just a quick question about the order
#help-0
obtuse niche
i would have to do the summation part first right
so (1^3+4)+(2^3+4)+(3^3+4)+(4^3+4)
lets say the outcome is x
it would be then 2 times x right?
quick halo
so (1^3+4)+(2^3+4)+(3^3+4)+(4^3+4)
Remember to multiply by 2
obtuse niche
ye but that is after summing it up?
quick halo
ye but that is after summing it up?
No
obtuse niche
so i multiply it with 2 after every index
gray isle
doesn't really matter
quick halo
gray isle
as written the summation should only apply to the i^3
though the writer may have intended otherwise
alpine sable
can anyone explain this to me
lone heartBOT
can anyone explain this to me
quick halo
can anyone explain this to me
What do you not get
alpine sable
What do you not get
i dont get how they got the answer
quick halo
i dont get how they got the answer
Do you know what it means to take the inverse of a function
alpine sable
Do you know what it means to take the inverse of a function
i know it's like something about reversing
i know i have to set f(x) to y
and then interchange
quick halo
i dont get how they got the answer
notice that if you do h(h^-1(x)), then you get x back
quick halo
i know i have to set f(x) to y
then that’s how they did it
quick halo
notice that if you do h(h^-1(x)), then you get x back
and if you do h^-1(h(x)), then it is also x
alpine sable
and if you do h^-1(h(x)), then it is also x
uhhh yes is that the verification
im just confused of where the squareroot went
quick halo
im just confused of where the squareroot went
the reverse of cube root is cube
alpine sable
the reverse of cube root is cube
oh so thats why there's ^3
how about the 2nd one
how'd they get the numerator 1 on the other side
alpine sable
the reverse of cube root is cube
thanks btw!
quick halo
how'd they get the numerator 1 on the other side
Try computing it yourself
alpine sable
Try computing it yourself
what happens next
quick halo
y=1/x-2
x=1/y-2
1/y=x+2
and then after the last step, take reciprocal of both sides
alpine sable
and then after the last step, take reciprocal of both sides
okay I don't really get that part sorry
quick halo
okay I don't really get that part sorry
Take 1/ both sides
alpine sable
Take 1/ both sides
so it just moves or something??
quick halo
y=1/x-2
x=1/y-2
1/y=x+2
$$ \frac 1y = x + 2 $$ \ $$ \frac 1{\left(\frac 1y\right)} = \frac 1{x + 2} $$
ocean sealBOT
rti
alpine sable
😭 thank you
lone heartBOT
@alpine sable Has your question been resolved?
atomic flower
is someone able to help me with this? I'm doing factorising quadratic trinomials i think me and my friends don't know how to do this
atomic flower
<@&286206848099549185>
unkempt vapor
(x-1)(x-2)
strange meadow
Don’t ping instantly also factorise x-2 out
umbral narwhal
. reopen
atomic flower
(x-1)(x-2)
wait what I don't understand how u got that
strange meadow
@umbral narwhal
atomic flower
Don’t ping instantly also factorise x-2 out
How do I do it?
neat copper
(x-2) is common, so you pull that out. Then, x-1 is leftover so it’s (x-2)(x-1)
lone heartBOT
@atomic flower Has your question been resolved?
dull cipher
Hi
lone heartBOT
lone heartBOT
Available help channel!
sharp minnow
does anyone know for the limacon equation, why is there a loop when b < a?
quick halo
does anyone know for the limacon equation, why is there a loop when b < a?
because theta goes to 0 more than once between theta = 0 and theta = tau
sharp minnow
but even if i dont change the value of theta and just the value of a and b, this rule still works?
cinder sundial
does anyone know for the limacon equation, why is there a loop when b < a?
is that a general case of a limacon equation
sharp minnow
cinder sundial
terrific
sharp minnow
does anyone get whyyy
grand girder
but even if i dont change the value of theta and just the value of a and b, this...
