<@&286206848099549185>
#help-10
tall wind
obtuse pebbleBOT
@tall wind Has your question been resolved?
obtuse pebbleBOT
@tall wind Has your question been resolved?
zenith raft
idt you wanted the sum to go to infty here but yea the idea looks fine
tall wind
idt you wanted the sum to go to infty here but yea the idea looks fine
yeah, it should be the number of points in P
zenith raft
do you need any help with the other question in the post still?
tall wind
no I think that comment answered it. If you want you can drop a comment on that post, maybe upvote because you could (might not be allowed to say that)
but yeah, thanks
.close
obtuse pebbleBOT
zenith raft
loll sorry i don't have a stackexchange acc
obtuse pebbleBOT
Available help channel!
tall wind
loll sorry i don't have a stackexchange acc
yeah dw you're alright
obtuse pebbleBOT
yeah dw you're alright
tall wind
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
ebon fossil
help pls
ebon fossil
some one i rlly need help
untold flax
what's your question
ebon fossil
i just need to know how do like find quicker answers for bigger multiplication sums
like a way to figure it out
nocturne minnow
Do you have an example?
knotty thorn
something multiplied by 1 digit should be able to done mentally
nocturne minnow
Just know shortcuts. Like 5 x 9 =45 and then tack on two 0s
knotty thorn
you should use long multiplication to do 2 digit * 2 digit and greater
ebon fossil
this is helping alot thx guys
nocturne minnow
And googling tricks is helpful too
ebon fossil
thx
obtuse pebbleBOT
@ebon fossil Has your question been resolved?
warped timber
"Let a and b be two vectors. Find |a-b| knowing that |a|=3, |b|=5 and the angle between a and b is 120º"
obtuse pebbleBOT
"Let a and b be two vectors. Find |a-b| knowing that |a|=3, |b|=5 and the angle ...
warped timber
I just don't know where to start
ruby path
Triangle law of vector addition
warped timber
|a-b|^2 = (a-b) • (a-b)
and is this some identity I'm supposed to memorise or is there somewhere it comes from?
obtuse pebbleBOT
@warped timber Has your question been resolved?
fierce lagoon
and is this some identity I'm supposed to memorise or is there somewhere it come...
|v|^2 = v • v
finite pollen
y = (x-7) / (x-2)(x-3) ... can anybody provide easier method to differentiate this function, just a hint would do
obtuse pebbleBOT
y = (x-7) / (x-2)(x-3) ... can anybody provide easier method to differentiate th...
teal turret
Either expand (x-2)(x-3) and quotient rule, or triple product rule would probably help
high lily
easier method than what
finite pollen
easier method than what
than differentiating the normal way
high lily
what do you consider the "normal" way
finite pollen
cause the normal one will be way too long
high lily
show the way you differentiated it
only then can we provide comments about whether there's a better approach
finite pollen
what do you consider the "normal" way
(f(x).g'(x) - g(x).f'(x)) / g(x)^2
high lily
missing () to clearly indicate numerators and denominators
teal turret
also ur ‘ are flipped
high lily
also ^
finite pollen
(f(x).g'(x) - g(x).f'(x)) / (g(x))^2
high lily
still wrong
finite pollen
urgh whats wrong lol
high lily
the terms on the numerator are the wrong way around
finite pollen
ok ( f'(x).g(x) - g'(x).f(x) ) / (g(x))^2
high lily
there isn't really anything better than quotient rule here
cause the normal one will be way too long
shouldn't be that long
finite pollen
ok, no options than i guess
high lily
its like 3-4 steps
finite pollen
.close
shadow lava
Is Exponential Rule considered a rule for derivatives?
obtuse pebbleBOT
Is Exponential Rule considered a rule for derivatives?
shadow lava
Like power rule, quotient rule, chain rule
sonic anchor
like are you asking for a proof of it? idk what the question is
shadow lava
The a^x derivative?
Ya, it involves ln(x)
To find d/dx
This is called the Exponential Rule?
Or is it just Chain Rule?
royal basin
what difference does it make whether it is "considered" a "rule" or not?
shadow lava
lol I’m just asking to know when I see it what to call it
Chain rule or exponential rule
shadow lava
We have rules tho.. product rule, quotient rule, chain rule
Why do they call it these if it’s just “the derivative of xy”
Both are correct I’m just wondering if exponentials have their own rule or if it uses chain rule
Why everyone always telling me “I’m overthinking it” … and “who cares?”
