When you move 15cm in the direction of the field, where are you going?
#help-0
placid zinc
storm oar
wdym?
tbh i don't think the direction matters
a lot of the questions have added words that are just there for confusion honestly
it's been annoying deciphering so much
lone heartBOT
@storm oar Has your question been resolved?
solid plover
tbh i don't think the direction matters
I think direction matters it tells you if energy is lost or gained.....
solid plover
I dont even remember the formula anymore, been 3 years since I last practised physics
solid plover
but tbh direction is too important in physics
F = E/Q, find the force applied by electrical field
ooh sorry find the charge with the help of F = E/Q
my bad formula is F = EQ
storm oar
i have the charge, i did that in the first part. it's (hopefully) 2.5*10^-4
solid plover
probably yes
find the potential difference at both points x (let) & x -15
& then subtract both of them, u'll get the change in potential difference
formula for potential at a point is KQ/r
storm oar
what value would i use for r though?
solid plover
put x for one & x-15 for the other
dont think it would matter, x can be anything
not sure abt it tho
but u have to keep it in mind that u r finding potential difference caused by field
the formula that I think u should use is V = E.r
storm oar
i can't find a formula that's v = er
i have the 2 values tho
V = 2247500/x and V = 2247500/x-15
solid plover
that'd be used if u had to find potential difference caused by sphere but u have to find the one caused by electric field
its given that we have to find potential diff. on the sphere, so basically potential difference caused by sphere on itself would be 0 ig bc r = 0 for that
storm oar
i think i'm just gonna leave the question tbh lol
it's only worth like, maybe 2 marks
thanks for ur help though, sorry
solid plover
I dont its worth that less, its a bit lengthy so i think its worth at least 4 marks
just saying
storm oar
it's out of 100 marks dw
i think i have everything else right anyway
so should still be like, 95%
solid plover
& u can take help of doubtnut if u need its a good platform
solid plover
so should still be like, 95%
lol yeah
storm oar
& u can take help of doubtnut if u need its a good platform
ooo the site looks cool lol
solid plover
let me know if u need help
storm oar
will do
solid plover
k
crimson compass
1+1 = ?
tacit arch
lone heartBOT
crimson compass
so good๏ผhow can you think about it?
stuck cape
<@&268886789983436800> underaged user
crimson compass
please tell me how you think
ornate condor
,w addition table
ocean sealBOT
crimson compass
haha~
molten pivot
Cool pattern
ornate condor
ikr
molten pivot
Now I want to see about taking a random walk of length n on an infinite addition table and finding the expected value
๐ถโโ๏ธ ๐ถโโ๏ธ
stuck cape
@crimson compass https://qr.ae/prrwfv
lone heartBOT
Available help channel!
crimson compass
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lucid stirrup
I am very bad at math, I just need an answer on this for a project I'm working on. Can anyone help?
So each token has 50 requests every 60 seconds & then I have a list of 100 gamertags that I need to be covering at at least 5 requests per second each so I will be doing 500 requests a second. How many tokens will I need?
stuck cape
@lucid stirrup .close to close this channel
lucid stirrup
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lone heartBOT
kindred anchor
<@1052423966758797473> https://qr.ae/prrwfv
There is also a proof for around 800 pages 
stuck cape
๐
lone heartBOT
Available help channel!
cedar field
How do I do this?
lone heartBOT
How do I do this?
austere frigate
try drawing it out
cedar field
try drawing it out
i did
austere frigate
can i see
cedar field
sure
vale wigeon
The length of the ladder is 4 meters longer than the distance from the base of the ladder to the wall.
cedar field
> The length of the ladder is 4 meters longer than the distance from the base of...
yes
vale wigeon
yeah, you'll need to take this into account.
vale wigeon
oh, right. there was quite a bit of space between it and the diagram
but ok, yeah, sure.
there's another equation you can write down
vale wigeon
bad notation.
i'm talking about the pythagorean theorem, yes. but in your case, the notation is different.
cedar field
i'm talking about the pythagorean theorem, yes. but in your case, the notation i...
oh what is it?
cedar field
yes
vale wigeon
with the letters h and a that you've already used for the hypotenuse (ladder) and adjacent (base-to-wall) sides
ok, so can you write down the pythagorean theorem as applied to this triangle?
cedar field
ok, so can you write down the pythagorean theorem as applied to this triangle?