is due to the value of this function at the extremes. If you take the derivative w.r.t theta and substitute it in the function at zero points, it will give you a clue. And I think yes it's not about theta it's about the coefficients
lone heartBOT
@sharp minnow Has your question been resolved?
dawn crest
im pretty sure i did the integration right but my answer doesnt look like the possible ones
ocean sealBOT
Dyssrupt
tardy tapir
power rule
tardy tapir
yw
dawn crest
.close
timid kelp
please help with the concept of the f:-> stuff
lone heartBOT
please help with the concept of the f:-> stuff
timid kelp
and the concept of the other question
echo socket
You can think of a function as a way of assigning certain values to numbers in some set that we call the domain of the function
And the notation that you mentioned, something like f: x -> 2x + 1, simply tells you how the assignment of those values works
I.e., to every number x, 2x + 1 is being assigned
echo socket
Yes, right
timid kelp
ohhh
echo socket
But here we are told f: x -> x^3
echo socket
So it's the same as f(x) = x^3
echo socket
For 10b, $x$ is the same as $(f \circ f^{-1})(x)$, right?
ocean sealBOT
A Lonely Bean
quick halo
and $$ (f \circ g)(x) = f(g(x)) $$ by definition
ocean sealBOT
rti
timid kelp
For 10b, $x$ is the same as $(f \circ f^{-1})(x)$, right?
ya but how is it found ?
do I put in (g(x))^3=x-1
echo socket
Ah okay actually that would be a simpler start yeah
Just take cube root of both sides
And you get $g(x) = \sqrt[3]{x + 1}$
ocean sealBOT
A Lonely Bean
echo socket
But for the second part you have g(x^3) = x + 1
Here you can introduce a variable t and say it's equal to x^3
Then you get $g(t) = \sqrt[3]{t} + 1$, right?
ocean sealBOT
A Lonely Bean
echo socket
It looks like you can't really do anything unless g is invertible
So I suppose we can assume that
echo socket
Then you end up saying that h(g(g(x))) is the same as h(x)
Which may not be the case
I'll just tell you what the first step is and the rest should become apparent
timid kelp
because next question is show g in f and h terms which is easy f^-1(h)=g
the first one is kinda hard
for expressing f
echo socket
If $a$ and $b$ are functions with $a = b$, then $a \circ c^{-1} = b \circ c^{-1}$ for any invertible function $c$, right?
ocean sealBOT
A Lonely Bean
echo socket
So just do the same thing here but with a and b replaced with the left and right hand sides of f o g = h and c replaced with g
echo socket
Yes
Wait no
\begin{align*}
f \circ g &= h \
f \circ g \circ g^{-1} &= h \circ g^{-1} \
f \circ Id &= h \circ g^{-1} \
f &= h \circ g^{-1}
\end{align*}
ocean sealBOT
A Lonely Bean
echo socket
"Id" being the identity function (the one defined by x -> x)
timid kelp
ok
echo socket
It's pretty similar to how we solve linear equations as well
So if you were given x * p = q, you would consider two cases, right?
p is either nonzero or p is 0
echo socket
You are welcome
timid kelp
.close
lone heartBOT
tardy stag
"over the domain of integers" means that you don't need to specify int(n)
everything is already assumed to be an integer
so if you just take those out it's right
yeah that looks good
lone heartBOT
@alpine sable Has your question been resolved?
woven gale
hi guys need help (rearrange equation) dm me 🙂
lone heartBOT
hi guys need help (rearrange equation) dm me 🙂
lone heartBOT
@woven gale Has your question been resolved?
woven gale
pls help
lone heartBOT
@woven gale Has your question been resolved?
tacit arch
rearrange to R
multiply both sides by R + R/n first
lone heartBOT
@woven gale Has your question been resolved?
dense garden
hi
dense garden
how do I solve this question?
pallid scarab
The exercise wants you to find ANY 2 vectors in the span that are not just multiples of u or v
So take any 2 numbers that are both not 0
dense garden
how is that possible?
vague coral
a vector in span{(u,v)} can be written as a linear combination of u and v
dense garden
i thought to be in a span is a scalar multiple?
vague coral
so take any coefficient for u and v you want
pallid scarab
So take any a,b not zero and compute au + bv
pallid scarab
i thought to be in a span is a scalar multiple?