I thought it was a good question but I guess not?
royal basin
if you twist our collective arms enough, we can tell you that d/dx (a^x) = a^x log(a) follows from the chain rule + the fact that e^x is its own derivative, whether by definition or immediate consequence of the definition depending on which of its properties you define it with.
sonic anchor
i mean it has nothing to do with maths if that really is the question
royal basin
if you so badly wish to use this to shove the derivative of a^x into the box of "Things That Follow From The Chain Rule" then so be it, i suppose.
not everything in math has one clearly defined logical predecessor.
empty sky
This is called the Exponential Rule?
yes you can call it that
it really ain't that deep
royal basin
^
shadow lava
yes you can call it that
just checking because for whatever reason it wasn't included here, maybe the author missed that
median dome
they didn't list that the derivative of e^x = e^x either
doesn't mean you aren't allowed to use it
shadow lava
they do here, but just naming it "Exponential Rule" along with the others, I was curious
royal basin
it is not that deep.
shadow lava
so for trig derivatives, these are the primary ones to know. if I know both of these, I can find tan, sec, csc, cot
shadow lava
but I don't think I can find arcsin, arccos, and arctan with just d/dx of sin and cos, right?
median dome
but I don't think I can find arcsin, arccos, and arctan with just d/dx of sin an...
i think you can
shadow lava
^ these ones I need to memorize like d/dx of sin, cos?
median dome
but you'll need implicit differentiation
shadow lava
i think you can
oh, but it's complicated, ya?
royal basin
"need to memorize" is a subjective matter.
shadow lava
hmmm
royal basin
it takes some work to rederive the derivative formulas for inverse trig functions if you do not remember them by heart.
if you are willing to do that work every time then don't memorize them.
shadow lava
like for you folks do you know all of these immediately? or sometimes forget for any of them?
royal basin
can't say i personally forgot any of these
but these are kind of like the multiplication table
for learning purposes that is
median dome
the last one seems weird
shadow lava
is there any trick to remembering arcsin, arccos, arctan?
median dome
i have never seen it in that form
royal basin
good to have on instant recall, bad to memorize mindlessly.
median dome
is there any trick to remembering arcsin, arccos, arctan?
i would say try to understand where they come from
empty sky
personally i never remember arcsin and arccos and just went through the work of deriving it if i needed to find it
median dome
that can help you to remember the structure of the derivatives
empty sky
but yea they are good to know rather than doing the work all the time
shadow lava
personally i never remember arcsin and arccos and just went through the work of ...
how do you derive with just sin and cos?
empty sky
you gotta use implicit differentiation
If you haven't covered implicit yet then dw about it, in general it will be easier to just memorize it anyway
shadow lava
If you haven't covered implicit yet then dw about it, in general it will be easi...
you mean d/dx(y) = dy/dx?
timid silo
i need help lads
obtuse pebbleBOT
i need help lads
timid silo
Yea
royal basin
progress so far?
timid silo
nope
royal basin
do you know how to solve rational inequalities in general?
timid silo
Yea just not this one
royal basin
ok
timid silo
I got -1<=x and x>=1
royal basin
recommend subtracting 1/x from one side, then making LHS into one fraction and doing sign analysis.
royal basin
I got -1<=x and x>=1
did you do casework?
median dome
I got -1<=x and x>=1
you're almost correct
median dome
did you do casework?
^^
royal basin
i will step away for the next few minutes
timid silo
Okay
obtuse pebbleBOT
@timid silo Has your question been resolved?
signal bramble
can someone explain this to me
obtuse pebbleBOT
can someone explain this to me
median dome
how can you simplify root(8)?
signal bramble
are you asking me or questioning the question
median dome
i am asking you
signal bramble
if ur asking me then ig you could do root 8 by root 2
median dome
what?
signal bramble
can u explain to me
median dome
$\sqrt{8} = \sqrt{4 * 2} = \sqrt{4} * \sqrt{2} = 2 * \sqrt{2}$
signal bramble
why is there a decimal in the roots
median dome
that is a multiplication sign
signal bramble
oh
warm shaleBOT
kheerii
signal bramble
better
warm shaleBOT
MathIsAlwaysRight
signal bramble
so root(8) = 2 root(2)
median dome
yes
median dome
can someone explain this to me
substitute root(8) = 2 root(2) into this equation
signal bramble
wont it just cancel it out then?
trim portal
is it division or +?
knotty thorn
addition
signal bramble
division
trim portal
wont it just cancel it out then?
