something like this i can
#help-27
dusty cosmos
acoustic leaf
if you have a repeated linear factor in the denominator, you do something like this:
[\frac{-3}{(x+1)(x-2)^2} = \frac{A}{x+1} + \frac{B}{x-2} + \frac{C}{(x-2)^2}]
woven radishBOT
cloud
woven radishBOT
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dusty cosmos
so im assuming its $$(x-3) and (x-3)^2$$ that are the factors?
woven radishBOT
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acoustic leaf
that would work essentially the same way, yes
dusty cosmos
yeah ive tried doing that
but i ran into a problem
so i got to the point where
$$2x+3=a(x-3)^2+b(x-3)$$
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dusty cosmos
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night grail
..
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final hound
Given a base (b_1, b_2, b_3) = ((1, 1, 1), (0, 1, 1), (1, 0, 1)) of R^3 space; vectors c_1 = (0, 0, 1), c_2 = (1, 2, -1), c_3 = (2, 2, 1) and a linear transformation T: R^3 -> R^3 such that T(b_i) = c_1 for i = 1, 2, 3.
(a) Represent the vector x = (x, y, z) as a combination of the basis vectors (b_1, b_2, b_3).
(b) Determine T(x) = T(x, y, z) for x ∈ R^3.
(c) Check that for the calculated T(x, y, z) T(b_1) does in fact = c_1.
(d) Determine KerT (null space), its base and the dimension of KerT.
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Given a base (b_1, b_2, b_3) = ((1, 1, 1), (0, 1, 1), (1, 0, 1)) of R^3 space; v...
vernal monolith
!status
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What step are you on?
1. I don't know where to begin.
2. I have begun but got stuck midway.
3. I got an answer but I was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
1
dapper gazelle
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Show your work, and if possible, explain where you are stuck.
final hound
for (a) I row reduced an augmented matrix with the b1,2,3 vectors on the left and x,y,z on the right, but how would I expres the answer? x+y-z(b_1) + z-x(b_2) + z-y(b_3)?
I think this part I understand but (b) I don't at all
dapper gazelle
for (a) I row reduced an augmented matrix with the b1,2,3 vectors on the left an...
Well that expression is definitely wrong because that involves a sum of scalars and vectors
Although I already see the weirdness in writing x = (x,y,z)
For Part B, what does T do? Can you explain in simple language
final hound
Well that expression is definitely wrong because that involves a sum of scalars ...
so how would i express the answer if I have something like this?
dapper gazelle
You mean only the rightmost column, right
Because [I | ...] isn't quite a vector in R^3
In any case, the question is this: let both LHS and RHS point to somewhere in R^3
Then we know that there exists a representation of this point using the LHS basis
We also know that there exists a representation of this point using the RHS basis
If you're not lost so far, then I think you should be able to express the answer perfectly
final hound
i'm lost
dapper gazelle
Ok so uhh, at this point I'd tell you to read a textbook but IDK what book you're on
It's easier to explain R^2 than R^3
There's no real difference, R^3 is just more work than R^2 (at this point)
Let's say you have a point (-1,1) on R^2. Given bases A=(1,1) and B=(-1,1). You'd express this point as
(-1,1) = 0A + 1B.
But the most usual bases for R^2 is C=(1,0) and D=(0,1). So in that case it would be written as
(-1,1) = -1C + 1D
Then (a) only wants you to use the bases b_1, b_2, and b_3 to represent any arbitrary point in R^3. You can see that different basis = looks different (the coefficient for each basis vector is different)
In fact we can go further with this idea.
In R^1 you can say that [1] and [-1] are different bases. And so on. But this is a bit contrived
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final hound
So am I supposed to pick some (x,y,z)?
dapper gazelle
You're "picking" an arbitrary (x,y,z)
Or to be more explicit, the LHS should be x*[1,0,0] + y*[0,1,0] + z*[0,0,1]
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viscid wagon
Find the value of floor((5+sqrt(21))/2)^5)
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Find the value of floor((5+sqrt(21))/2)^5)
viscid wagon
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vast cedar
I found this problem online in a textbook and they solved it by using L'Hopital's rule twice.
