but yeah, you want A'(1/2) and A'(7)
#help-0
glass lichen
glass lichen
yep
quartz osprey
ok im not too sure now cuz i put - and still got it wrong
glass lichen
,w d/dx 0.23xe^(-.4x)
ocean sealBOT
glass lichen
,w e^(-.4*.5)(.23-.092*.5)
ocean sealBOT
glass lichen
missed the factor of t
quartz osprey
im so confused what
glass lichen
$A(t)=0.23te^{-0.4t}$
ocean sealBOT
Mosh
glass lichen
not $0.23e^{-0.4t}$
ocean sealBOT
Mosh
quartz osprey
ji dont get it still how am i wrong
glass lichen
as in, didnt attempt to do so
quartz osprey
oh
ohhh i see
no i lied i dont see it
alright so what i have so far is from only chain rule
f = 0.23t
g=e^oiwejfowiejf?
quartz osprey
how do i figure out whats f and whats g
glass lichen
wdym
glass lichen
it's a product... it doesnt matter which is f and which is g since it's commutative
quartz osprey
yea i have no clue
glass lichen
what are the 2 functions of t being multiplied together?
glass lichen
no
shut scaffold
-0.4(0.23xt) is being multiplied with e^-0.4(t)
glass lichen
no it isnt
shut scaffold
ye
glass lichen
no
quartz osprey
i kinda need to find out whats f and g to do product rule
glass lichen
read the actual function
glass lichen
0.23t is one of the functions...
quartz osprey
f is t and g is e?
glass lichen
e^(-.4t) is the other
quartz osprey
f*g'+f'+g
glass lichen
that was their failed attempt
glass lichen
Yes.
quartz osprey
what
glass lichen
$(uv)'(x)=vu'+uv'$
shut scaffold
product rule is uv'+vu'
ocean sealBOT
Mosh
quartz osprey
oh yea i added an extra + on accident
my bad alright let me figure this out
i have to chain rule again :/
shut scaffold
not really
quartz osprey
well i kinda have to find the derivitve of g
shut scaffold
not if you know the rule for dy/dx of e^f(x)
glass lichen
not if you know the rule for dy/dx of e^f(x)
that's... chain rule.
quartz osprey
lol
shut scaffold
u dont need to do the full thing
glass lichen
???
shut scaffold
just use the shortcut
glass lichen
the shortcut you're suggesting... is chain rule
glass lichen
It isnt
shut scaffold
is what i thought he meant
glass lichen
well no shit, you're not going to do everything by first principles
shut scaffold
he was complaining about it so I assumed that's what he was planning on doing
quartz osprey
ok so waht i got is -0.092t(-0.4e^-0.4t)+(-0.092(e^-0.4t)
shut scaffold
well no shit, you're not going to do everything by first principles
you some kinda mod around here?
glass lichen
$A'(t)=0.23e^{-4t}-0.092te^{-0.4t}$
ocean sealBOT
Mosh
alpine sable
<@&268886789983436800> streamer role?
sly mantle
<@&268886789983436800> streamer role?
added
glass lichen
or did i just do it completely wrong lmao
looks like you did it wrong
not sure how the 1st term arised
glass lichen
so then what's the 2nd term...?
quartz osprey
f'*g
glass lichen
yeah...
glass lichen
yeah that's wrong.
glass lichen
wdym
quartz osprey
oh
quartz osprey
ok let me redo
shut scaffold
just write out u and v
then u' and v' below them respectively
and work it out systematically
glass lichen
@alpine sable in use.
quartz osprey
ok (0.23t*-0.4e^-0.4t )+(0.23 *e^-0.4t)
shut scaffold
yeah now I see why posting shit in channels that are busy is annoying
glass lichen
ok (0.23t*-0.4e^-0.4t )+(0.23 *e^-0.4t)
2nd term should be positive, not negative
quartz osprey
oh shit my bad
glass lichen
why do you have -e^(-0.4t)?