Yes
knotty thorn
if the question was 5 root(2) + 4(root(2)
ignore this, then
trim portal
So what result did you get?
ruby pebble
obtuse pebbleBOT
ruby pebble
can someone explain this, I don't understand any of it 😦
how'd they go from the linear system to the matrix
royal basin
think about how matrix multiplication works.
the product of a matrix A by a vector x is a linear combination of the columns of A, with the entries of x acting as the coefficients in said linear combination.
ruby pebble
the product of a matrix A by a vector x is a linear combination of the columns o...
so am I trying to recreate the linear combinations (ie a-b=e1)?
with the matrix multiplication
royal basin
well yeah
ember venture
i dont
signal bramble
What does ASA mean again
knotty thorn
these are proofs for congruent (and 3 non-congruent) triangles
knotty thorn
thats what they mean and all
but how you use them is if two triangles have exactly the same relative side angle side (right next to eachother)
then they are congruent
knotty thorn
this is side angle side
it means if two triangles have two connecting sides of same length
and the angle is the same size, too
they are congruent
that is the rule you call SAS
knotty thorn
you'll have to look at each pair individually and determine if they follow a rule (put them under a rule) or do not follow any (non-congruent)
these two, you can see, are SAS
do you need the other rules explained?
knotty thorn
including the one i just explained?
ember venture
yes
knotty thorn
what part of my explanation did you not understand?
ember venture
all of it bruh
knotty thorn
do you understand what it means for two triangles to be congruent?
(to one another)
ember venture
just be the same
ember venture
yeah
knotty thorn
you can tell they are congruent without literally all of the information
through the rules above
lets start again with SAS
here we have two triangles where all we know are two sides and an angle
but specifically, the two equal sides join and form the same angle
inbetween them
SAS means side, angle inbetween, side
the order and position of the letters in SAS matters
knotty thorn
HL = Hypotonuse-Leg
let me draw more diagrams
If the hypotonuse and one other (relative) same side is equal
then two right angled triangles are congruent
ember venture
so would these two be under HL?
ember venture
woohoo!
knotty thorn
all you are given is 3 angles are equal to their relative angle
this is not a congruence theorem
AAA could be any 3 triangle with those angles
not one with the same sides, too
so you would put it in not congruent
ember venture
would that same thing apply for triangles where both are only given 2 sides and nothing else
like these
knotty thorn
there are other rules we havent said which some of those apply to
also not that you arent only gien two sides in two of those
these two lines will be equal on both
because they are the same line
these two will actually be congruent by the next rule
SSS = Side Side Side
if all 3 sides are the same, they are congruent
so these two pairs would both be congruent by SSS
knotty thorn
you will have to apply an angle theorem here
vertically opposite angles are equal
so really, you have this
ember venture
so that would be SAS
knotty thorn
Yes
knotty thorn
👍
ember venture
1qyujm
unreal musk
dark stirrup
close if you don't need this open, pls
ember venture
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
silver plover
obtuse pebbleBOT
silver plover
could i get some help with this please
warm canopy
do you think a big sphere has more or less drag force than a small sphere
silver plover
do you think a big sphere has more or less drag force than a small sphere
more
warm canopy
argue the same for the other two parameters and you're done
silver plover
ok
warm canopy
although they've given you dimensions for eta so i guess they expect you to do some dimensional analysis once you've figured out how it depends proportionally
silver plover
silver plover
argue the same for the other two parameters and you're done
is this suitable?
warm shaleBOT
ΣAC
warm canopy
and use dimensional analysis to solve for a,b,c
warm canopy
k might be tricky to solve for from scratch without doing an experiment
warm canopy
what you wrote in words is that F is directly proportional to all 3
silver plover
what you wrote in words is that F is directly proportional to all 3
yes realised
fickle turret
right so now you can actually set up an equation
$F = -6\pi\etarv$
warm shaleBOT
Kohlemaennchen
fickle turret
That's Stokes friction for low velocities
warm canopy
right my point is you'd need to do an experiment to actually find 6pi
warm canopy
you can yeet the k away because its dimensionless
silver plover
ok
warm canopy
and then just compare powers of M L T because theyre independent
silver plover
ok
silver plover
and then just compare powers of M L T because theyre independent
is a b c all 1?
warm canopy
they are indeed
fickle turret
is a b c all 1?
Only for low velocities you can assume this (like in this example). For higher velocities we need Newton friction, which depends quadraticly on v
fickle turret
Well done 👍
silver plover
Well done 👍
thank u for the help and EAC
obtuse pebbleBOT
@silver plover Has your question been resolved?
silver plover
.close
rigid fog
So what if it didn't specify y=0
Would the bounds be 0 to 1, or -1 to 1
because x=y^4 , $x=2-y^2$
warm shaleBOT
Meep
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
rigid fog
setting them equal to each other I got -1 and 1
obtuse pebbleBOT
Available help channel!
daring salmon
can someone help me with the expression part
obtuse pebbleBOT
can someone help me with the expression part
royal basin
do you know the definition of the derivative?