No, linear combination of the vectors of the span
Otherwise the span wouldn't be a subspace
pallid scarab
Sure but your first vector is wrong
Were you trying 2u + 2v?
Check again on those coefficients
dense garden
Were you trying 2u + 2v?
yep edited
pallid scarab
And so the final vector also changes
dense garden
<0, -2, -6> right
pallid scarab
Yes
pallid scarab
Is it because you haven't input the second vector combination?
What is the error message?
dense garden
pallid scarab
That's not right
pallid scarab
I really don’t understand how it can be marked as wrong
pallid scarab
Ok yes
visual mantle
I need help solving Question 10 (b). I do not know how to do any of it bar the general term.
visual mantle
Replace it where
alpine sable
its given x=1
visual mantle
The answer has x in it
alpine sable
u sure?
You get the answer
Multiply the answer by 1
And as 1=x
Itwould be
x times (answer)
visual mantle
alpine sable
You can do x² x³ whatever cus its just one
visual mantle
Yeah
alpine sable
its ex=2.5?
alpine sable
lemme see wait
visual mantle
I don’t know how to do that
alpine sable
come on cancel x powers and y powers
visual mantle
Wdym come on ?
alpine sable
visual mantle
Clearly this isn’t a very helpful server , I ask for help and you make fun of me. Nice
alpine sable
alright
let me be absolutely clear
simplify means cancel x powers
u have x^9 in numerator and x^3 in denominator
so when u cancel xs, u get x^6 in numerator..
need any better explanation?
lone heartBOT
@visual mantle Has your question been resolved?
gray jetty
I am sorta confused about the closure properties of subspaces
glacial patrol
Which ones
gray jetty
both
The plane of vectors (b1, b2, b3) with b1 = b2 for instance
is this a subset of R^3
subspace
glacial patrol
Oh
Has to be closed under addition and scalar multiplication so let's see 
let c be a constant
Then c(b1, b2, b3) = (cb1, cb2, cb3)
gray jetty
right
glacial patrol
If b1 = b2 then cb1 = cb2
So it's also an element of the plane, I. E. Closed under scalars mult
gray jetty
what if c is a negative constant
glacial patrol
and if you add (b1, b2, b3) + (a1, a2, a3) that's (b1 +a1, b2 + a2, b3 + a3)
glacial patrol
what if c is a negative constant
Still works. Maybe you're thinking about inequalities where multiplying by a negative switches the direction
anyways b1 = b2 and a1 = a2 implies b1 + a1 = b2 + a2
past karma
glacial patrol
so closed under addition also 
glacial patrol
Open ur own help channel pls
Also when u do tell them what omega is supposed to be
past karma
Open ur own help channel pls
how
glacial patrol
,help
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glacial patrol
!help
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Please read #❓how-to-get-help
gray jetty
anyways b1 = b2 and a1 = a2 implies b1 + a1 = b2 + a2
so then its closed under adition righr
glacial patrol
yee
gray jetty
if it was not closed under addition and multiplication what would that look like
glacial patrol
for instance the union of two no parallel lines. If that's hard to see then think about the union of the x axis and the y axis. Won't be closed under addition
Also any finite subset of R^n is not a subspace
gray jetty
also for the q i posted above, would you need to show the 0 thing
are linear combinations finite?
finite subsets
glacial patrol
if the subset only includes the linear combination of two vectors I guess
Finite just means you can count the number of elements if you have enough time
Showing it's closed under scalar multiplication implies 0 is in it
Cus 0(the scalar) times any vector is the 0 vector
glacial patrol
The set of vectors in R^3 where b=1 would not be a subspace cus it's not closed under either addition or scalar mult.
e. G (a, 1,c) + (d, 1,f) = (a+d, 2,c+f)
gray jetty
ohhhhh
glacial patrol
Also if the scalar (imma call it m in this instance) is not 1 then the b will not be 1 but m
gray jetty
Also if the scalar (imma call it m in this instance) is not 1 then the b will no...