quartz osprey
uhh misread
shut scaffold
(e^0.4t)(0.23)
quartz osprey
no im blind
shut scaffold
so i think its what i just worked out
and the thing i said before
u add together
shut scaffold
(e^0.4t)(0.23)
this
shut scaffold
first term should be (0.23t)(-0.4)(e^-0.4t)
and
quartz osprey
aite
thanks
sec
alright with everything plugged in for 1/2 i got 0.150
which is 15% right
shut scaffold
yes
quartz osprey
ok i went wrong somewhere
quartz osprey
i did
yea i did something wrong
(0.23t*-0.4e^-0.4t )+(0.23 *e^-0.4t)
this is the derivitive
dont i need the derivitve of the outside shwich is -0.4
shut scaffold
i think you're doing something wrong in the calcultator
unless my differentiation is wrong
is it ok @glass lichen
quartz osprey
shut scaffold
right so 0.15 which is what my answer gave as well
quartz osprey
where tf did i go wrong lma o
quartz osprey
right so 0.15 which is what my answer gave as well
yea i plugged it in and it was wrong i need 3 decimal places
quartz osprey
oh
its not 15%
let me try that way
so like
what eth fuck
why does it accept it like that
glass lichen
why did you multiply by 100
quartz osprey
doesnt it want percentage?
glass lichen
no
quartz osprey
i mean the other problems did that
glass lichen
it wants the rate
quartz osprey
mmmmmmmmmm
glass lichen
.15m/s vs 15m/s for example, very different things
glass lichen
it does not
A(t) gives the percentage of alcohol
A'(t) gives the rate of change of the percentage
quartz osprey
ohhhhhhhhhhhhhhhhhhh
youre right
yea i
im bad at reading
it asks how fast is the perchentage tchanging
which yea means rate
my bad
thanks
bleh
quartz osprey
it is lmao
quartz osprey
thanks
quartz osprey
lol
i usually ask alot cuz im stupid as fuck and my teacher doesnt respond to emails that much
shut scaffold
i usually ask alot cuz im stupid as fuck and my teacher doesnt respond to emails...
ah rip
what grade/year are you in
last year im guessing?
quartz osprey
uni
quartz osprey
lol
shut scaffold
💪
quartz osprey
same
sudden smelt
i have no clue on how to do this
quartz osprey
same homie
celest anvil
alr
ashen anchor
what have you done so far? @sudden smelt
tidal thistle
what're the similarities in solving between rational equation and inequality?
lusty notch
Can someone help me make a spaceship on desmos using function equations please 😭
sudden smelt
what have you done so far? <@!546377544090255361>
I have no clue on what it’s asking for
clever folio
Can someone help me make a spaceship on desmos using function equations please �...
If you don't need anything fancy you can probably just use equations of lines thru pts and then restrict the line equations to build up all the lines you need in your ship picture.
Like in the part labelled domain/range restrictions.
clever folio
I have no clue on what it’s asking for
If you have a number that is square its prime factorization has even exponents.
Like 9=3^2 4=2^2 etc.
So I'd start by prime factoring first and seeing which exponents in ur prime factorization aren't even.
clever folio
Like 9=3^2 4=2^2 etc.
Or for a bigger ex notice 2^4 * 3^6 = 11664 = (2^2 * 3^3)^2 = 108^2
tidal thistle
Can a rational equation have multiple answers(value of x) or just one?
clever folio
Idk ur defn for rational eqn but would it include something like 2/x^2 = 1?
Or like x^2+1=3?
Etc
tidal thistle
do rational equation only have one value of a variable
raw shard
divide it by 2 4 times
inner sequoia
an = a1(r^n-1)
inner sequoia
divide it by 2 4 times
yeah but would after 4 years
would it be 1800 during 1st year
raw shard
yes
inner sequoia
or 1800 during 2nd year
inner sequoia
divide it by 2 4 times
ok so my original answer
quartz osprey
how do i find the derivitve of this
what i have so far is
f=-1000t-13000 f'= -1000
g=e^-0.1t g'=-0.1e^-0.1t
product ru le
into -0.1e^-0.1t(-1000t-13000)+(-1000e^-0.1t)
im not sure if this is right?
tight locust
T'(t) = ?
flint badger
Can a rational equation have multiple answers(value of x) or just one?
they can have multiple x values yes
raw shard
@quartz osprey the derivative of a constant is 0 so just drop the 13000
probably multiply the -1000 by (t+13)
tidal thistle
they can have multiple x values yes
For a single equation?
flint badger
yeah I mean if you have something like
@tidal thistle $\frac{6x}{x+4}+4=\frac{2x+2}{x-1}$
ocean sealBOT
eggdog
flint badger
Assuming a "rational equation" is something that has a rational expression in it
tidal thistle
What's the difference in solving a rational equation and inequalities?