daring salmon
the formula?
royal basin
idk what you mean by "the formula".
maybe you could write it out, and i could tell you if you're thinking of the right thing or not.
daring salmon
f(x+h) - f(x)/h
tardy epoch
f(x+h) - f(x)/h
missing a limit and parentheses, but yea
royal basin
the limit part is written out in words
tardy epoch
oh yes
royal basin
also what you wrote reads as $f(x+h)-\frac{f(x)}{h}$ instead of the $\frac{f(x+h)-f(x)}{h}$ that it should be
tardy epoch
then just 
warm shaleBOT
Ann
royal basin
if this issue is fixed, though, then you have the correct expression.
warm shaleBOT
riemann
obtuse pebbleBOT
@daring salmon Has your question been resolved?
daring salmon
if this issue is fixed, though, then you have the correct expression.
it says f is not defined
variable f is not defined
royal basin
... well duh, you shouldn't just copy that as is...
you should actually evaluate f(x) and f(5)
daring salmon
i cannot use the letter f at all
wait
yeah no i dont get it
h is also not defined
<@&286206848099549185> can someone please help
i dont understand what expression it is asking for
blazing stump
i dont understand what expression it is asking for
You have to take the derivative then plug in x=5
I am on the public bus right now so can't write it out
daring salmon
wouldnt that be me just finding the limit
blazing stump
But the answer is 3/2 * 1/(4 + 3*5)^(1/2)
blazing stump
wouldnt that be me just finding the limit
Not exactly. To calculate from first principle you're doing the Lim as h goes to 0
daring salmon
so plug in 5 into the derivative?
blazing stump
It's not hard for this one the trick is you'll need to factor under the square root and the h out of there so that they cancel on top and bottom
blazing stump
so plug in 5 into the derivative?
Correct after you find the derivative from first principles.
(Sorry wish I could help more but it is crowded and I cannot type on my phone well)
daring salmon
it doesnt work
blazing stump
Ok you have to be careful. The question is not asking for f'(5). It is asking you for what value of x does it need to approach in the original expression sqrt(4 + 3x) so that it equals f'(5)
@daring salmon once you FIND f'(5) set that numerical value to sqrt(4 + 3x) then SOLVE for x.
This will be your limit that x needs to approach.
The question is badly worded. Don't blame yourself. 🙂
obtuse pebbleBOT
@daring salmon Has your question been resolved?
daring salmon
<@988866375810433055> once you FIND f'(5) set that numerical value to sqrt(4 + 3...
so plug in sqrt(4+3x) into the x value of the derivative?
hexed agate
Yeah plug in stuff
blazing stump
so plug in sqrt(4+3x) into the x value of the derivative?
Not quite.
First find derivative. Then plug in x=5 into derivative.
This gives you a number.
Take THAT number, set THAT number to be equal to sqrt(4+3x)
Then solve for x using that
The value you find for x will be the limit you need.
@daring salmon
obtuse pebbleBOT
@daring salmon Has your question been resolved?
warm shaleBOT
Тwin
ebon raven
Thx
sweet edge
yeah I figured the video would be better than me typing out a bunch of stuff
keep watching the video
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
placid linden
Can someone just check if this math is correct?
obtuse pebbleBOT
Can someone just check if this math is correct?
@placid linden Has your question been resolved?
obtuse pebbleBOT
@placid linden Has your question been resolved?
timid silo
obtuse pebbleBOT
nocturne minnow
Use the arc length formula
timid silo
Use the arc length formula
How do I do that?
next lantern
obtuse pebbleBOT
next lantern
could anyone show me where i went wrong
this should converge
it has to do with the first set of lns bc it converges to (15/2)ln3
so im not quite sure where
obtuse pebbleBOT
@next lantern Has your question been resolved?
slim leaf
@next lantern This is a telescoping series. Plug in some values of n to see a pattern of cancellation.
next lantern
so i wouldnt use partial fractions for this?
slim leaf
You would
slim leaf
Plug in values of n after partial fraction decomposition
next lantern
let me grab my ipad one second
next lantern
Plug in values of n after partial fraction decomposition
i can still factor out the 15/2 first correct
slim leaf
Yes
next lantern
ok
how does that look
actually i misscancelled the end there
that should be it i think
and i assume just take a limit?
however i dont think the answer is 45/4
nevermind it is
thank you (:
.close
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
tired sierra
would you guys say these are equivalent?
obtuse pebbleBOT
would you guys say these are equivalent?