But when I search it up, I get conflicting answers that using L'Hopital's rule with higher order derivatives is undefined or that it works if you can prove it, etc.
devout snowBOT
I found this problem online in a textbook and they solved it by using L'Hopital'...
vast cedar
so which is it?
near trout
I found this problem online in a textbook and they solved it by using L'Hopital'...
if you use l'hopital and then what you get satisfies the conditions for l'hopital again, you can use l'hopital again
vast cedar
I also should've mentioned we're taking the limit at infinity
vast cedar
if you use l'hopital and then what you get satisfies the conditions for l'hopita...
but in any event, can I test if it satisfies the condition with any constant?
near trout
?
winter torrent
what are the conditions for lhopital?
vast cedar
plugging in c
can I change what c is to see if it gives me the same value as the previous derivative?
vast cedar
so basically, I need to get out 0 (or infinity) from f'(x) and g'(x) when evaluated at C in order to use L'Hopital's rule again?
winter torrent
yes
lunar ice
A is 2X2. Your are told that A'A=[265 35; 35 290] and AA'=[313 -11; -11 242]
lunar ice
how would i find A in this
sinful gust
could just assume A = [a b; c d]
lunar ice
i used Eigvec of A'A and Eigvec of AA' then square rooted the eig value to find A
sinful gust
there might be a more elegant way probably
lunar ice
could just assume A = [a b; c d]
yeah this is a brute method
i think we are meant to use svd
so tryna do that
lunar ice
i used Eigvec of A'A and Eigvec of AA' then square rooted the eig value to find ...
not sure if this is necessary correct
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vocal garnet
unable to solve this question, tried several times
u need to find the angle 'x'
EF is the tangent of the circle, AC is the diameter
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unable to solve this question, tried several times
u need to find the angle 'x'
...
vocal garnet
<@&286206848099549185>
sinful pilot
Do you know any angle to start?
sinful pilot
What about angle ACE
vocal garnet
nope not given
sinful pilot
But you can find it
vocal garnet
but ACE will be 90 since the radius is perpendicular to tangent
sinful pilot
Yes
vocal garnet
this is all i could find
vocal garnet
i am not getting any other theorems to use to find x
sinful pilot
Well you actually cant i think
Like if you move D on the circle x changes
And there is nothing to stop that
vocal garnet
wdym? could u elaborate pls
sinful pilot
this is all i could find
What if the diagram looks like this
AC is still the diameter BCE is still 66 but angle x is different
vocal garnet
yep, that was the entire question
sinful pilot
Ok then its wrong
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stoic swallow
so your first step is to break 21 into tens and ones, right?
crisp trench
!15m
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gentle mantle
anyone have any thoughts on how i inputed this incorecctly
devout snowBOT
anyone have any thoughts on how i inputed this incorecctly
sullen geyser
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woven radishBOT
everg
cold bough
in fact i didn t give you the full answer ..but you can use what i wrote to solve the problem
cold bough
**everg**
that inequality works even for complex numbers
so you have to do the same steps for both complex and real numbers
sullen geyser
but for like real numbers this is trivial, whereas in complex numbers , |z| represents the distance of it from origin, i dont see how to understand that the distance of (z+1/z) is always more that the difference of distances of z and 1/z from origin
sullen geyser
i still dont get it
cold bough
hint:
sullen geyser
still lost
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bleak pond
How many permutations of {0, 1, 2, 3, 4, 5, 6} have no adjacent even digits? For example,
a permutation like 5034216 is not allowed because 4 and 2 are adjacent. My ans is 7c36C6 + 7c46c6 . but i m not too sure
devout snowBOT
How many permutations of {0, 1, 2, 3, 4, 5, 6} have no adjacent even digits? For...
bleak pond
ok so 7c3 * 6c6 because from 7 numbers we are choosing 3 odd numbers and multiplying that with 6c6 becasue there are 6 positions to choose from in a way - 0| 1|2|3|4|5|6 - so like the bars are the positions to choose from.