flint badger
well first of all do you know what a rational equation is @tidal thistle
quartz osprey
probably multiply the -1000 by (t+13)
alright i got it but had to find the second derivitive since it asks for the rate at maximum
instead of what is max capacity
it asked for the rate at the max capacity
if it asked for the max capacity it would be first derivitve
fierce linden
Hi, how do i find the real roots of a rational function?
glass lichen
solve f(x)=0
fierce linden
basically its 7x/9x+11 - 12 = 1/x
glass lichen
$\frac{7x}{9x}+11-12=\frac{1}{x}$
ocean sealBOT
Mosh
glass lichen
you have 7/9-1=-2/9
so 1/x=-2/9 means x=-9/2
However I highly doubt that is actually the equation written on the sheet
fierce linden
wait....11 is also in the denominator
glass lichen
yeah
fierce linden
7x/ (9x+11) - 12 = 1/x
glass lichen
there you go
so yeah, bring everything over 1 one side, then combine into 1 fraction
$\frac{7x}{9x+11}-12-\frac{1}{x}$
ocean sealBOT
Mosh
fierce linden
yes
i combined everything
and got a quadratic in the numerator
i set the numerator to 0
and solved...correct?
@glass lichen
glass lichen
yes
fierce linden
i should have gotten -111x^2 + 11x/ 9x^2 +11
glass lichen
$\frac{7x(x)-12(9x+11)(x)-1}{x(9x+11)}$ I think
ocean sealBOT
Mosh
glass lichen
,w simplify 7x^2-12x(9x+11)-1
ocean sealBOT
glass lichen
looks like you're missing a minus on the linear term
fierce linden
**Mosh**
shouldnt the top have 1 more 9x+11?
since we are combining terms?
@glass lichen
glass lichen
wdym
fierce linden
1/x= 1(9x+11)/x(9x+11)
right?
so it would become 9x+11 / x(9x+11)
then tack it onto the eqnation
@glass lichen
ocean sealBOT
Mosh
fierce linden
thats what i was thinking it would look like
glass lichen
,w simplify 7x^2-12x(9x+11)-9x-11
ocean sealBOT
fierce linden
,wsimplify -115x^2 +123x +11
glass lichen
that's already simplified
glass lichen
but yeah, it's just careful multiplication to simplify the numerator
and yeah i'd just use quad formula
fierce linden
okie
glass lichen
cause cba to check if that factors
fierce linden
cba?
glass lichen
cant be asked
flint badger
i dont think thats factorable man
glass lichen
you can have roots and not be factorable over Q
flint badger
-101x^2-141x-11?
glass lichen
,w graph y=-101x^2-141x-11
ocean sealBOT
flint badger
that has real roots
glass lichen
it has real roots
flint badger
discriminant
glass lichen
it just doesnt have Q roots
fierce linden
How do i solve this:
flint badger
$8x+3\le 2x+1\le 17x-8$
ocean sealBOT
eggdog
flint badger
this?
ocean sealBOT
eggdog
ocean sealBOT
eggdog
tight locust
and you should also probably use the transitive property
fierce linden
didnt learn the transitive property
tight locust
it's very simple
let's say i tell you that a = b
and then i tell you that b = c
then what can be said about a and c?
flint badger
lmao why did I find that funny
flint badger
**eggdog**
@fierce linden So rewrite the inequality in terms of this
fierce linden
then what can be said about a and c?
they are equal
flint badger
yes
tight locust
they are equal
yes. but in the context of this problem we don't have an equal sign. we have a less than or equal to sign
so what changes
if a leq b, and b leq c, then what can be said about a and c?
flint badger
yes it's ok because of the rule I just showed you
and logically it makes sense, right?
or wait are you talking about the transitive property or what I showed you
flint badger
**eggdog**
so tell me how you would rewrite the original compound inequality into this form
flint badger
$8x+3\le :2x+1\quad \mathrm{and}\quad :2x+1\le :17x-8$
ocean sealBOT
eggdog
flint badger
You set it up like this right?
fierce linden
yes
flint badger
uhhh i don't think that's right
what did you do to get 6x leq 4
ok for the left one, subtract 2x
it should be 6x + 3 leq 1 correct?
you might wanna redo it.
actually 9 leq 15x is right
if thats for the second
fierce linden
flint badger
except u need to isolate x
ok simplify 9/15
dont forget to simplify
wait
you said it was 8x+3
but you wrote 8x-3 on the paper
did you tell me the wrong thing? lol
flint badger
no its ok
fierce linden
im right tho?