plucky pond
y=(5(x+2)^2)-6
not at all. expand it out and youll see they are noot the same at all
next lantern
and y=(5x+2)^2-6
assuming youre going from this one to the one written above, pulling the 5 out from that bracket would also have to apply to the 2 inside the bracket, as well as go through that ^2 on its way out
tired sierra
hmm
so when a question like this shows, do I just put 5x+2 then?
so when does the 5(x+2) thing come around?
plucky pond
you are supposed to apply the 5 or 1/5 to the (x+2) not just the x
next lantern
^
tired sierra
well you didn't write it right but you still get your point across
next lantern
2am brain >_<
tired sierra
but how do I know whether its one or the latter?
tired sierra
both
like for this question I know its 5x+2
but how do I know if they would want 5(x+2)
next lantern
putting the 5 in those respective places are different
from what i can tell this question just wants a dilation of 1/5
aka compress it by a factor of 5
so putting that 5 inside changes the vertex of the function and does some other non-important things
tired sierra
ah
next lantern
but if we want to compress the whole function by 5
it just has to go infront
im not sure if there is a formal way i can define it to you
but any horizontal compression/dilation will go infront (:
tired sierra
is it a if you know, you know
next lantern
exactly
next lantern
im sure there is some way to prove/define it better
but that is a rule of thumb i guess you could say
next lantern
yup, playing around on desmos a bit could make understanding all of the transformations easier
tired sierra
alright, thank you
next lantern
no problem
tired sierra
.close
timid silo
$-\sqrt[4]{32k^5m^{12}}$
obtuse pebbleBOT
$-\sqrt[4]{32k^5m^{12}}$
timid silo
simplify
warm shaleBOT
okokok
warm shaleBOT
warm shaleBOT
timid silo
so 32^5/4
Where did the 5 come from
b
32 is raised to the power of 1, not 5
$\sqrt[4]{2 * 2 * 2 * 2 * 2 * k^5 * m^{12}}$
@fathom flicker
timid silo
<@456226577798135808>
4 isnt prime so prime factor that still
timid silo
4 isnt prime so prime factor that still
?
show me
Like what two numbers multiply to give you 4?
2
Okay
So rewrite the 4's to 2's
so 2 * 2 * 2 * 2 *2
Yes
warm shaleBOT
okokok
timid silo
Now do you see how four of those can be taken outside of the root?
timid silo
Now do you see how four of those can be taken outside of the root?
so just make it (2 * 2)^4
timid silo
Now do you see how four of those can be taken outside of the root?
so you can cancel out 4 of the 2's with the 4th root
so its jsut 2
timid silo
so its jsut 2
Yes
Sure
"Cancel"
So you pull out four of the 2's outside and one remains in
timid silo
So you pull out four of the 2's outside and one remains in
what does that look like
obtuse pebbleBOT
@timid silo Has your question been resolved?
teal horizon
my math aint mathing, tried this question like 4 or 5 times
9 - k = sqrt14 * sqrt(k+10) * 0.5
how do i solve for k
obtuse pebbleBOT
my math aint mathing, tried this question like 4 or 5 times
9 - k = sqrt14 * sqr...
teal horizon
i keep on getting to a polynomial, but each time i keep getting different numbers and i dont even know what
glossy basalt
my math aint mathing, tried this question like 4 or 5 times
9 - k = sqrt14 * sqr...
interesting, lemme try
teal horizon
i had mathway do it and it got the right answer
glossy basalt
$(9-k)^2=(\sqrt{14}\cdot\sqrt{k+10}\cdot0.5)^2$
warm shaleBOT
OldBiscuit
glossy basalt
i had mathway do it and it got the right answer
like that?
teal horizon
yeah
glossy basalt
you might wanna post your working so that we can check what is wrong with your previous attempts
teal horizon
if you want i can but i would rather just see the process and see where i went wrong
i have done this so many times
glossy basalt
$k²-18k+81=14\cdot(k+10)\cdot0.5^2$
warm shaleBOT
OldBiscuit
teal horizon
ok yep
drifting wraith
81 − 18k + k² = 14(k+10)/4
324 − 72k + 4k² = 14k + 140
4k² + 184 − 86k = 0
glossy basalt
$2k^2-36k+162=7k+70$
warm shaleBOT
OldBiscuit
teal horizon
what
glossy basalt
haha
drifting wraith
you get two solutions, and the larger one is fake
glossy basalt
i first multiply 14 by 0.5 one time
and then multiply the while thing by 2
the most difficult part of this question is probably the 0.5^2
glossy basalt
i first multiply 14 by 0.5 one time
and then multiply the while thing by 2
and to get rid of it, you can multiply the whole thing by 4, or just do what i did here
drifting wraith
the most difficult part is knowing that one of the solutions is fake
teal horizon
well its apart of a larger question so i can find out with one is fake
as 1/2 was originally cos 60
and so u can just substitute both values back in for cos (angle)
glossy basalt
and so u can just substitute both values back in for cos (angle)
yep
teal horizon
what answers did you get by the way?