(a+d, 2,c+f) how is this not in R^3
glacial patrol
(a+d, 2,c+f) how is this not in R^3
It is in R^3
It's not in the subset of vectors such that b=1 though
Oops lmao
Called it a subspace by accident
gray jetty
wait i think i get it...
lone heartBOT
@gray jetty Has your question been resolved?
gray jetty
It is in R^3
tysm
alpine sable
In how many different ways can five couples of husband and wife arrange themselves around a bonfire, if the men and women alternate?
alpine sable
I think the answer is: (5-1)! = 24 x 2 = 48
If you consider the couples as entities, you have 24 combinations, then if you alternate men and women, you can either have man-woman-man-woman-man-woman-man-woman-man-woman, or woman-man-woman-man-woman-man-woman-man-woman-man
So you multiply 24 and 2 to get 48
Is this reasoning correct?
manic flame
you have 5 and 5
manic flame
the first place can be filled by any 5 men, so you have 5 ways to fill the first place.
alpine sable
but in couples of 5
alpine sable
oh, I think I thought the couples had to be in pairs
alpine sable
I think you are right
manic flame
they can arrange themselfs as they want
alpine sable
Yes
manic flame
ok let me know if you can fdigure out the rest
alpine sable
mm I think maybe you have to do this: 4! x 4!
manic flame
5 different men can fill up first spot, 4 can fill 4
5x4x3x2x1
=120
this is only for men
alpine sable
mm no, bc you need to eliminate 1, bc it doesn't matter if you turn it
manic flame
and since they alternate with woman, and they have to be togehter, you divide with 2
why eliminate 1?
alpine sable
- Circular: $(n-1)!$
One variation doesn't matter in a circle, what matters is the order.
ocean sealBOT
ale.r
alpine sable
Circular permutation is the total number of ways in which n distinct objects can be arranged around a fix circle.
You need to eliminate 1 to discard the ways in which you rotate the circle
(5-1)!
alpine sable
but noone is being left out
wdym
bc in the circular permutation is not about leaving one out
If men and woman can accommodate each one in 24 ways, I think you should multiply them
manic flame
Maybe you are right yea
no it should be way more then 24
oh man I havent done one of these in ages
alpine sable
oh man I havent done one of these in ages
Don't worry I'll post it again
manic flame
😄
rustic notch
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lone heartBOT
@rustic notch Has your question been resolved?
rustic notch
there's no )
Thanks
rustic notch
I don't see any question but it looks like coding.
Alr
unreal kestrel
is this right
lone heartBOT
is this right
carmine beacon
Your old area is 20 times 9 = 180...
Your new area is (20+x) times (9+x) = 570
Is that what you did? @unreal kestrel
unreal kestrel
Your old area is 20 times 9 = 180...
Your new area is (20+x) times (9+x) = 570...
Yea
lone heartBOT
@unreal kestrel Has your question been resolved?
unreal kestrel
So your equation to solve for x is x^2 + 29x + 180 = 570, right?
Yea
carmine beacon
@unreal kestrel Sorry, I was helping someone else while I was waiting...
So if you the answer you give, 35.5 is not correct. I recommend resolving for x for the equation that you got 🙂
unreal kestrel
So your equation to solve for x is x^2 + 29x + 180 = 570, right?