flint badger
no uh
check ur inequality signs
and also simplfiy the fractions first
you can simplify 4/6 and 9/15
fresh parcel
2/3 and 3/5
fierce linden
just did
fierce linden
lol
ocean sealBOT
eggdog
flint badger
yeah
flint badger
it tells us that x is in between 3/5 (inclusive) and 2/3 (also inclusive)
fierce linden
no problemo buttercup
ayo...buttercup?
alpine sable
wait
alpine sable
my turn : )
fierce linden
lol
flint badger
no hay problema
alpine sable
ive found the derivative ,my thought process right now is to set it to zero and solve ,but i know thats wrong
flint badger
this channel is busy man
jovial cosmos
oh sorry
alpine sable
its ok
flint badger
ive found the derivative ,my thought process right now is to set it to zero and ...
alright so you can differentiate both sides right?
is that what you did?
alpine sable
yeah
flint badger
what did you get
alpine sable
i got 2x/3y-27
alpine sable
oops
flint badger
because it would be y' = 2x/3y^2-27 right
alpine sable
yea
alpine sable
find where the denominator equals 0
flint badger
right so
set up an equation where the denominator = 0
it seems like you understand the thought process lol
knowing that y' is vertical we set the denominator = 0
it should be easy from there
alpine sable
how would i find the x value though?
flint badger
well where do you get the actual points from
alpine sable
the original equation?
flint badger
exactly
plug in the y values back into the original equation
to find the x values
and then pair the (x,y) values to find the points
if you solve for y you should get y = pm3 right
alpine sable
wouldn't this only produce 2 points?
flint badger
well yeah, if you substitute 1 of the values in you get 2 points
you need to plug in both y values that you get
namely 3 and -3
back into the original equations
wait hold on a sec
hmm
wouldn't it just be (-6, 3) and (6, 3)
what am I missing here
oh wait bruh
I forgot there was a -27y
so yeah you should get (12, 3) and (12, -3) also
those are the 4 points
just plug y = 3 and y = -3 back into the original eq
i was like wait there's only a cubed that throwing me off
alpine sable
huh,i got (2sqrt(y),3)
flint badger
how'd you get that
warm belfry
Hey guys, can anyone help me?
√3x²-kx+√3=0
∆=0
K=?
flint badger
wait so you plugged in 3 back into the original equation, right
flint badger
Hey guys, can anyone help me?
√3x²-kx+√3=0
∆=0
K=?
busy
alpine sable
i plugged 3 into the original equation and solved for x
flint badger
$y^3-27y=x^2-90$
ocean sealBOT
eggdog
flint badger
by original eq I mean this one
alpine sable
ohh
flint badger
that's the one that gives you the points on the graph, right
alpine sable
i squared
alpine sable
yeah
flint badger
and your thought process wasn't wrong, idk why u thought it was wrong
alpine sable
im wrong alot
flint badger
its ok 😔
flint badger
smallest to largest y
oh
wait what
idk how that's wrong
maybe they want a space lol
thats weird man
alpine sable
flint badger
oh wait I just realized why this is wrong
im so stupid
holy shit
you forgot the -12
and you wer esupposed to keep y the same -3
cuz its
WAIT OMG
I FUCKED YOU UP
IM SO SORRY
i had the right answer but if ucked you up
(-6, 3) (6, 3) (-12, -3) (12, -3)
oh my god
jovial forum
How do i get from dP/dt = 0.015P - 0.15 to 1/(P+10)dP = 0.015dt?
flint badger
ive never made such a horrible mistake
yeah so the order should be like (-12, -3) (-6, 3) (6, 3) (12, -3) oh my lord
I swear if I wrote it wrong again
I DID OH MY GOD
there
alpine sable
where did you get the 12's from for y inouts?
flint badger
,w (-3)^3-27(-3)=x^2-90
ocean sealBOT
alpine sable
yeah
flint badger
noooo
alpine sable
but we get multiple tries!