and the same for starting with even numbers but itll be 7c4 becasue im using 0 as an even number.
and we add them cuz theyre mutually exclusive.
but it doesnt rly feel right
sand dove
I'm not sure if permutations is about choosing numbers
bleak pond
yeah i just need a pointer in the right direction
sand dove
And 6c6 is 1 because there's only one way to choose 6 things from a list of 6
So as a hint :
Call abcdefg the positions of numbers in a permutation
For example, 3210456 and 0 is in position d
sand dove
Try to find which positions are possible for even numbers
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elder meteor
IBP
elder meteor
Too late
upper schooner
Any ideas?
elder meteor
Any ideas?
First step is obv
Derive ln and integrate x
Rest becomes complicated
I added 1 and subtracted 1 to x²
narrow cradle
I thought you could use usub, but that may not be the case
upper schooner
Looking good to me 
elder meteor
Looking good to me <:happyCatThumbsUp:1201376212803657818>
Gamer
@upper schooner hello
upper schooner
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fast stirrup
hey
winter patrol
to get f(whatever)
replace all x in the equation with that value
add () where appropriate
or in general put () around that value regardless, and remove later if they aren't needed
fast stirrup
can you make an example /
restive river
how do i solve this
do you mean find k?
fast stirrup
yes
winter patrol
g(x) = x + 5
to get g(-6) replace all x in the equation with (-6)
g((-6)) = (-6) + 5
removing unnecessary () and simplifying
g(-6) = -1
winter patrol
that's fine
fast stirrup
but how do i do this f(x)=2x² - k and f(-1) = 3
winter patrol
read what i said above
fast stirrup
so like 3=2 x 1² - k ?
winter patrol
don't use x for multiplication,
skipping steps but that works
winter patrol
#old-network but its not as active
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covert geyser
can someone help me with a methodology on solving this transform?
covert geyser
or a simpler one rather
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woven radishBOT
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stark sinew
Every other (second) term will carry a negative sign. it looks like your table automatically does that by putting a - on every second u
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fiery imp
h
fiery imp
is this correct
lilac patio
is this correct
the equation is incorrect. the equation would be y - y1 = ... but your y1 = f(7) = -44, not 44
fiery imp
so is it y+44= -14(x+7)
fiery imp
the equation is incorrect. the equation would be y - y1 = ... but your y1 = f(7)...
?
nvm
im confused on this one
says its wrong
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wicked turtle
problem statement is missing
and the top half is hard to read, what's with the colors
fiery imp
problem statement is missing
???
wicked turtle
ok that's better, thx
fiery imp
so what do i do
fiery imp
yes
wicked turtle
when it says "at a = -1" i assume it means "at t = -1"?
there's no a referenced anywhere
fiery imp
oh im dumb i think its the variables
wicked turtle
oh yea probably wants t
wicked turtle
well this one is wrong, what did you get for the derivative of f(x)
fiery imp
not sure how to find that for this
wicked turtle
where did you get -0.05
wicked turtle
well you would have to take the limit of that first fraction as x->7, is that what you're doing?
fiery imp
yes
wicked turtle
how did you get -1/(2x-6)
fiery imp
yes
wicked turtle
that's not -0.05
wicked turtle
ahh that would explain it
wicked turtle
cheers
boreal saffron
I'm trying to calculate some probabilites and am unsure how to do it.
There will be trials of independent random events, each with the same probability. Each event's chance of success is P and its chance of failure is 1-P.
The trials end after N trials total occur or after F trials total result in failure.
What is the average number of successful trials, S, under these conditions, in terms of P, N, and F?
devout snowBOT
I'm trying to calculate some probabilites and am unsure how to do it.
There will...
@boreal saffron Has your question been resolved?
boreal saffron
<@&286206848099549185>
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boreal saffron
I've tried to use both GPT and Bard but both are clearly incapable of understanding the question no matter how much I try to clarify it for them
trim flame
So the experiment ends either when N total trials have been made, or after F failures have occurred, whichever comes first?
boreal saffron
Correct
supple knot
Do you know the negative binomial distribution
Part of your question is solved by that distribution
boreal saffron
That sounds familiar but only in the sense of "I think I learned that in stats class" I don't remember it in a meaningful sense
supple knot
But you need to min it with the N trials
boreal saffron
Like I know that if F >= N, S = NP which is simple enough
But idk how to handle F when it's less than F and thus applicable
boreal saffron
But you need to min it with the N trials
Can you elaborate on this?