Idk what it is in this instance
vale wigeon
when you talk about a, b and c in a^2 + b^2 = c^2, which letter stands for what?
cedar field
when you talk about a, b and c in `a^2 + b^2 = c^2`, which letter stands for wha...
a=adj, b=opp, c=hyp
cedar field
yes
vale wigeon
are you now able to apply the same thing to your problem?
surely you can identify which sides in your triangle are the legs and which is the hypotenuse (in fact you have already done so)
cedar field
are you now able to apply the same thing to your problem?
yes
vale wigeon
ok, so can you now
write down the pythagorean theorem as applied to this triangle?
cedar field
well, a^2+b^2=12^2
vale wigeon
no
vale wigeon
you don't have any b in your problem
your letters are a and h
also, answer me this: is 12 the hypotenuse of your triangle?
cedar field
noooo
vale wigeon
then why put it on the right hand side?
cedar field
yeah.
vale wigeon
h = a + 4
h^2 = a^2 + 144
are you able to solve this system of equations?
cedar field
h = a + 4
h^2 = a^2 + 144
are you able to solve this system of equations?
solve for what?
I gtg soon so I need to speed up
vale wigeon
well, you're primarily interested in h. but solving a system means finding values for all its variables
cedar field
oh no...
cedar field
well, you're primarily interested in _h_. but solving a system means finding val...
ok
h^2=144+a^2
and...
austere frigate
the idea is to get everything into one variable to solve for that variable
cedar field
-a^2=144-h^2
austere frigate
earlier, you already wrote down h in terms of a right
cedar field
the idea is to get everything into one variable to solve for that variable
yeah im just rushing I gtg really soon
vale wigeon
do you need this done urgently?
if not, come back to it later when you have more time.
cedar field
if not, come back to it later when you have more time.
how much longer do you think we will be?
cedar field
i will keep going a little longer
vale wigeon
well, in either case, don't rush.
if you don't see a way to proceed, i can give you a suggestion.
cedar field
if you don't see a way to proceed, i can give you a suggestion.
what would that be?
vale wigeon
substitute h = a+4 into the second equation
this way you will get (a+4)^2 = a^2 + 144
this equation is an equation in a only, and you can solve it for a, from which you can get h easily
cedar field
this equation is an equation in _a_ only, and you can solve it for _a_, from whi...
Does a=16?
cedar field
It was a bit of a guess ๐
vale wigeon
don't guess.
vale wigeon
ok
cedar field
.close
lone heartBOT
vale wigeon
you can ping me later for follow-up, i guess.
cedar field
you can ping me later for follow-up, i guess.
ok
cedar field
you can ping me later for follow-up, i guess.
it may be like in 12 hours lol
I'm out for a while
c ya
lone heartBOT
Available help channel!
swift sky
lone heartBOT
swift sky
So I have already done a and I am struggling with
Btw the second pic is from the answer sheet
What does the question even say?
vale wigeon
"T maps v1 to v3" means T(v1) = v3. do you understand this?
vale wigeon
no, they are working with the basis B
v_3 = 0v_1 + 0v_2 + 1v_3
What does the question even say?
i was under the impression that something about the wording of the question confused you. is that the case?
swift sky
I think so
vale wigeon
"I think so" = "I am unable to identify the source of my own confusion"?
swift sky
Yeah cuz at first I thought I misunderstood the question but even after looking at the answer sheet I was confused I guess
$v_3 = 0v_1 + 0v_2 + 1v_3$ how come
ocean sealBOT
afeAlway
vale wigeon
ok, how about i break down the statement of the question into pieces and you tell me which point, if any, confuses you?
swift sky
Alright
vale wigeon
[1] Let T : R^3 -> R^3
[2] be the linear transformation
[3] that maps v_1 to v_3 ...
[4] ... and v_3 to v_1,
[5] and for which v_2 is an eigenvector ...
[6] ... corresponding to the eigenvalue lambda = -5.
[7] Find the coordinate matrix [T]_B
[8] that describes the map T with respect to the basis B.
tell me the earliest line in this that confuses you, or if there is none, tell me that the statement of the question is clear
swift sky
So line 4, I just dont understand that statement
vale wigeon
you understand line 3 but not line 4?
swift sky
I mean both
vale wigeon
tell me the earliest line in this that confuses you
but ok, so line 3 is lost on you, is that it?
swift sky
3
vale wigeon
"T maps v1 to v3" means T(v1) = v3.
swift sky
Yes
swift sky
I mean I understand that, T(v3) = v1 but how did they get the answer [0, 0, 1] when they don't have the transformation matrix
vale wigeon
i will be a little obstinate here
we are currently addressing your confusions regarding the question statement itself
not how it was solved
we will get to the answer key solution later
swift sky
Yeah that is why I said I was not sure what I found confusing. I feel like I understand the question but since I don't even know where to begin I constantly go back to the question to check if I am missing something. Now after seeing your points clearly I haven't misunderstood the question and I am just struggling.