glossy basalt
**OldBiscuit**
anyways all good till here?
teal horizon
yes
glossy basalt
oh
i haven't complete it, so probably Wolframalpha would do the work
,w 2k²-43k+92=0
warm shaleBOT
glossy basalt
i can explain that
onyx salmon
so you just multiplied everything by 2 to do what exactly
you see 0.5^2 is just annoying
glossy basalt
oh, okay Shon will be explaining😆
onyx salmon
sorry my bad pls continue
teal horizon
my answer is completely wrong
glossy basalt
$k²-18k+81=14\cdot(k+10)\cdot0.5^2$
$k²-18k+81=14\cdot(k+10)\cdot0.5\cdot0.5$
warm shaleBOT
OldBiscuit
glossy basalt
$k²-18k+81=(14\cdot0.5)\cdot(k+10)\cdot0.5$
warm shaleBOT
OldBiscuit
glossy basalt
**OldBiscuit**
and back to this
teal horizon
wait
ok so you are allowed to do that
that makes sense but it feels weird
to like turn it into two timeses then move on
ok anyone im up to speed now
glossy basalt
ok so you are allowed to do that
yea, it's just the definition of squared
teal horizon
anyway*
i dont know what i did wrong
i did it differently from you, but my answer is wrong
teal horizon
oh
glossy basalt
i think that's the only part that makes the whole thing falls down
i am not really good at handling decimals, so i would usually change them into fractions and then into whole numbers if possible
ah
btw
teal horizon
i still was wrong
glossy basalt
$\frac{-b\pm\sqrt{b^2-4ac}}{2a}$
warm shaleBOT
OldBiscuit
teal horizon
when i sub it back in i do not get 60 degrees
glossy basalt
and not $-b\pm\frac{\sqrt{b^2-4ac}}{2a}$
glossy basalt
yea
warm shaleBOT
OldBiscuit
teal horizon
wait a second
glossy basalt
yea?
teal horizon
bruh
im
nvm
anyway thanks for your help
i made a mistake all the way at the start
glossy basalt
have a nice day
ruby path
Suppose there exists an infinite rail line with infinite stations, and if a train stops at one station it must stop at the next one. Prove that the train stops at all stations.
obtuse pebbleBOT
Suppose there exists an infinite rail line with infinite stations, and if a trai...
ruby path
I think this is some induction stuff, but I've never done this before so no idea how I'd word it
Also if there were infinite stations, is it safe to assume that the train starts at 0 on the number line and makes it way and stops at every integer?
Because if the train started at a different number then it wouldn't stop at every station
drowsy burrow
Well it screams imduction cuz of tran stopping at every following station
ruby path
I think this is some induction stuff, but I've never done this before so no idea...
Yup I got that
But uh formally
gleaming ridge
I am assuming that this is countable infinite cause unaccountably infinite stations makes no sense
drowsy burrow
Yep, theres a first station where train stops
gleaming ridge
if yes then this screams mathematical induction
frigid prism
creams??
frigid prism
for someone who has never done induction why would this be true
thorn kernel
But uh formally
Just follow the induction steps, if there is one stop then it stops at every station, that's the base
ruby path
And if the train stops at s_n then it stops at s_n + 1
ruby path
Just follow the induction steps, if there is one stop then it stops at every sta...
Yeah the dominoes thing
gleaming ridge
assume that the starting point of the train is 0 and each subsequent stations are at natural numbers
drowsy burrow
Well, it stops at first station, and if it stops for one then it has to stop for next one
thorn kernel
Then let's assume when are on station k , we have to prove it also stops at k+1
ruby path
assume that the starting point of the train is 0 and each subsequent stations ar...
Yup was going for that
thorn kernel
But that is self evident
ruby path
But that is self evident
Yeah
thorn kernel
So by induction it stops at every station
ruby path
Do I just say "by induction" 
thorn kernel
Yup
thorn kernel
Because you proved if it stops at station k it also stops at station k+1
gleaming ridge
This question only even makes sense if the instructor wants you to practise induction a bit more abstractly
sonic anchor
yes they're kind saying 'if you can prove this by induction why is it true'
gleaming ridge
otherwise it's pretty trivial
sonic anchor
well becuase you can prove it by induction lol
sonic anchor
tbf is it stated that the train does stop at any point?