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green crypt
In determinant if we multiply a row with a certain number lets say k, we put 1/k outside the determinant but we don't do this in matrix form why?
devout snowBOT
In determinant if we multiply a row with a certain number lets say k, we put 1/k...
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river island
What do you mean with we dont do this in matrix form ?
river island
In determinant if we multiply a row with a certain number lets say k, we put 1/k...
If you multiply one row with a scalar lambda you have to multiply the determinant of the matrix with the same lambda.
Has this solved your question?
If not, try it with a simple 2x2 matrix
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boreal saffron
I'm trying to calculate some probabilites and am unsure how to do it.
There will...
I never actually got an answer to this
devout snowBOT
I never actually got an answer to this
boreal saffron
What?
topaz axle
ok i was thinking average per trial, that's just called probability, we don't care about that
nvm
if the answer is equal to P × average experiment length, we can find experiment length numerically
boreal saffron
And how would we do that?
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topaz axle
e.g. probability that there's 4 failures after 9 trials equals (3 failures after 8)(1−P) + (4 failures after 8)P
then we can sum the right things and get average length
and it should be equal to average successes if multiplied by P
i'm not saying there's no shortcut, haven't googled it yet
boreal saffron
Could you please paste the code here so I can copy it instead of having to type it out from a sceenshot?
topaz axle
np
P = 0.3
N = 10
F = 5
table = [[0 for _ in range(F+1)]for _ in range(N)]
table[0][0] = P
table[0][1] = 1-P
for length in range(1,N):
for failures in range(F):
table[length][failures] = (table[length-1][failures] * P +
table[length-1][failures-1] * (1-P))
for x in table: print("".join(f"{x:8.5f}" for x in x))
avg_length = N * sum(table[-1])
for r in range(1,N):
avg_length += (r+1) * table[r-1][-2] * (1-P)
I'm trying to understand this code but I can't make heads or tails of it
topaz axle
it fills up a table
after 2 trials there was 1 failure with probability 0.42
0.3 * 0.7 + 0.7 * 0.3
so we take the number above and the number diagonally left above
multiply and add them, always 2 numbers
then the entire last row added up is the probability that we never reached F failures
we multiply that by 10
and then the last column we calculate by only looking at the top left neighbour (1 less failure, 1 less trial)
that's why it's all zeroes, it's calculated separately
those are trials that ended with 5 failures
boreal saffron
Oh so it's not actually calculating probabilities it's just running trials then averaging the results?
topaz axle
no
you would see import random if it was about that
let's try negative binomial formula, see if it matches
no 😦
yeah
boreal saffron
So what does that mean?
topaz axle
it means it probably finds the average number of trials you get to do correctly
i'll check if times P gives the same result as the formula 1 minute
yes
so the negative binomial computes the last column directly, and then we can use regular binomial for the last row
and like there's still no closed form
from math import comb
P = 0.3
N = 10
F = 5
pf = 0
avg_length = 0
for x in range(F,N+1):
pr = comb(x - 1, F - 1) * (1-P)**F * P**(x-F)
avg_length += x * pr
# add to probability of ending with a failure
pf += pr
#otherwise we end with success and the length is N
avg_length += N * (1 - pf)
print(avg_length * P)
@supple knotcan we do better, or it has to be that?
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supple knot
I don't know if there's a closed form unfortunately. Z = min(X, Y) sometimes exists for nice X and Y, but to my knowledge there's no easy way to find it here with Y = negative binomial and X = stopping time.
Or maybe there's a way to X random variable such that X = not a stopping time, but a sum of F-1 failures + F-2 failures + ...+ 1 failure.
Where each F-i failures implies N-(F-i) successes so the trial reaches N coin flips
boreal saffron
What is a closed form? Like a general formula that's always true?