vale wigeon
okay
alright so let's forget about this problem for a moment
are you familiar with vectors in the pre-linear-algebraic sense? particularly, R^3 and its basis {i, j, k}?
swift sky
Yes
swift sky
001
vale wigeon
bad
(0, 0, 1)
if you just concatenate the coordinates like you just did, you will be unable to tell the difference between (42, 0, 69), (4, 20, 69) and (4, 206, 9).
not to mention when negative numbers end up involved...
anyway
(0, 0, 1) = 0i + 0j + 1k = k
do you agree or disagree with this?
swift sky
True but I feel like you'd know in this case
vale wigeon
True but I feel like you'd know in this case
bad notation is still bad notation.
swift sky
Noted
swift sky
(0, 0, 1) = 0i + 0j + 1k = k
Nope
swift sky
You asked If I disagreed
vale wigeon
i asked "do you agree or disagree"
swift sky
I AGREE
vale wigeon
ok
i was confused by your response a bit
ok
do you see how, in the same token, when we write the coordinates of v3 in the basis {v1, v2, v3}, we get (0,0,1) as well?
0v_1 + 0v_2 + 1v_3 = v_3
swift sky
But isn't (0, 0, 1) from the standard base, and also from question a) I got that v_3 =sqrt 2 / 36 [1, -4, -1]
Aren't we supposed to work in basis B
vale wigeon
but we ARE working in basis B.
i am trying to tell you that.
i am deliberately ignoring the value of v3 in the standard basis, because it is in fact irrelevant
swift sky
0v_1 + 0v_2 + 1v_3 = v_3
What are the vectors v_1, v_2, v_3? Are they the vectors given in the question?
vale wigeon
yes, as they always have been.
i am not using their names in any different sense than the problem does.
swift sky
i am deliberately ignoring the value of v3 in the standard basis, because it is ...
Isn't that what you are doing when you use (0, 0, 1)?
vale wigeon
...come again?
ebon field
mhm
vale wigeon
no, sorry, i don't understand your question.
let's start over
what you are saying is that you are failing to understand why $[v_3]_{\mathcal{B}} = \bmqty{0 \ 0 \ 1}$. is that correct?
ocean sealBOT
Ann
vale wigeon
@swift sky
vale wigeon
do you agree that, by definition of the coordinate vector, $$[c_1 v_1 + c_2 v_2 + c_3 v_3]_{\mathcal{B}} = \bmqty{c_1 \ c_2 \ c_3}?$$
ocean sealBOT
Ann
swift sky
That is what I find confusing tbh. [c1, c2, c3] is the coordinates in basis B
vale wigeon
yes, exactly.
swift sky
Or you explain it instead
vale wigeon
and what it MEANS for a vector to have coordinates [c1, c2, c3] in basis B is that this vector equals c1v1 + c2v2 + c3v3.
swift sky
c1v1 + c2v2 + c3v3 is in standard base right?
swift sky
That is what I find confusing tbh. [c1, c2, c3] is the coordinates in basis B
given this, what is $ [v1, v2, v3]^T$ then?
swift sky
and what it MEANS for a vector to have coordinates [c1, c2, c3] in basis B is th...
But they are something tho, they are the vectors given in the question.
So If I understand it correctly c1, c2 amd c3 in c1v1+c2v2+c3v3 gives me how many steps I take in each vector v_i where i = 1,2,3 so c1, c2 and c3 can just be refered to the vectors coordinates in basis B. Am I correct or totally lost?
vale wigeon
... you're in that kind-of-correct-but-poorly-worded territory.
i am afraid i'm currently running low on energy and will not be able to correct you.
swift sky
Okay so even I still don't completely understand why (c1, c2, c3) = (0, 0, 1) but what is [v1, v2, v3]^T equal to then?
swift sky
i am afraid i'm currently running low on energy and will not be able to correct ...
Thank you so much for putting up with me this long anyways tho
lone heartBOT
@swift sky Has your question been resolved?
swift sky
Still need help if anyone can help?
lone heartBOT
@swift sky Has your question been resolved?
lone heartBOT
@swift sky Has your question been resolved?
lone heartBOT
@swift sky Has your question been resolved?
gentle jackal
@swift sky you can try continuing in #linear-algebra
slim swan
How could I calculate a cartesian equation for a plane that has an intersection point of 3 other planes, x+y+z = 1, x+2y+z=1 and x+4y+2z=1 and goes through the points (1,1,0) and (0,1,1)?
slim swan
I dont get what strategy I should use
lethal berry
Hoola hooch
lone heartBOT
Hoola hooch
lethal berry
Well do u still want it ?