I redid it, is it 10?
lone heartBOT
I redid it, is it 10?
carmine beacon
No @unreal kestrel ... Since it's quadratic, you should see two roots
unreal kestrel
No <@1072266627497852988> ... Since it's quadratic, you should see two roots
And -39
carmine beacon
Actually sorry, yes it is 10 lol
Sorry for a second I thought you said -10. Apologies
It's not -39 because that would imply that your rectangle would shrink
unreal kestrel
OH
carmine beacon
Eurika? 🙂
carmine beacon
What really?
carmine beacon
Is this something else? I don't see how this applies to the pool problem lol
alpine sable
In how many different ways can five couples of husband and wife arrange themselves around a bonfire?
west girder
Are rotations considered distinct?
carmine beacon
Husband 1, Wife 1
Husband 1, Wife 2
Husband 1, Wife 3
Husband 1, Wife 4
Husband 1, Wife 5
Husband 2, Wife 1
Husband 2, Wife 2
Husband 2, Wife 3
and so forth...?
lone heartBOT
@alpine sable Has your question been resolved?
prime badge
(5−1)! arranges the couples
but each couple can be independently flipped
i think the idea is they stick together
alpine sable
I have done this
lone heartBOT
alpine sable
.reopen
lone heartBOT
✅
alpine sable
Number = women
Letters = men
You can arrange the groups in 24 ways
and there are 5 ways for each arrangement of groups
so 24 x 5 = 120
alpine sable
Are rotations considered distinct?
no
alpine sable
Husband 1, Wife 1
Husband 1, Wife 2
Husband 1, Wife 3
Husband 1, Wife 4
Husband ...
mm these are the possible groups
alpine sable
(5−1)! arranges the couples
yes
alpine sable
i think the idea is they stick together
they don’t say that
west girder
It’s just 9! right?
prime badge
i don;t think theywant that
they don;t say what to do i agree
you guess, i don;t agree with your guess
alpine sable
It’s just 9! right?
no, men and women are alternated
alpine sable
you guess, i don;t agree with your guess
It’s not a guess
- Order matters
- The only condition is that men and women are alternated
prime badge
oh wait, there's a third way
like kappa says
it's also better than yours
but i think it's wrong
prime badge
It’s not a guess
i don;t understand if that's what it says or it's what you think
oh there's a fourth way, 4!×5!
yours still the worst
alpine sable
like kappa says
9! is not right
men and women are alternated
alpine sable
i don;t understand if that's what it says or it's what you think
Is what I think
prime badge
with your conditions you would do 4!×5!
alpine sable
oh there's a fourth way, 4!×5!
why
worn fable
i keep getting an undefined answer. i tried adding both and canceling (x-5) on top and bottom and still got undefined answer
serene junco
can you show your work?
serene junco
you're all good up to $\frac{2+(x-5)}{(x-3)(x-5)}$
ocean sealBOT
tatpoj
serene junco
but you cannot cancel (x-5) from there
notice (x-5) is not actually a factor of the numerator
it's attached by addition, not multiplication
serene junco
I think you'll just get something indeterminate still
try simplifying the terms in the numerator
worn fable
my algebra is so bad sometimes
serene junco
all good no worries
worn fable
okay i just got the answer thank you
serene junco
no problem good work 👍
worn fable
.close
bleak horizon
At the end of the summer, I decided to drain the 1,500 gallon swimming pool. I noticed that it drains faster when there is more water in the pool. The was interesting to me, so i decided to neasure the rate at which it drains. I found that 3% was draining out of the pool every minute. t=minutes
So i got the equation f(t)=1455*0.97^(t-1)
Then this question wants me to find how much minutes will it take for the pool to be empty
bleak horizon
Then i get 0=1455*0.97^(t-1)
Then i got 0=1500*0.97^t
then 0=0.97^t
i think i did something wrong but i dont know what
placid zinc
If your model is "3% drains every minute", then the pool will never empty
As no matter how little is in there, you can't lose all of it, just 3% of it
placid zinc
Real world models do sometimes have problems like this. They're probably just trying to get you to notice that
lone heartBOT
crystal glade
.reopen
lone heartBOT
Available help channel!
gusty sable
How do I solve these?
lone heartBOT
How do I solve these?
gusty sable
im not sure how or where to start
gusty sable
write the expression as a power of x
vivid wind
ah okok
vivid wind
so this is about indices correct?