If it helps at all in the case I actually want to calculate, P varies between 0.90 and 0.93, N varies between 13 and 23, and F varies between 1 and 23.
All the values I actually want to use this to calculate exist within those ranges
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proper violet
A genetically modified cow that produces milk less likely to cause allergic reactions has been engineered by New Zealand scientists. Up to 3% of infants are allergic to cow's milk in their first year of life. The modified cow produced milk without beta-lactoglobulin - a whey protein to which some people are allergic. The study has been labelled a "milestone" by one scientist, but some campaign groups say it raises ethical concerns.
Which one of the following is an underlying assumption of the above argument? It is impossible to avoid exposure to food allergens
A few people are allergic to some proteins in cow's milk
Genetically modified organisms raise ethical concerns
New Zealand scientists are worried about their children
New Zealand scientists are doing research to treat allergies
devout snowBOT
A genetically modified cow that produces milk less likely to cause allergic reac...
topaz axle
this makes no sense
first of all, there's no argument above
they tell you some stuff, nothing is being argued
we have to guess the underlying assumption without knowing what the argument is and the only relevant option is just more or less the conclusion again
it's like the stupidest thing i've seen in 2024
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topaz axle
i would choose an option that starts with "New Zealand", either one, because they at least aren't explictily stated in the text, so there's some underlying
i guess the children one
"treat allergies" makes sense, it just sounds incorrect to call it treatment but i'm not a doctor
blazing mason
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blazing mason
How do I find the critical value here?
when I watched tlmaths he said if you're on the aqa board you're supposed to be supplied with it
¯_(ツ)_/¯
proper violet
I have seen this type on Italian education books
It is an type of question that is asked on IMAT usually
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blazing mason
It is an type of question that is asked on IMAT usually
IMAT?
proper violet
Sry wrong channel 😕
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tranquil tartan
The critical value depends on the type of test and can be determined once the significant level is known. I've always been told to refer to this chart:
df means degrees of freedom and is equal to $n-2$ in the case of a correlation coefficient
woven radishBOT
RiN
blazing mason
df means **degrees of freedom** and is equal to $n-2$ in the case of a correlati...
At no point during my college's course did we learn that why tf did my teacher set me that
This also doesn't appear in the aqa spec as far as I can tell as we are supposed to be told this value
Oh well
Thanks
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late moth
I'm not quite sure where to go with this, I know the general idea but when its abstracted to F_1 and F_2 with several maps I'm not quite sure how to relate the different elements.
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I'm not quite sure where to go with this, I know the general idea but when its a...
late moth
$\beta_1(f)$ is defined as ${ q\in\mathbb{Q} \mid i_1(q) < f }$ where $i_1$ is the unique injective map from $\mathbb{Q}\to F_1$ and $\alpha_2(S) = \sup S\in F_2$
woven radishBOT
94tj
late moth
So I guess for $a+b\in F_1$, $\beta_1(a+b)= { q\in\mathbb{Q} \mid i_1(q) < a+b }$, but I'm not sure how to relate this to $F_2$
woven radishBOT
94tj
late moth
Like this is a dedekind cut but $a+b\in F_1$ right? So if I want to find the least upper bound of the set in $F_2$ would it $\sup {q\in\mathbb{Q} \mid i_2(q) < f(a+b)}$ ?
woven radishBOT
94tj
late moth
actually i dont think that gets me anywhere since that just tells me f(a+b)=f(a+b)
I guess my confusion comes from going from a dedekind cut to taking the supremum in F_2
Oh can I define the Dedekind cuts $A = { q\in\mathbb{Q} \mid i_1(q) < a}, B = { q\in\mathbb{Q} \mid i_1(q) < b}$, then $A+B = { q\in\mathbb{Q} \mid i_1(q) < a+b}$ and say the supremum taken in $F_2$ is $\sup (A+B) = \sup A + \sup B = f(a) + f(b)$?