Next time just put some random word to mark this channel as urs ig
.close
lone heartBOT
spiral lily
xd
lethal berry
I will use another channel
lone heartBOT
Available help channel!
naive silo
claimed
naive silo
NonH 2nd ODE so there will be a yc and yp
for i) would the general eq be x''+2x'+5x=5y? if so does the step of 20 become a boundary condition?
manic jasper
naive silo
That was probably abit of word soup..
I'm looking at some practice Qs for an exam I have at the end of Jan. I don't quite understand how I'm meant to start to solve this...
I'm aware that it is a non homogenous 2nd ODE and the steps that requires to complete.
for part i) i have used the given values and used the equation to give x''+2x'+5x=5y as my initial equation
solving the yc i get e^-t(c1cos2t+c2sin2t)
roots are complex -1 (+/-) 2i
lone heartBOT
@naive silo Has your question been resolved?
naive silo
.close
alpine sable
we have X = {2, 3, 6} and the relation ฯ that is defined as: x ฯ y=x | y (x can divide y)
how do we check if the statement on the image (lets assign a variable p to it) is correct?
lone heartBOT
we have X = {2, 3, 6} and the relation ฯ that is defined as: x ฯ y=x | y (x can...
alpine sable
can't send any pics at the moment because my phone is dead, but here's what I did:
- I checked for all cases where x=y and p is correct
- I checked all cases where x cannot divide y and p is correct
- I checked for all cases where x can divide y and p is correct
However, I'm not confident enough to be sure that I proved that p is always correct
ruby current
you only have to check cases where the antecedent of the implication is true
this is because the implication is automatically true in all other cases
alpine sable
you only have to check cases where the antecedent of the implication is true
so, where x can divide y and where x!=y basically
ruby current
yes
so assume that, and see whether the consequent is always true
you only have a few possibilities to check
alpine sable
so, where x can divide y and where x!=y basically
consequent is always true tho right?
because when x|y is true, y|x is never true
and with the negation, its always true
also because x!=y
ruby current
because when x|y is true, y|x is never true
only if x and y are distinct
but you luckily already have that
ruby current
so you're done
alpine sable
We have a groupoid (A, โฆ) with a neutral e, how do we prove that any neutral e is unique?
lone heartBOT
We have a groupoid (A, โฆ) with a neutral e, how do we prove that any neutral e ...
mortal trellis
take two neutral elements e and f
e = (something) = f
for the equality signs use that e and f are neutral
ornate condor
suppose e and f are identity elements with e != f
mortal trellis
no need to do a proof by contradiction here
ornate condor
hm
ornate condor
e = (something) = f
how wld u do this something bit tho
mortal trellis
well I didn't wanna completely spoonfeed it
it's literally only one step
there is not that much that you can even do
alpine sable
what about this:
a * e1=a
a* e2=a
ae1=ae2 (probably won't work in all cases, since a!=0 has to be true)
ornate condor
eaa^-1 = faa^-1
thus e = f, contradiction
mine feels scuffed
yea i guess then * a^-1 in front
mortal trellis
dont take any other element in A
you only have to replace the (something) I wrote down with two letters
ornate condor
OH
i was wondering if u can do that
but i thought like unless the grp is abelian u cant just throw it on the right or left randomly
but for the identity it doesnt matter ig
alpine sable
but for the identity it doesnt matter ig
it doesn't, because the condition for identity is that it's valid on both sides e * a=a * e=a
alpine sable
btw english is not my native language so i called identity "neutral" :p
mortal trellis
neutral element is also pretty standard in english
alpine sable
.close
alpine sable
if (A, โฆ) is a monoid with the identity e, how do we prove that every element a from A has only one inverse element?
lone heartBOT
if (A, โฆ) is a monoid with the identity e, how do we prove that every element a...
alpine sable
when we look for an inverse, we're basically solving this equation: a * x = e
but how do we know for sure that there is only one solution to that equation?
the operation here was ,
but if we have an operation โฆ that could be like this: x โฆ y = x1/|y| then we have
a*1/|x|=1 (let's say that the identity is one in this case),
inverse can be -1 and 1 here
lone heartBOT
@alpine sable Has your question been resolved?
ruby current
if (A, โฆ) is a monoid with the identity e, how do we prove that every element a...
in a monoid? inverses aren't required in a monoid
am i understanding your question correctly?
