answer based on the question, not find the question based on the answer
timid solar
you're thinking backwards. find the answer based on the question, not find the q...
is the unit not the answer? it does relate the slope to the total force and acceleration like asked
quasi sparrow
i disagree the answer is as simple as two words, but sure the units of the slope are part of it.
sick pollen
I got distracted give me a sec to read your stuff
sick pollen
you're thinking backwards. find the answer based on the question, not find the q...
the question right before says to calculate the slope with units
timid solar
the question right before says to calculate the slope with units
did you manage to do that one?
sick pollen
did you manage to do that one?
I have the value but I don't have the value with units
timid solar
I have the value but I don't have the value with units
Force=?
sick pollen
N
sick pollen
Newtons
timid solar
what is the unit for newtons
sick pollen
Newtons is the unit isn't it
quasi sparrow
did you learn SI units
sick pollen
is it like Jules or something
quasi sparrow
oof
timid solar
Yes, but i mean, N=kg*m/s^2
sick pollen
ngl I don't understand what you're trying to say
graceful viper
,w SI units
clever fjordBOT
sick pollen
wtf is that
sick pollen
I just know N what is used to measure the amount of force applied
quasi sparrow
Yes, but i mean, N=kg*m/s^2
do you know what kg, m, and s stand for here
graceful viper
a lot of quantities can be decomposed into these units
quasi sparrow
all*
late sinew
Theres no steradian 
sick pollen
You're confusion me more
graceful viper
have you seen these units?
sick pollen
some of them
graceful viper
you have seen kg, meters, and seconds, yeah?
timid solar
wtf is that
okay so. SI units are the international units used everywhere. We have a few base ones, like m for meter (distance), and s for seconds (time). All other units are composed of these basic units.
Force is equal to mass times acceleration. In the SI units, mass is kg, acceleration is meters per second, per second (change in velocity). So it's kg*m/s^2.
Do you understand this part?
sick pollen
I have to do a chore can I keep this open and come back
timid solar
sure
graceful viper
it might close due to timeout but dont worry, u can always reopen it
sick pollen
Okay thanks
odd edgeBOT
@sick pollen Has your question been resolved?
timid solar
are there any solutions to 2^x=-2? or for that matter any solutions for equations in the form a^x=b where a is positive and b is negative? complex included.
graceful viper
yes there are
timid solar
yes there are
how would i solve one of these? i couldnt find anything on google
graceful viper
rewrite -2 in complex exponential
timid solar
rewrite -2 in complex exponential
what is a complex exponential?
graceful viper
e^(ix)
timid solar
oh
viscid flint
there are no solutions in the real line
timid solar
doesnt that just give numbers in a circle?
carmine idol
$-2=e^{x+iy}$
clever fjordBOT
Element118
carmine idol
You need the real part to encode magnitude
viscid flint
it'll be easier if you write it as $-2 = re^{i\theta}$
clever fjordBOT
Austrayley
carmine idol
Or you can write $re^{i\theta}$
clever fjordBOT
Element118
timid solar
so it's $e^(-2)(cosy+isiny)$?
clever fjordBOT
maxtsg
timid solar
it's e^-2
timid solar
**Element118**
oh
viscid flint
hmm this feels gross. first convert 2^x into e^(something)
timid solar
hmm this feels gross. first convert 2^x into e^(something)
is something = x ln 2
viscid flint
seems good
timid solar
because 2=e^ln2 and then 2^x is (e^ln2)^x=e^x ln2
viscid flint
so then rewrite $-2$ as $2e^{i\pi}$
clever fjordBOT
Austrayley
viscid flint
and then you should be able to algebra it out
timid solar
$e^{x ln2}=2e^{i\pi}$
clever fjordBOT
maxtsg
viscid flint
maybe do the same thing on the right with the 2?
sick pollen
<@770427154676318251> Has your question been resolved?
No
timid solar
No
oh uh
copy your question into a free channel i dont think you can use this one anymore
late sinew
New help channel please
timid solar
maybe do the same thing on the right with the 2?
wdym?
put it into the exponent...?
oh yeah
viscid flint
wdym?
or like -- do you have an idea of how to solve this? if you know how already feel free to go ahead
timid solar
$e^{x ln2}=e^{ln2i\pi}$
clever fjordBOT
maxtsg
timid solar
that's an error, take it step by step
ok
timid solar
that's an error, take it step by step
what is an error? taking the ln of both sides?
viscid flint
no, the thing i put an ❌ next to
viscid flint
yep
timid solar
so $x ln(2) = ln(2)+i\pi$
clever fjordBOT
maxtsg
viscid flint
yeah that looks better
clever fjordBOT
maxtsg
viscid flint
yep seems good
timid solar
nice
viscid flint
usually written as $x = 1 + \f\pi{\ln2}i$
clever fjordBOT
Austrayley