woven radishBOT
94tj
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lyric moat
Hey guys, I know a ball is held at the point (0,1,4) on the surface z = f(x,y) = (5x+4y)e^{-5x}
we let the ball lose and let it roll. I need to find at which direction (x,y,z) the ball will roll. any help of how to even start this quetion?
devout snowBOT
Hey guys, I know a ball is held at the point (0,1,4) on the surface z = f(x,y) =...
near trout
find the gradient
graceful cosmos
You're looking for the direction of steepest descent
lyric moat
so if I'm right the gradient is
x: $(1-5x-4y)5e^{-5x}$
y: $4e^{-5x}$
but I'm not sure what to do from here
woven radishBOT
mtr123
lyric moat
or now I'm suppose to compute
$-\nabla f$ at the point (0,1,4)?
so i get
x: $(1-0+4)5\cdot 1 = 25$
y: $4\cdot 1 = 4$
we gonna take $-\nabla f$ so it gonna be (-25,-4,0)?
woven radishBOT
mtr123
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near trout
or now I'm suppose to compute
$-\nabla f$ at the point (0,1,4)?
so i get
x: $...
the x and y look about right but you need to work out how quickly f will decrease if you go in that direction
z shouldn't be 0
it should be negative
lyric moat
z shouldn't be 0
any help explaining me how to compute it? like what's the method, honestly im really confused about it. sorry that my question is that basic
near trout
well ok we can hack it a little bit
you know the gradient which is like some (df/dx, df/dy)
and the direction you're going is like (-25, -4) in x and y (i'm assuming you've gotten those calculations right, haven't checked)
so suppose you take a little step like
(-25h, -4h)
so you're moving from like (0, 1, 4) to (-25h, 1 - 4h, f(-25h, 1 - 4h))
and then you can do like $\lim_{h \to 0} \frac{f(-25h, 1 - 4h) - f(0, 1)}{||(-25h, -4h)||}$
woven radishBOT
Kaisheng21
tranquil flower
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tranquil flower
how would i go about solving this
near trout
integrate
tranquil flower
so far i writen out the point of intersection
but
i dont know how i would start the integration
neat solstice
we can solve the oval for a function y=f(x)=...
we will get an "upper" and "lower" function
tranquil flower
we can solve the oval for a function y=f(x)=...
we will get an "upper" and "lowe...
do you mind elaborating?
neat solstice
we should start by getting the values for the orange and purple lines here
in order to split up the integral
for the oval shape, we can get an equation f(x)=+-sqrt(1-(x/2)^2)
we can seperate this into two function (one positive one negative)
then for example, A1 is the integral over |f_Oval,neg(x) - f(x)|
tranquil flower
how did you get the equation to be f(x)=+-sqrt(1-(x/2)^2)
neat solstice
tranquil flower
i thought we could square root it and simplify the equation to
y = 1- (x/2)
is my thinking wrong here?
tranquil flower
i see
tranquil flower
then for example, A1 is the integral over |f_Oval,neg(x) - f(x)|
can we continue from here
this notation is kind of confusing
are we also taking the absolute value of this?
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neat solstice
yes, |...| is absolute
$f_{Oval,+}(x) \text{ is what i call the negative function that we get for the oval shape}$
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Martin
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unique gale
The aim is to generate a magnetic field by letting two electric currents, called I1 and I2, flow through long parallel cables separated by a distance "r", as shown in the figure.
An electrical law indicates that the force FL per unit length exerted on one wire due to the magnetic field surrounding the other wire is jointly proportional to the currents I1 and I2, and inversely proportional to the square of the distance "r" between the two. cables.
Express this variation with an equation. What would be the effect on FL if the distance "r" is reduced by half?
devout snowBOT
The aim is to generate a magnetic field by letting two electric currents, called...
lusty sapphire
The aim is to generate a magnetic field by letting two electric currents, called...
Do you know what it means for one quantity to be in direct propotion to another?
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pallid ravine
can someone help me with c??? i dont understand this at all, i know what MVT is but idk how it applies in this context
this is an assignment ive already handed in but i didnt get it correct
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can someone help me with c??? i dont understand this at all, i know what MVT is ...