gusty sable
some of them yes
vivid wind
i would start by getting rid of the square on the bracket
gusty sable
how does distributing the square to the other exponent work
vivid wind
u can literally just times the power by two
gusty sable
so it turns into 4c-1
vivid wind
so u would get x to the power of 4c-2
vivid wind
look ath the first rule
fromm the pic i sent
u just add the powers
so x to the power of 5c - 3
do u need help with the second one too?
gusty sable
yes pls
gusty sable
so x to the power of 5c - 3
wait why is it -3
vivid wind
get rid of the bracket first
vivid wind
wait why is it -3
because -1 + -2 =-3
vivid wind
and then ur left with x to the power of c+1 times x to the power of 4c-2
remember it was -2
oh my fault
i mis saw
ur right
its -1
sry bout dat
vivid wind
sry i ll be back later try the second on ur own first
gusty sable
o ok
vivid wind
if u still need help dm me if u want
tiny breach
lone heartBOT
alpine sable
if im correct
tiny breach
i feel like its 140
lone heartBOT
<@&286206848099549185>
Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
alpine sable
h=150
tiny breach
Ohh
lone heartBOT
360-210 = 150
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
alpine sable
ok
tiny breach
Ty
tiny breach
Alr
tiny breach
it equals 180
tiny breach
thats 80
tiny breach
ye
tiny breach
mhm
alpine sable
so e = ?
tiny breach
how would i apply alternate interior angles
tiny breach
ohhh
alpine sable
so therefore e = ?
tiny breach
100
alpine sable
perfect
tiny breach
ok so one quesiton
alpine sable
sure
tiny breach
in the future how can i tell when they are alternate interior angles
tiny breach
yeah for parralel
alpine sable
that means they are parralel
any two parralel lines bisected
by a
line
produces alternate interior and alternate exterior
let me do a paint
tiny breach
Ohh
alpine sable
to demonstrate
tiny breach
Ok
tiny breach
c and f
alpine sable
alternate interior and exterior
tiny breach
g and b
tiny breach
no sorry
alpine sable
okayt let me find a diagram
tiny breach
alr
tiny breach
h and e and f and g>?
tiny breach
ohh
alpine sable
so those are the exterior angles
so now we look at alternate meaning opposite side of the line
7 is exterior left side
tiny breach
Uh huh
alpine sable
2 is exterior on the right side
tiny breach
ohh
alpine sable
so they are alternate exterior angles
tiny breach
And those 2 are equal
alpine sable
And those 2 are equal
YES
good
which angl;es are in the running for interior
angles
alpine sable
7?
tiny breach
Alr
tiny breach
3 and 6 and 4 and 5
tiny breach
alr
tiny breach
Yes
alpine sable
now using which angles does e = ?
tiny breach
100
alpine sable
which alternate did we just use
tiny breach
we used e and i
tiny breach
I think they are interior
alpine sable
perfect
tiny breach
Theres no exterior in this right>
alpine sable
yes
good
e = 100 i = 80
h = what we are trying to find so we need to find
c now
we have another line
where onbe angle is 150
so c = ?
tiny breach
30
tiny breach
210
alpine sable
any quadralateral angles add up to ?
tiny breach
wait im tweakin
tiny breach
Yes
alpine sable
what does h equal
tiny breach
So 150
alpine sable
good
tiny breach
OH
tiny breach
Thanks man
alpine sable
np
tiny breach
Dont close channel yet may i go over it
alpine sable
mkay
tiny breach
Alr thanks
alpine sable
if u wanna close it u can just open a new one or dm me
tiny breach
Have a good day
alpine sable
i just joined today
tiny breach
if u wanna close it u can just open a new one or dm me
Oki
alpine sable
so i dont know the systme
alpine sable
c ya
tiny breach
cya
subtle blade
im not sure what magnitude is, is it the length of the slope of the velocity curve since acceleration is the velocity curve?
subtle blade
what do they mean by absolute value?