alpine sable
im not understanding where the other 2 points come from
alpine sable
by myself i got (12,-3) and (6,3) with +-3
flint badger
when you're writing out points though
don't do any plus minus shenanigans, only do that for the x and y solutions but not the points
if you looked at ur x and y solutions it should've been y = +-3, while x was +-12, and +-6
flint badger
all u really had to do tho was plug in y = 3 into the original equation, and then y = -3 into the original equation
yah
now plug in the -3 also
and you should get $\pm 12$
ocean sealBOT
eggdog
alpine sable
yeap
alpine sable
Texas ,yeehaw
flint badger
cool
jovial forum
How do i get from dP/dt = 0.015P - 0.15 to 1/(P+10)dP = 0.015dt?
tardy plank
can someone explain the algebra step for this, I can't figure it out?
fast geyser
im brain farting on this question.. could someone please help me out 😩
indigo jetty
| |u+v| |^2 = (u+v)•(u+v)
fresh parcel
is the || || absolute value
oak chasm
@fresh parcel It's the norm of the vector.
fresh parcel
oh okay
ocean sealBOT
squirtlespoof
fair osprey
What don’t you get? What do you think needs to be done to solve
fair osprey
Are you finding the end result to enter or the equation?
fair osprey
I’m not 100% sure abt equation, but you need to find 2.5% of the salary, then add that and find 2.5 percent of that, repeat until 4th year?
long valve
no there is like an equation that i need
fair osprey
Then I’m not sure, do you have notes to reference?
fair osprey
I don’t think your allowed to ping individuals but not too sure on that
warm brook
I believe so, assuming that your example holds. I think one way to think of this is that the flow is invariant to its other components
warm brook
so there’s a gain of 2.5 percent per year
in other words the salary after 1 year is €20 000 + €20 000 * 0.025
this happens every year so if the quantity after year one is f(1), then the quantity after year two is f(2) = f(1) + f(1)*0.025
so
what does the quantity of year 4 equal?
there is an equation you should know for this
but you can derive it using this method
long valve
Un = U1 . r n-1
is it this
long valve
r should be 2.5
warm brook
what is r in this case
long valve
and n is 4
warm brook
r should be 2.5
should it?
warm brook
what is 2.5% equal to?
warm brook
I believe so, assuming that your example holds. I think one way to think of this...
also @buoyant ocean, you should be careful with the invariant statement, as it will only apply if every part of your diffeq is in terms of 1 variable
warm brook
divide 102.5 by 100, as a gain of 2.5% means that the rate, r=0.025, is (1+r)
this is a rate of 102.5%
long valve
can u tell me what the equation should be
im very lost lol
@warm brook
i think i got it
20000.1.025^4
warm brook
you have it right
long valve
so if i put it all in a calculator
it should give me the answer for the first question?
@warm brook its 22076.2
right?
warm brook
That sounds about right
long valve
ty so much
warm brook
@light kestrel distribution
light kestrel
WRONG PIC I SENT
hybrid plume
The derivative is 2x+8
light kestrel
ok i am just dumb
now i just use the slope intercept formula
right
?
and plug in the y and x
sage vale
any channel for geodesy?
hybrid plume
Yes
light kestrel
:/
fast geyser
| |u+v| |^2 = (u+v)•(u+v)
i did do that 😭 i think it’s very possible that i’m just brainfarting or something lol, if you expand it out should they naturally equal each other?
hybrid plume
Yup don’t mess up that double negative though
hybrid plume
I messed up sorry, plug x and y into your original equation then put that into the slope point form
But for that pic u sent just put in 26
hybrid plume
You don’t have to multiply it out, teachers accept that @light kestrel
Any problems?
hybrid plume
Same thing every time for those
Get the derivative
Plug the x value into the derivative for your slope (m)
Plug x and y into the original equation (not the derivative) and get x1 and y1
Put those into the slope intercept formula
alpine sable
so we know that the tangent slope of the line at a point is the derivative, and we also know we can find the inverse of a function by saying $f(x) = y$ and then swapping y and x
ocean sealBOT
bertaunth
alpine sable
we first want to find the inverse of f(x), and then find the derivative of this inverse
ocean sealBOT
bertaunth
alpine sable
so if we're looking for the derivative of y in this case, lets break it down
so we know that the -4 is a constant, so the derivative of that is just 0
now all we need to do is find the derivative of root x
alpine sable
then you plug in (9, -1) into that and you have your slope
light kestrel
it doesnt have a y valur
so i just plug in the x right
in the sqrt of the denominator
?
alpine sable
so i just plug in the x right
i think the slope checks out if you move it to x=9
upper escarp
is this channel free?
upper escarp
can someone guide me to solve this q?
alpine sable
page area = w * h
knowing what page area is, we can then say
968 = w * h
how can you write the value of w in terms of h?
upper escarp
w = 968/h ?
alpine sable
yeah
upper escarp
how about b?
alpine sable
how about b?
this is how i would approach it
i probably shouldn't have included those last two lines but hopefully you can see what i did here
upper escarp
oh i get it thanks
but where did the h go in the q?
i expanded ur equation but the h isnt there at the end
unless i expanded wrongly?
alpine sable
We can see in the question for b that there's a -4h^2, and in my equation for A there's a -4. We know that when we expand the original A, we get
-4h + some numbers + (something/h).