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fervent patio
https://math.stackexchange.com/questions/1591990/birational-equivalence-of-diophantine-equations-and-elliptic-curves I need help understanding this math stack exchange post. I have the function 6n^4-12n^3+66n^2+84n+144=(12m)^2 and I am trying to convert it to an eleptical integral and prove that there are finite amount of rational points on it
devout snowBOT
https://math.stackexchange.com/questions/1591990/birational-equivalence-of-dioph...
fervent patio
I'm trying to find when this equals a power of two for positive integer values of n. (n^4-2n^3+11n^2+14n+24)/24 . If it does it equals a square or twice a square
n^4-2n^3+11n^2+14n+24) = 24m^2
n^4-2n^3+11n^2+14n+24) = 48m^2
multiply by 3 and 6 respectively
6n^4-12n^3+66n^2+84n+144) = 144m^2 = (12m)^2
3n^4-6n^3+33n^2+42n+72) = 144m^2 = (12m)^2
If I convert the first one or the second equation into an eleptical curve preserving the rational points, and then prove that there are finitely many solutions
fervent patio
n^4-2n^3+11n^2+14n+24) = 24m^2
It should prove that there are a finite amount of powers of two in this
In case two in the stack exchange I just don't understand what they first do
mystic citrus
In case two in the stack exchange I just don't understand what they first do
Not sure I understand the question
weak cove
in which post of the stack exchange, the question or one of the replies?
could you show like a screenshot and highlight what you are confused about
mystic citrus
Oh I'm tripping I didn't see the link
Chat gpt thinks you should consult the experts in the field
weak cove
Chat gpt thinks you should consult the experts in the field
posting chatgpt is against the rules
mystic citrus
Wait really
weak cove
yes
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fervent patio
🤓
sorry for the late replies
It starts from here
I confused about how he goes from
y^2 = ax^4 ... e
to that
y^2z^4 = ...
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quaint moth
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gusty merlin
can surd 12 be simplified
devout snowBOT
can surd 12 be simplified
restive river
Yes, of course
weak cove
does 12 factor into anything
wooden zodiac
Clearly
gusty merlin
so 3 surd 4?
restive river
Start by prime factorising 12
gusty merlin
restive river
so 3 surd 4?
No
what is the prime factorisation of 12?
i.e. how do you represent 12 as a product of prime numbers only
gusty merlin
so 2 surd 3
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knotty echo
Hello So I need to find A. D= -4,0 C= 2,0 B= 0,-8. I know that A’s y is -8, but I can’t find the x. AB is parallel to the x axis. I don’t know if that helps
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lost laurel
let P and Q be the vertices of $y=x^2+bx+c$ and $y=-x^2+dx+e$. P and Q are the points of intersection of the parabolas, find the slope of the live via P and Q
devout snowBOT
let P and Q be the vertices of $y=x^2+bx+c$ and $y=-x^2+dx+e$. P and Q are the p...
woven radishBOT
Why am. I here
lost laurel
P and Q are the points of intersection of the parabolas:- Why is this information important
oh yeah, before I forget, the options are
mild comet
It would be important if P and Q were not the same point
lost laurel
It would be important if P and Q were not the same point
wdym
lost laurel
b=c=d=e=0 works, though technically there would be no slope
oh,ok
thanks
can I close this now?
lost laurel
Thanks!
drifting sierra
oh yeah, before I forget, the options are
options are what?
lost laurel
Well, as It turns out, I'm not too sure, I;ll post my working
uncut orbit
lost laurel
The turning point for the first parabola is (-b/2, c-b^2/4) and that of the other is (d/2,d^2/4+e)
I'm guessing what I hae to do is substitute the x coodinate of one into the equation of the other parabola to solve it?
drifting sierra
might work
lost laurel
yup, it works beautifully
thanks!