oak quiver
faint tusk
Three divided by how many three times to get 0,1?
lone heartBOT
Three divided by how many three times to get 0,1?
limpid spade
3/x=0.1
faint tusk
I did.
faint tusk
3/x/x/x=0,1
low quartz
ohh
limpid spade
3/x/x/x=0,1
???
low quartz
that will be like
ruby current
3/x^3 = 0.1
low quartz
3x/x^2
limpid spade
too many trees
faint tusk
Mmm... Let Me see.
low quartz
3/x=0.1
limpid spade
tree(3)
minor needle
but it's still 3/x
faint tusk
So how do I calculate x?
minor needle
so it does nothing
minor needle
So how do I calculate x?
solve what they've suggested
faint tusk
What?
limpid spade
but it's still 3/x
solve for x
minor needle
ah it's badly formulated
then
it should be 3/x^3 = 0.1
it works
then x = cbrt(30)
faint tusk
So x^3 is 3/0,1? Could be?
minor needle
yes it's equivalent form
faint tusk
then x = cbrt(30)
Aha! Yeah, that seems logical. Must work!
Thank you, and everybody! This is the value of x.
.close
rigid mesa
hi - i have the following problem
lone heartBOT
hi - i have the following problem
limpid spade
is the shape of the room given?
plain flame
it could be as long as you want it to be
there is no bound
unless you restrict the shape
rigid mesa
okay say i restrict it to a square
rigid mesa
50
boreal verge
what is the average largest possible distance in that room?
define distance
between 2 points in the enclosed shape?
or a point and a side
rigid mesa
i am restricting the maximum distance between the sides to be 1m
so from side - side
cant be more that 1 m
now with that restriction
how can i find
the largest distance
in all possible cases
boreal verge
again the distance from what to what
plain flame
square of sidelength 1?
boreal verge
and the shortest can be 0
rigid mesa
no, no
i mean
| <this distance cannot be less than 1m> |
| |
| |```so the distance between 2 sides
like literally in between them
boreal verge
and you want to find the avarage distance of 2 points in that shape?
rigid mesa
cannot be less than a meter
boreal verge
any 2 points
rigid mesa
average 2 most distant points
so on average how much will be the largest possible distance
boreal verge
well if the distance between the 2 sides is exactly one, that means the other sides must be 50, so by pythagoras it would be sqrt(2501)
minimum
maximum would be the opposite case
rigid mesa
actually yes- essentially what i mean is that there cannot be a side less than 1 meter
boreal verge
exept you can go to infinity on the other side
boreal verge
actually yes- essentially what i mean is that there cannot be a side less than 1...
oh
well both are sqrt(2501)
so the avarage is that
boreal verge
well since you know the area of the shape is 50 that means the area of a triangle composed from 2 sides and a diagonal is half that, aka 25
now the area of the whole thing can be expressed by s1 * s2
and since its 50 always
that means c1 * c2 is constant
and equal to 50
so by a theorem in the right triangle idk the name of you can compute that the distance from a vertex to the diagonal is going to be 50/hypothenuse
now the area can be computed in 2 ways
(50/hypothenuse * hypothenuse)/2 = 25
which is true
rigid mesa
i understand what you're saying but
boreal verge
now take the case where the hypothenuse is going to be the smallest
when s1 and s2 are equal
rigid mesa
that hypothenuse is going to change
boreal verge
yeah
but if you just do the smallest and largest case
and do a mean
its your avarage
when s1 = s2 that means they are both 5 m
so hypothenuse is going to be 5sqrt(2)
now do a mean
boreal verge
thats what i did
oh right
sorry i messed up
if its 5sqrt 2 that means diagonal is 10
so its approximately 30
the avarage
rigid mesa
is 30
boreal verge
30.0045
rigid mesa
alright do you have the nerves to take it one step further?
rigid mesa
oh
well
thank you then
helped me a lot
i didnt know i could do that without higher level math like calc
.close
buoyant linden
how does helicobacter pylori cause stomach cancer?
lone heartBOT
how does helicobacter pylori cause stomach cancer?
left mesa
?