So to get -4h^2, we just have to rewrite the (969/h - 4) part so that -4 turns into -4h
we can do this since h / h is 1, so 4 * 1 is also 4 * (h/h)
alpine sable
to get rid of the h in 7744, you can multiply everything by h, but remember that changes the entire equation. instead, we can use the 1 = h/h trick so that we multiply the whole thing by h/h
then you get an h in the denominator
hybrid plume
@light kestrel I forgot you had to get the inverse first. I took that course last year, sorry.
hybrid plume
Was that an assignment?
hybrid plume
Phew lol didnt want u to lose marks
light kestrel
ofc not dont worry about it
upper escarp
to get rid of the h in 7744, you can multiply everything by h, but remember that...
ah i see, alright thanks
sharp hare
lapis valley
how to go from this to this
indigo jetty
i did do that 😭 i think it’s very possible that i’m just brainfarting or someth...
After you expand both (u+v)•(u+v) and (u-v)•(u-v), you'll see some terms cancel out
real crescent
hi can someone pls help me with this thank uu!!
little night
hi can someone pls help me with this thank uu!!
(5)^(2*555 - 110) * (2)^999
So 5^(1110 - 110) * 2^999
Make the power of 10 using 2*5 that should be number of zeroes
paper egret
$5^{-110} \times 8^{333} \times 25^{555}$
\$=5^{-110} \times(2^{3})^{333}\times (5^{2})^{555}$
\$=5^{-110} \times (5^{2})^{555}\times(2^{3})^{333}$
\$=5^{-110} \times 5^{1110} \times 2^{999}$
\$=5^{1000} \times 2^{999}$
\$=5^{1}\times5^{999}\times 2^{999}$
\$=5\times10^{999}$
\$\Rightarrow$ There are 999 zeros
ocean sealBOT
CP the Caesar
karmic sandal
does bolzano weirstrauss theorem holds for this sequence ? :
{an} = {1,2,3,4}
karmic sandal
So sequence has to be atleast countably infinite right ?
vale wigeon
the sequence has to be infinite
there's no such thing as an uncountably infinite sequence
karmic sandal
like natural numbers, even numbers, rational numbers
they are countably infinite right ?
vale wigeon
those are countably infinite sets.
karmic sandal
the sequence has to be infinite
got it thanks!
karmic sandal
those are countably infinite _sets_.
ohhh i see, thanks!
vale wigeon
how exactly are you getting 0?
rocky cape
so, x and x cancel.
that make the x^2 into a x^1
then only the top remain, i subtract and boom, 0
vale wigeon
what
alpine sable
then only the top remain, i subtract and boom, 0
yo bro that makes no sense
rocky cape
damn
vale wigeon
are you saying you did some algebra to (x^2 - x)/x and turned it into just x?
because yeah, that's nonsensical. it simplifies to x - 1.
and even then, the derivative of x isn't zero either.
rocky cape
are you saying you did some algebra to (x^2 - x)/x and turned it into just x?
yeah i divided the X^2 by the x on the bottom
vale wigeon
you realize you cannot just ignore the -x on the numerator, right?
rocky cape
oh its not possible to simplifly?
rocky cape
you realize you cannot just ignore the -x on the numerator, right?
yeah i was tryna cancel that before the x^2
but then i kept getting 2
vale wigeon
it is possible to simplify, just not with the whole "let me blindly cancel things out" mentality you seem to have
vale wigeon
$\frac{x^2 - x}{x} = \frac{x^2}{x} - \frac{x}{x} = x - 1$
ocean sealBOT
Ann
vale wigeon
something like this, perhaps.
and then take the derivative properly. which will not give you zero.
rocky cape
damn i would have never thought of that to be honest.
rocky cape
and then take the derivative **properly**. which will **not** give you zero.