quick halo
what do they mean by absolute value?
absolute value is how far a number is from 0. For example, the absolute value of -7, written as |-7|, is 7, because 7 and 0 are 7 units away on the number line
quick halo
the absolute value of a positive number is itself
subtle blade
so do i find the slopes of each part?
quick halo
im not sure what magnitude is, is it the length of the slope of the velocity cur...
the slope of the velocity is the acceleration
subtle blade
and see what slope is biggest?
alpine sable
and see what slope is biggest?
yea
take the intervals
do rise/run
compare
its not too diffcult
just make sure to abs value ur slopes
subtle blade
the slope of the velocity is the acceleration
right
quick halo
so would the slope of the first part be 8/5?
it gives the values in terms of v_0 and T
alpine sable
subtle blade
ah so -2v0 over T
alpine sable
slope seems to be (by coefficients) 4 /2
quick halo
ah so -2v0 over T
Yes
quick halo
slope seems to be (by coefficients) 4 /2
it isn’t, because of the scale of the axes
subtle blade
from 3T to 4T the slope would be 2v0 over 3T?
subtle blade
from 3T to 4T the slope would be 2v0 over 3T?
oh would it be -2v0 over 4t instead
quick halo
which would then be 2v0 over T because of absolute value?
No, because the slope is positive, which you can tell from the graph because it is going up
quick halo
oh would it be -2v0 over 4t instead
Yes, not 3T
subtle blade
No, because the slope is positive, which you can tell from the graph because it ...
oh its going up by 2v0 right
quick halo
oh would it be -2v0 over 4t instead
this is still wrong
did you calculate the difference in height?
and the difference in time
subtle blade
difference in height?
quick halo
oh its going up by 2v0 right
because it’s going up, the slope is positive
subtle blade
because it’s going up, the slope is positive
right
quick halo
oh wait is itt going down by -4v0?
Yes, that’s the rise, or difference in height
subtle blade
so the slope from 3T to 4T would be -4v0 over T
which would thten be 4v0 over T because of absolute value?
quick halo
which would thten be 4v0 over T because of absolute value?
Yes
subtle blade
so 4v0 over T vs 2v0 over T
quick halo
ah so -2v0 over T
how did you even get -2v_0/T here
subtle blade
it would be T = 3.5 since the slope from 3 to 4 is bigger?
subtle blade
how did you even get -2v_0/T here
the line started at -2v0 and i forgot 😅
quick halo
it would be T = 3.5 since the slope from 3 to 4 is bigger?
Yes
By the way
there’s a quicker way to do this
you look at which lines are steeper
the left line is less steep than the right line
subtle blade
does steeper always mean a higher slope?
quick halo
so the right one has higher magnitude of acceleration
subtle blade
ohh
quick halo
does steeper always mean a higher slope?
No, if it were steep but going to the bottom right, then it would be a big negative slope
but here, you only need the magnitude of the acceleration
so you only need to care about how steep it is
sage hedge
lone heartBOT
sage hedge
I am on my last attempt and for (a) I think the answer is .00333
but im not sure
this is a snippet of my work if that helps you understand what I WAS thinking
alpine sable
DO you know what your $\epsilon$ is in those questions?
ocean sealBOT
Replaced by new brandon H
alpine sable
😭 bro said they were impatient but then doesn't respond
lone heartBOT
@sage hedge Has your question been resolved?
sage hedge
DO you know what your $\epsilon$ is in those questions?
is that like the delta but for the y axis
I wrote delta = 0.01 but I meant to epsilon
if thats what you mean
alpine sable
I wrote delta = 0.01 but I meant to epsilon
for the first question sure
sage hedge
for the first question sure
wym?
alpine sable
It looks like you just made a small mistake on the first question
sage hedge
oh
alpine sable
You already know that $L = 28$, $\epsilon = 0.01$
ocean sealBOT
Replaced by new brandon H
ocean sealBOT
Replaced by new brandon H
alpine sable
you then solved for x and got
sage hedge
ye
alpine sable
the correct answers
sage hedge
so its .00333 repeating?