buoyant linden
need to describe process
worn fox
wanton pebble
ayo wrong server
desert tendon
Lol
buoyant linden
.close
glass tree
My solution: ||instead of moving laterally and vertically, rotate the whole problem so that you can only move in fur ways: {(1,1),(-1,1),(1,-1),(-1,-1)}, and now you need the total of at least one of the coordinates to be 0. Add 1 to each coordinate and divide by two to instead set the problem to {(1,1),(0,1),(1,0),(0,0)} with a requirement of 3. For this to happen, there must be exact 3 positive moves on one of the coordinates. Now, imagine it as two separate lists of six binary bits. There are nCr(6,3) ways to order one list to have 3 positive bits. In each of these cases, there are 2^6 ways for the other list to be. This comes to a total of 2^7 * nCr(6,3) possible sets of lists. The cases where both lists have 3 positive bits are double-counted. There are (nCr(6,3))^2 possible cases for this. The total number of possible cases is simply 2^12. (2^7 * nCr(6,3) - (nCr(6,3))^2)/(2^12)=155/256, and 155+256=411.|| Where is my mistake?
prime badge
i don't get the dividing by two part
glass tree
It was just so that my list of possible moves becomes {(1,1),(0,1),(1,0),(0,0)} and not {(2,2),(0,2),(2,0),(0,0)}. Not reallt required but it just makes it look nicer
prime badge
that's your solution, it's 4720
oh, my bad
right
basically you made a typo at some point?
tribal oxide
My solution: ||instead of moving laterally and vertically, rotate the whole prob...
Is the answer 263 by any chance?
Oh wait mb
135*
glass tree
basically you made a typo at some point?
Yes. That's exactly what happened. On the test I'm studying for you're not allowed calculators.
.close
old sinew
lone heartBOT
old sinew
I'm so not sure how this is going to be helpful
wary stream
Not suggest to use chatgpt to do math tasks
keen mason
chat gppt rarley gets the answer right
but it does really good like foundation work
especially for programming
old sinew
The way chatgpt tries to convince what they say is true is mind blowing
keen mason
^^
old sinew
maybe that's what they are trying to achieve
keen mason
all u have to do is correct them and they say 'Sorry i apologize'
old sinew
seamless conversations
old sinew
all u have to do is correct them and they say 'Sorry i apologize'
I lost my faith in it.
but actually gives out strong answers to conceptual questions in math
limpid spade
they cant do computational questions only theoretical
keen mason
they can u just have to give it a kick
like i told it to integrate something
but it got it wrong
so i told it to use a different substituion
old sinew
they can't do integer arithmetic
reminds myself and my days
thanks for the time,
.close
worthy thicket
I need help with studying
Having a mock exam on friday
Andrew Tate
Thats not nice
Trying to work here
15abยณ/20aยฒb , I need to shorten it
worthy thicket
I dont know Im stupid
I need to shorten it
But
I do believe that I can change 15 and 20 with 3 and 4
alpine sable
use the property of exponents of $\frac{a^m}{a^n} = a^{m - n}$
ocean sealBOT
โกLexQaโก
limpid spade
No
worthy thicket
How do I cut it out then
limpid spade
**โกLexQaโก**
Use this
worthy thicket
My mother language isnt english so I dont understand it
And im 15???
So I dont need university maths
fringe sleet
$\frac{\cancel{a}}{a^{\cancel{2}}}=?$
ocean sealBOT
Duh Hello
worthy thicket
oh
worthy thicket
but thats what I said
limpid spade
No
worthy thicket
I said a-aยฒ to get a on the bottom
fringe sleet
well you wrote a-a^2
worthy thicket
Oh
fringe sleet
thats not what you are doing
limpid spade
a!=1/a
fringe sleet
but yes you have the idea then
worthy thicket
The same?
fringe sleet
you already did that one earlier
fringe sleet
I can cut out one b and make it b2 instead right?
here
worthy thicket
Yesss
fringe sleet
so you are done
worthy thicket
Why isnt it correct?