Thanks 💯
oh wait so u can cross
harsh atlas
empty?
rocky cape
Yeah should be good now
harsh atlas
nice ty
grizzled sundial
just a quick question
if you have to find a direction of a vector, do you have to find the unit vector?
<@&286206848099549185>
static saffron
yes, but dont ping helpers without waiting 15 mins, thats a great way to never get help
they will remember that 😉
static saffron
given the following:
let $\phi (r) = q* \delta (\vec r) - \theta (r)$ ($\theta(r)$ is not important for the question).
I need to calculate $\int dV phi(r)$ in spherical coordinates, however the delta distribution in spherical coordinates has a singularity when $r_0=0$ or $\vartheta _0=0$
$$\frac{\delta (r-r_0) \delta (\vartheta - \vartheta _0) \delta (\phi -\phi_0)}{r_0 sin(\vartheta _0)}$$
Whats the mathematical correct way to handle this "pseudo-singularity"? I am not allowed to switch coordinate systems here.
ocean sealBOT
derdotte
static saffron
can i just use limits here and dV= r^2 sin(ϑ) dr dϑ dϕ and assume that the dirac delta converges uniformly?
tired gyro
Hello guys!
static saffron
such that i can swap the limit with the integral. After that it reduces nicely assuming that r_0 and ϑ_0 fall into the integration interval
room is in use
tired gyro
I have a math test right now at algebra
Define the notions: group, ring, body, field, vector-dependent linear system, basis,
vector coordinates.
static saffron
we dont help with math tests
static saffron
thats your fault for not learning.
alpine sable
wait if you're on discord...
jade birch
static saffron
you are probably right, well gonna wait a bit and ping helpers after but i suspect not many are awake atm and have had higher mathematics
clear narwhal
Can somebody ping the question?
tired gyro
we dont help with math tests
at least can someone help me understand this question
umbral birch
clear narwhal
Thanks
umbral birch
i somehow am stuck
umbral birch
its the only question i got puzzled in my paper
gilded quarry
if fuction f is defined by
show that for all real positive x:
I have no idea how to solve this
does anyone know anything ?
clear narwhal
what does par mean again?
gilded quarry
oh right mb its in french
its just a conjunction
the function f is defined by [0; + ∞] through ...
placid zinc
Hint:
2x = ln(e^(2x))
placid zinc
ln doesn't distribute, if that's what you're saying
I'm just noticing that there's some random 2x in the answer. Why would that be?
It's worth keeping a page of logarithm properties nearby, if you don't have them down yet
gilded quarry
yeah i got that part but im unsure on how they connected both ends
pretty confused about the
2e^-x becoming a 2e^(-3x)
indigo jetty
how can you make 2e^-x to become 2e^(-3x)?
gilded quarry
2e^-x*e^-2x
gilded quarry
ah alright
still estuary
Is this channel free
gilded quarry
after using some log rules
Oh right so
i would do
ln(e^2x)+ln(1+2e^(-3x))
and then the ln(e^2x) just becomes a 2x
alpine bloom
who is good at math and can help me out dm me pls
gilded quarry
Is this channel free
yep
indigo jetty
and then the ln(e^2x) just becomes a 2x
👍
sharp barn
How to solve (c) and how does the speed time graph look like for (d)
ionic jewel
I can't believe im asking this... but why isn't it 2y^1/2 how come the x is -5 but the y remains 1 instead of 2
alpine sable
I can't believe im asking this... but why isn't it 2y^1/2 how come the x is -5 b...
basically, you add like terms. so imagine $x^{1/2} y^{1/2}$ is the variable $a$. We can then write this as $-6a + 1a$ which is $-5a$
ocean sealBOT
bertaunth
ionic jewel
basically, you add like terms. so imagine $x^{1/2} y^{1/2}$ is the variable $a$....
... Thank you so much this makes so much sense now
fading zephyr
don't use the questions channels to meme
this is your only warning
you are muted for 5 hours. repeated offenses will escalate.
they dm'ed me random bs immediately lol. banned.
vale wigeon
trash took itself out huh 😌
odd obsidian
what exactly am I supposed to do here? I've tried to use the modulus formula, and got something in terms of a (for a complex number a + bi), but I don't know what to do from there
ionic jewel
basically, you add like terms. so imagine $x^{1/2} y^{1/2}$ is the variable $a$....