thorn kernel
"The proof is trivial"
It is not trivial, it is proved by induction
You followed the induction logic
ruby path
:/ alright then I'll just write out some statements and show it's true
sonic anchor
it wouldnt be true then. induction needs a base case
ruby path
But we need to make a core assumption that the train does indeed stop at s_1
thorn kernel
it wouldnt be true then. induction needs a base case
We proved it for 1
thorn kernel
But we need to make a core assumption that the train does indeed stop at s_1
What you need to prove is that it stops at every station
gleaming ridge
yeah the point is that IF it stops at some station then it must stop at all stations if it doesn't then there's nothing to prove
ruby path
What you need to prove is that it stops at every station
Well there's nothing to prove since it's stated
thorn kernel
If there is 1 station then you prove the base case
sonic anchor
i guess you just assume that it has to start somewhere
which would techincally be it 'stopping'
ruby path
Yeah
ruby path
yeah the point is that IF it stops at some station then it must stop at all stat...
So it's not necessary that the train would have to stop at 1
sonic anchor
like its not already in motion. its at a standstill from the beginning
ruby path
It could stop at 2 and then stop at everything after 2
thorn kernel
Well there's nothing to prove since it's stated
It isn't, if it is then no need to prove anything lol
ruby path
-_- atleast give us a proper induction problem lmao
It's one of em "no fucking shit" ones
gleaming ridge
yeah, that's what is bugging me a bit like say it stops at some station that doesn't imply that it stopped at stations before it
ruby path
But in the limit wouldn't it stop at everything or am I wrong
frigid prism
It would
sonic anchor
i think the tricky part is the base case
gleaming ridge
Like with induction if the base case starts at k then everything would be true from k and onwards
not before
sonic anchor
but i think what you have to do is just consider when the train first starts moving
it has technically started at a stop point
because its not moving yet
ruby path
The number of stations would be countably infinite right
thorn kernel
The number of stations would be countably infinite right
You are over complicating it...
ruby path
sonic anchor
i think thats resonable
ruby path
Because if the stations were uncountably infinite wouldn't we have to model it over the set of real numbers and not naturals and then there's no way it could stop at all stations
gleaming ridge
well I googled the question and it seems like you missed a key sentence that, "it stops at the first station"
thorn kernel
Because if the stations were uncountably infinite wouldn't we have to model it o...
By the logic of the question then yes, there is no meaning for half a station
sonic anchor
well I googled the question and it seems like you missed a key sentence that, "i...
ok ye that makes it a lot easier lol
ruby path
well I googled the question and it seems like you missed a key sentence that, "i...
Wait give me a second
sonic anchor
i still think it works though doesnt it?
gleaming ridge
nah, without this it wouldn't work
sonic anchor
like lets say for the base case: there exists some n such that the train is not moving (becuase its assumed to be moving). then construct the rail line from there
thorn kernel
Because if the stations were uncountably infinite wouldn't we have to model it o...
But for induction it doesn't matter since k and k+1 are not defined and can be any number
ruby path
Yeah you're right
ruby path
But for induction it doesn't matter since k and k+1 are not defined and can be a...
I see
gleaming ridge
lmaoo
sonic anchor
💀
ruby path
I always do this when I enter help channels 💀
thorn kernel
Yeah you're right
If you trace all my comments you have the full proof
ruby path
If you trace all my comments you have the full proof
Yup I'll go by what you said
Thanks everyone, and sorry for the mishap
gleaming ridge
I always do this when I enter help channels 💀
happens with the best of us
ruby path
.close
wicked current
can somebody explain please ?
obtuse pebbleBOT
can somebody explain please ?
wicked current
i thought if we put 1 - - - 5 we have 3 spaces left and 3 numbers so 3 x 2 x 1 ??
thorn kernel
i thought if we put 1 - - - 5 we have 3 spaces left and 3 numbers so 3 x 2 x 1 ?...
You are getting the question wrong, at the last position you only have 2 options 1 or 5 .
wicked current
sorry my bad
thorn kernel
First one doesn't have to be 1
wicked current
yes its last number 1 or 5 not 1 at start and 5 at last
obtuse pebbleBOT
wicked current
.reopen
obtuse pebbleBOT
✅
thorn kernel
What about it?
thorn kernel
Why do the options go down?
wicked current
5!
because at first i have 5 letter to put at first position, then 4 letter then 3 letter for third postion
thorn kernel
But you can repeat the letters
thorn kernel
because at first i have 5 letter to put at first position, then 4 letter then 3 ...
This is right thinking, but why do you go down to 4 letters then 3?
wicked current
we have 5 options for all places
thorn kernel
Yup
uneven night
Determine the mapping matrix A for the linear mapping corresponding to an oblique projection on the xy-plane along the (1,1,1) direction. Is the image surjective? Enter the null space of A.
obtuse pebbleBOT
Determine the mapping matrix A for the linear mapping corresponding to an obliqu...