fringe sleet
you didnt properly remove the b from the top and bottom then
limpid spade
^
limpid spade
Yes
fringe sleet
btw one way to make it simpler with these types of questions for when you are starting is thinking like $$\frac{15ab^3}{20a^2b}=\frac{15\cdot a \cdot b\cdot b\cdot b}{20\cdot a\cdot a\cdot b}$$
ocean sealBOT
Duh Hello
worthy thicket
yesss
fringe sleet
so here you can more easily cross out things $$\frac{15ab^3}{20a^2b}=\frac{3\cdot \cancel{a} \cdot \cancel{b}\cdot b\cdot b}{4\cdot \cancel{a}\cdot a\cdot \cancel{b}}=\frac{3b^2}{4a}$$
ocean sealBOT
Duh Hello
fringe sleet
would not recommend it when the powers are high tho
fringe sleet
but you can learn the pattern a bit easier
worthy thicket
I have 10th grader math
fringe sleet
and understand why it is that case
worthy thicket
fringe sleet
I have 10th grader math
it wouldnt be crazy for them to ask you to simplify $$\frac{a^{100}}{a^{95}}$$
ocean sealBOT
Duh Hello
worthy thicket
These are my problems
fringe sleet
and if this is what is asked for doing my way is very very bad
but it is still an easy problem
fringe sleet
**โกLexQaโก**
this is an example where you would wanna use this one
worthy thicket
$$\frac{a^{5}}{a}$$
ocean sealBOT
catus
fringe sleet
not quite
fringe sleet
$\frac{a^{100}}{a^{95}}=a^{100-95}=a^5$
ocean sealBOT
Duh Hello
fringe sleet
not divided by a
worthy thicket
Yeah but you just removed the bottom one
worthy thicket
Oh
fringe sleet
**โกLexQaโก**
the one at the bottom is gone here
fringe sleet
so if you imagine a row of 100 a's in a row you know that 95 of them will cancel with the 95 a's in the bottom, leaving only 1 at the bottom and $a^5$ at the top, hence you get $\frac{a^5}{1}=a^5$
ocean sealBOT
Duh Hello
amber phoenix
lone heartBOT
Available help channel!
wispy nebula
lone heartBOT
wispy nebula
I said that g IS a function
it seems that they're arguing that g is not injective so it's not a function
am i wrong or is the mark scheme wrong
plain flame
thats not exactly what injective means
and g is not a function so it cant be an injective function in the first place
keen plinth
what's g(1)
lone heartBOT
lone heartBOT
Available help channel!
alpine sable
lone heartBOT
alpine sable
is this right
limpid spade
What's 4^2?
alpine sable
16
limpid spade
Yes
limpid spade
,w (4y^3)^2
vague mirage
ok is it right then ?
Nah
alpine sable
so its 16y^6
alpine sable
im doozy
vague mirage
so its 16y^6
Yeah
alpine sable
so with problems like these you just multiply the exponents
vague mirage
Yupp we just multiply
fiery yacht
You're distributing the outer exponent and when you have an exponent on an exponent you just multiply
vague mirage
$(a^v)^u=a^{vรu}$
ocean sealBOT
Arnab Pal
fiery yacht
bruh lol
alpine sable
is 6687 in scientific notation .6687 ? or 6.687
limpid spade
None
plain flame
6.687 * 10^3
fallen verge
you dont have the power of 10, but it would be the latter
gaunt dragon
lone heartBOT
lone heartBOT
Available help channel!
azure mirage
lone heartBOT
azure mirage
<@&286206848099549185>
distant pasture
can i get help
abstract fractal
<@&286206848099549185>
!15m
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.
abstract fractal
can i get help
abstract fractal
We don't give answers
azure mirage
We don't give answers
how do i do it
abstract fractal
What have you tried
azure mirage
i didnt know what to try
distant pasture
abstract fractal
abstract fractal
i didnt know what to try
It tells you what to try in the question
Round each number to 1 s.f.
azure mirage
It tells you what to try in the question
bro stop being so wierd just tell me how to do it damn
abstract fractal
I'd rather just leave
azure mirage
do i add the two numbers then round it or do i round them than add them?
azure mirage
I'd rather just leave
i think i will
abstract fractal
do i add the two numbers then round it or do i round them than add them?
The latter
azure mirage
so i round them then add them alr
lone heartBOT
@azure mirage Has your question been resolved?
flint dust
How do I approach this:
Calculate the following limit using Riemann Sums:
flint dust
clever locust
The limit is $\lim_{n\to\infty}\sum_{k=1}^n\frac{k}{n^2+k^2}$, perhaps it's easier to see when written this way
ocean sealBOT
Lorago
marsh rapids
k / (n^2 + k^2) = 1/n * k/n / (1+k^2/n^2)
I think that should make f quite obvious. It also integrates nicely
clever locust
To make the typesetting a bit better,
$$\lim_{n\to\infty}\sum_{k=1}^n\frac{k}{n^2+k^2}=\lim_{n\to\infty}\sum_{k=1}^n\frac{1}{n}\cdot\frac{k/n}{1+(k/n)^2}$$
ocean sealBOT
Lorago
little peak
https://www.amazon.com/dp/B00TFYYWQA?linkCode=ogi&th=1&tag=zd-buy-button-20&ascsubtag=528a617b79804850b235f1aaaf38bbb1|a9e3ac62-1ff0-42ea-8e01-4138128eacd6|dtp
would this be a good calculator to buy?
left mesa
yes
little peak
why did the bot pin that lol
silver robin
hi
rustic coral
why did the bot pin that lol
It pins the first message sent in a channel after being opened
remote heron
https://www.amazon.com/dp/B00TFYYWQA?linkCode=ogi&th=1&tag=zd-buy-button-20&ascs...