sage hedge
ye
sage hedge
damn
alpine sable
$0 < \abs{x-4} < \delta$
sage hedge
I thought .00333 would be the delta
ocean sealBOT
Replaced by new brandon H
alpine sable
you put in the x's you got
which were $x=4.00166666667$ or whatever and $x=3.99833333333333$ or whatever
ocean sealBOT
Replaced by new brandon H
ocean sealBOT
Replaced by new brandon H
sage hedge
oh snap
alpine sable
which is just
alpine sable
You have to open your own help channel
sage hedge
I just subtract the 2 DIF x values
lone heartBOT
alpine sable
yee
sage hedge
damnnn
alpine sable
you have to remember the definition
alpine sable
alpine sable
so the correct answer would be .00167?
yeah
lone heartBOT
Available help channel!
sage hedge
this makes a lot of sense
lone heartBOT
this makes a lot of sense
sage hedge
.close
acoustic plover
I need help with 1c of this question:
lone heartBOT
I need help with 1c of this question:
lone heartBOT
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Please only use the <@&286206848099549185> ping once if your question has not been answered for 15 minutes. Please do not ping or DM individual users about your question.
@acoustic plover Has your question been resolved?
lone heartBOT
@acoustic plover Has your question been resolved?
acoustic plover
<@&286206848099549185>
lone heartBOT
@acoustic plover Has your question been resolved?
quick halo
This is what I eventually did is it correct tho
Oh
quick halo
Can you state the existence and uniqueness theorem?
acoustic plover
if the derivates are all continuous at x then there exists a unique solution to the IVP
@quick halo
lone heartBOT
@acoustic plover Has your question been resolved?
opal pendant
lone heartBOT
lone heartBOT
lone heartBOT
✅
opal pendant
.close
cinder sundial
lone heartBOT
cinder sundial
Why it is incorrect
naive crystal
You missed 2
marsh rapids
What you wrote only holds for the cardinal
cinder sundial
What you wrote only holds for the cardinal
“Cardinal”
marsh rapids
Number of elements
cinder sundial
What you wrote only holds for the cardinal
Why?
marsh rapids
It doesn't make any sense when talking about sets
What's A+B, if not A U B ?
And why take away A n B, which is clearly part of A U B ?
cinder sundial
Is it because that set wouldn’t have more than one of same element
cinder sundial
So they wouldn’t overlapping each other
simple slate
The a intersection b statement is there to remove the overlap
simple slate
Hence it works when counting the number of elements
Or evaluating probability
Tbh you shouldn't be using a formula to find such unions
marsh rapids
Or evaluating probability
Which, in the context of finite sets, is the same thing
marsh rapids
Tbh you shouldn't be using a formula to find such unions
Because it doesn't work
simple slate
Yep
marsh rapids
It doesn't give the union
The operations aren't even defined here
Unless - is intersecting with the complement
And + is the union, which makes no sense
lone heartBOT
@cinder sundial Has your question been resolved?
cold pumice
How do I solve this limit?
lone heartBOT
How do I solve this limit?
vale wigeon
multiplying top and bottom by 1/x is a good start.
cold pumice
When I try L'Hôpital's rule I just get stuck in a loop with this root
vale wigeon
you do not need l'hop!
cold pumice
multiplying top and bottom by 1/x is a good start.
And then what? I get infinity divided by infinity in the denominator
sterile hill
How do I solve this limit?
I would factor out x^2 and turn it into |x|
And then you’d know |x| = x because x > 0 as x approaches infinity
vale wigeon
$\frac{6 - 4x}{\sqrt{x^2 - 3x}} = \frac{\frac{6}{x} - 4}{\sqrt{1 - \frac{3}{x}}}$
ocean sealBOT
Ann
vale wigeon
is what you'll get
sterile hill
How do I solve this limit?
Then I’d force factor an x from the numerator