What are those rules called ? At this point i think i need a cheat sheet for all the basic stuff even tho im at college level...
placid zinc
Let's say you did do z = a + bi
|(a + 2) + bi| = |a + (b - 1)i|
√[(a + 2)² + b²] = √[a² + (b - 1)²]
placid zinc
Perfect. That's the answer
There's an entire line of solutions, and that describes them.
odd obsidian
oh, I think that makes sense
I'm just confused because this is the answer from the book:
and I'm not sure how they got that exactly
placid zinc
Let me check your work
odd obsidian
(I know it says exercise 8, it's the same exercise tho :P)
alpine sable
What are those rules called ? At this point i think i need a cheat sheet for all...
This is essentially the distributive property. For example, say you had 2(3) + 4(3) + 5(5). Based on the distributive property, we can simplify this to (2+4)×3 + 5(5), which implies that you add the coefficients of like terms
odd obsidian
Let me check your work
oh, should I send it here?
placid zinc
,w simplify √[(a + 2)² + b²] = √[a² + (b - 1)²]
still estuary
Can I ask help here or is it not yet done?
placid zinc
Yes, you have a calculation error somewhere
still estuary
If it's done I really need step to step guidance for this urgently
alpine sable
If it's done I really need step to step guidance for this urgently
convert into partial fractions and then integrate both terms
still estuary
Yea idk after partial fraction
I can't integrate after that idk
Like after this
I haven't moved a step
odd obsidian
Yes, you have a calculation error somewhere
okay so I redid it and I got exactly the answer to which Wolfram provided
but it still isn't the one like from the solution of the excersize
I'm just confused as to how they got that
placid zinc
Okay. So note that b = -2a - 3/2
odd obsidian
oh!
placid zinc
That should match their answer.
odd obsidian
you simply put b in terms of a
placid zinc
Your answer is also correct. Nothing different about them. That's just the way they chose to express it
odd obsidian
yeah, that makes sense now. Thank you so much!
placid zinc
Np, feel free to ask if you have anything else
still estuary
Like after this
I haven't moved a step
Can u help me now if ur not busy?
Pls and thank u
odd obsidian
where's your partial fraction decomposition?
still estuary
Idk anything I'm literally blank at the moment
And it's urgent so I'm trying to seek help
alpine sable
And it's urgent so I'm trying to seek help
multiply both sides by the denominator of the left side
alpine sable
there should be an x term on the left and an x^2 term, x term, and a constant on the right
still estuary
I got the x on the left
alpine sable
oh also make sure to expand the right side
alpine sable
yep
still estuary
Now?
alpine sable
then expand the c term and then group together all of the x^2 terms together, the x terms together, and the constants together
alpine sable
yep
then we also know that the side with only x can actually be represented as 0x^2 + x + 0
still estuary
Yea
alpine sable
which means all of the sum of the x^2 coefficients on the left will equal 0, the sum of the x coefficients will equal 1, and the sum of the constants will be 0
then you can set up a system of linear equations
to then find the values for A, B, and C
still estuary
Ax²+cx²=0
Ax+bx-cx = 1
B+c =0
alpine sable
it's
Ax²+cx²=0x²
Ax+bx-cx = 1x
B+c =0
but you can cancel out the x^2 in the first line and the x in the second line to get:
A + c = 0
A + b - c = 1
B + c = 0
still estuary
Ooo
steep mortar
if the line m= mx+c passes through the points (2,4) and (3,-5), then what is the value of m and c?
alpine sable
if the line m= mx+c passes through the points (2,4) and (3,-5), then what is the...
Use $\frac{y_2 - y_1}{x_2 - x_1}$ for m and then use point-slope formula to find c
ocean sealBOT
bertaunth
still estuary
it's
Ax²+cx²=0x²
Ax+bx-cx = 1x
B+c =0
but you can cancel out the x^2 in the firs...
After this what should I do?
(Sorry for the trouble I really needed help in this bcos this is the only sum which threw me off everything thx)
alpine sable
Solve the linear system of equations. So you want to basically want to reduce equations with 3 different constants to 2 different constants. In this case, the third equation let's us say b = -c. Then substitute -c everywhere for b
still estuary
So I got
A= -2/3
B= 1/3
C= -1/3
alpine sable
oh hold on
alpine sable
So I got
A= -2/3
B= 1/3
C= -1/3
try recalculating A
still estuary
The rest r correct?
alpine sable
yeah
still estuary
Ah shi
1/3
alpine sable
yeah