overpriced
IMO
remote heron
https://www.amazon.com/dp/B00TFYYWQA?linkCode=ogi&th=1&tag=zd-buy-button-20&ascs...
look on ebay, you can find the older non-color models for much cheaper
or the color ones for a bit cheaper
lone heartBOT
@little peak Has your question been resolved?
rocky grove
Casio fx-CG50 is quite nice tbh
Graphs
Colorful
Programmable
And really nice price
Happy owner of one
alpine sable
Hi
alpine sable
Can i send a picture?
rocky grove
Yes please
wary stream
,rotate
ocean sealBOT
final ember
Number 16 pls because 17 is easy
so part b?
wary stream
Number 16 pls because 17 is easy
16 and 17 are the concept, except 17 gives a table, 16 gives a plot
So if you are able to do 17, 16 is similar
final ember
16 is confusing because
i don't think you did part a right
wary stream
Write an equation based on that plot
alpine sable
I got no idea Im just trying to finish this whole page so i can do my history project
wary stream
Do you understand 17?
final ember
But 16 is a graph so idk what to do
do you know how to find slope?
alpine sable
Yes except theres no line on the graph
wary stream
As I mentioned, it's the same concept as 17. Write 2 of the points as coordinate pairs
Then find the slope, and use point slope formula
final ember
Yes except theres no line on the graph
there are points which make a line
alpine sable
Did I do the line right?
final ember
y=mx + b where m is the slope and b is the y int
wary stream
It wasn't necessary to draw a line
alpine sable
Ohโฆ
wary stream
First, given the standard equation of a line, y = mx + b
alpine sable
Which is?
wary stream
Can you use two of the points on that graph to find the slope?
alpine sable
Technically yes right? Cuz I do that on the table
wary stream
Do you know methods in finding the slope?
alpine sable
Yes
wary stream
Like do you know the slope formula?
alpine sable
The middle of a square right?
wary stream
What?
alpine sable
Hard to explain look
wary stream
Do you know the equation to finding slope?
wary stream
That is not what I am asking
wary stream
Do you know the equation to finding slope?
.
wary stream
Because if you know how to do 17, it applies that same formula
wary stream
Can you determine the slope of that graph, given the formula and using two of the points on that graph?
wary stream
So try it
wary stream
,rotate
ocean sealBOT
alpine sable
wary stream
Those are literally two points out of the 6 that are given
alpine sable
Also Y is always on top when doing this right?
wary stream
You looked up the slope equation, use that to aid you
wary stream
,rotate
ocean sealBOT
wary stream
First off, just realized this, do you know how to form coordinate points from a graph?
Is x or y first?
wary stream
Yes and? You need to find the slope to do that
alpine sable
Ok i got 3/2
wary stream
As mentioned before, you're going to apply the slope formula for question 17, so you can apply it to question 16 as well
wary stream
Ok i got 3/2
And no
alpine sable
Mann. What
wary stream
Let's do the method that uses the slope equation
alpine sable
U want me to erase everything?
wary stream
As mentioned, you need to pick two points from that plot
What are two of the points, you want to use?
alpine sable
And do I have two?
wary stream
Do you have anything that is in the form of (x, y)?
wary stream
Each point on that graph can be represented as a coordinate pair, an (x, y)
You need to formulate two points in that form
alpine sable
Yes
wary stream
Are you sure
alpine sable
But the thing is so is 50 but I choose to ignore it
wary stream
As mentioned, coordinate points are in the for of (x, y)
Do you have anything that is written like that?
alpine sable
Yes
wary stream
And are those valid points on that plot?
Does (3, 0) exist on that graph?
Or (2, 0)?
wary stream
So then present two coordinate points, that exist on that graph
https://www.youtube.com/watch?v=Qjp77H-YL4Y&ab_channel=RachelDeFelice
Here's a video on how to write coordinate points
alpine sable
Ok
wary stream
You don't seem to understand the basic concept of coordinates
alpine sable
Yeah
wary stream
Then you can use this to find the equation of the line based on that plot
https://www.youtube.com/watch?v=4vXqMsvPSv4&ab_channel=BrianMcLogan
Because once you determine two points, you need to find the slope
wary stream
No you did not
wary stream
This was the original two points you used
wary stream
The led line
Okay and?
alpine sable
Im confused were the points I used wrong?
wary stream
Across and over means nothing when it's not done properly
wary stream
Im confused were the points I used wrong?
Yes