@uneven night Has your question been resolved?
uneven night
.close
tepid birch
For what values of m does the system have a non trivial solution, i am struggling to do Gaussian elemination here, im not sure if that's how i proceed, this is the first provlem ive seen with m+1 as a number
obtuse pebbleBOT
For what values of m does the system have a non trivial solution, i am strugglin...
tepid birch
Picture if you don't understand my handwriting, its from a mock exam
neon eagle
just do what you normally do
obtuse pebbleBOT
@tepid birch Has your question been resolved?
tepid birch
I can't figure out the steps here, do i do gaussian elemination or through determinants
neon eagle
have you tried to gaussian eliminate
you could compute the determinant
they probably both work
tepid birch
Via determinant i get a quadratic equation, of m1 and m2
I cant seem to figure out gaussian elemination
Figured it out
.close
valid yarrow
obtuse pebbleBOT
neon eagle
where are you stuck
worldly trench
what is the minimum size of rsa bits required for security?
obtuse pebbleBOT
what is the minimum size of rsa bits required for security?
worldly trench
Is it RSA 512? 1024? or 2048?
obtuse pebbleBOT
@worldly trench Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
quartz mortar
I’m confused with this question
obtuse pebbleBOT
I’m confused with this question
gleaming ridge
power is VI right?
tawny fog
p=VI yes
tawny fog
P=v²/r btw
tawny fog
Yes
trail cloak
@quartz mortar
quartz mortar
quartz mortar
tawny fog
p=(6.8)²(7.5)
quartz mortar
Ohhh ok
quartz mortar
Do I use P= V^2/R?
obtuse pebbleBOT
Do I use P= V^2/R?
quartz mortar
I want to make sure it’s right before I submit
velvet cypress
use V = IR
velvet cypress
yes
obtuse pebbleBOT
@quartz mortar Has your question been resolved?
spark field
would this be correct
obtuse pebbleBOT
would this be correct
spark field
so MPG was converted to L/100km
11.7607
For part a
then for part b
I add up all factors where gas is consumped which would be y
in liters
I then divide distance by 100 and multiply by by 11.7607 = x
y = liters consumed * 100/distance
then total = y+x
is this correct?
rich plume
Your question seems unclear
spark field
Your question seems unclear
I want to know if this is the correct
to calculate gas mileage
rich plume
Please organise the given information
spark field
Okay
For the fuel economy of the car I convert the MPG into L/100km and that number is 11.7607
rich plume
The mpg is 11.7607?
spark field
Now there are certain factors like brake pads, tire conditions etc.. that affect the gas consumed and I add up all of them in liters and multiply by 100/ distance to get L/100km
spark field
The mpg is 11.7607?
no L/100Km is 11.7607
spark field
I then Divide distance by 100 and multiply it by 11.7607
Then I add both these factors
to get the gas mileage
is that correct
rich plume
Is there a question picture i can get?
spark field
Is there a question picture i can get?
rich plume
Now there are certain factors like brake pads, tire conditions etc.. that affect...
It seems you should multiply the total factors by distance/100
spark field
It seems you should multiply the total factors by distance/100
wdym
rich plume
See
I am not sure but as I have interpreted the question
You have L/100 which is around 11
You have some factors that affect fuel usage
spark field
yes
rich plume
Total fuel usage increase will be just distance×extra fuel usage(by those factors)
spark field
but isnt what i did correct?
rich plume
I don't think so
Let's solve with an example
Let L/100 be 100
Those factors increase fuel usage by suppose 10L/km
spark field
Those factors increase fuel usage by suppose 10L/km
well i didnt conver it into that
rich plume
Wait
spark field
Let L/100 be 100
I took this and multiplied by distance/100
For the factors
I did GasTw0 = (totalliterconsumption* 100) / distance
then added up all factors
spark field
Let L/100 be 100
GasTwo +100 = totalgas /100km
rich plume
Let me get on pen and paper
rich plume
then total = y+x
Here you mean total gas consumed is x+y?
spark field
Here you mean total gas consumed is x+y?
yes
rich plume
I took this and multiplied by distance/100
That is wrong
spark field
That is wrong
how so?
rich plume
You don't get anything by multiplying that
spark field
distance /100 * the L/100 Km
rich plume
Sorry I can not understand your question properly
I apologize for wasting your time
You may seek to other helpers
obtuse pebbleBOT
@spark field Has your question been resolved?
obtuse pebbleBOT
obtuse pebbleBOT
Available help channel!
slender nebula
gotta integrate this with respect to dx