Also I think I should disclose the source
NEST 2023
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celest nimbus
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celest nimbus
good evening
devout snowBOT
good evening
celest nimbus
i just said -x^2 and -(x-2)^2 + 2
i think its wrong
i could just do x^2 and (x-2)^2
inland seal
That isn't what the question is asking
You need two equations, only involving a and b
Two relations
a + b = 1 is an equation involving a and b for example
native snow
limber vigil
i can answer ur q - so BC is 5cm, meaning the radius of semicircle BC (the whole not shaded section) is 2.5cm. now do area of semicircle BC-area of triangle BAC to get those two not shaded sections outside the triangle. now, calculate the are of the two semicircles BA and AC and subtract the two not shaded sections from them
finite briar
Is there a general solution to this recurrence?
devout snowBOT
Is there a general solution to this recurrence?
sonic smelt
Iirc it approaches the square root of a assuming a is nonnegative
As can be proven by monotone convergence theorem
finite briar
yes ik that much
but that is the limit the sequence approaches as n approaches inf
I was looking for a general solution
sonic smelt
Ah you mean the nth term
woven radishBOT
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finite briar
hmm
There is a possible solution, $\sum_{i=1}^{n-1} \frac{a}{x_n} - x_{n+1}$
but I have no idea how to even begin to find a closed form expression
woven radishBOT
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finite briar
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finite briar
<@&286206848099549185> How do I solve this equation? does there exist no closed form solution? I mean cubic formula just gives undefined
Where does this even come from 💀 what did wolfarmalpha even do
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white lava
when we have the following problem, when were trying to mulitply 2 with x* \sqrt{5}
devout snowBOT
when we have the following problem, when were trying to mulitply 2 with x* \sqrt...
halcyon yew
I have questions about physics 11
devout snowBOT
I have questions about physics 11
halcyon yew
Ik its not directly math but im rlly confused
How is fg weight? (After third bullet
acoustic leaf
weight is defined as the force of gravity acting on an object
on earth, where the force of gravity is effectively uniform, we often conflate weight with mass (since they are proportional to each other), but they are separate concepts
halcyon yew
My teacher rlly confused me tdy
Cause she said normal force is weight and made a mistake and its not fg
acoustic leaf
Fg is a different way of saying weight
halcyon yew
Question 7 is rlly confusing me 😭
halcyon yew
Fg is a different way of saying weight
My teacher said its Fn (normal force) but it makes NO sense
I talked to her directly
dense jay
Fn can be Fg, but this is usually only on a flat plane
acoustic leaf
normal force Fn is a different force, which happens to be equal to weight sometimes
graceful cosmos
We're ahead of ourselves. Have you drawn the FBD yet?
acoustic leaf
weight points down, if you are on flat ground and not accelerating then normal force has an equal magnitude upwards
halcyon yew
weight points down, if you are on flat ground and not accelerating then normal f...
But how is weight up
According to answer of question and my teacher
acoustic leaf
Question 7 is rlly confusing me 😭
when you are standing on a scale, the scale can't measure your weight, just the normal force that you exert on it (which by newton's third law is the equal and opposite to the normal force exerted on you)
halcyon yew
when you are standing on a scale, the scale can't measure your weight, just the ...
Why cant it measure the weight?
How much force on it
acoustic leaf
the force on the scale is the normal force, not weight
halcyon yew
the force on the scale is the normal force, not weight
But normal force is up
The normal force not applying forge to scale
acoustic leaf
there are two normal forces:
- the normal force you apply on the scale, downwards
- the normal force the scale applies to you, upwards
newton's third law says that these must have the same magnitude and opposite direction
halcyon yew
Normal is always up
acoustic leaf
no
halcyon yew
So isnt gravity just the equal one down
acoustic leaf
normal is always normal, which means perpendicular, to the surface of contact
halcyon yew
Ic
But im still confused how weight is up
Fn will usually be up for my type of questions tho
acoustic leaf
usually, yes, because usually things are on the ground
halcyon yew
And the scale is measuring force u apply on it i thought not normal force it jus dont make sense to me
acoustic leaf
the normal force on you is pointing upwards and exerted by the scale, so by newton's third law you must be exerting a force of equal magnitude downwards on the scale, and that force is what the force measures
acoustic leaf
the normal force on you is up, and the weight/gravity force on you is down. you know the magnitude and direction of the gravity, so you can solve for the magnitude of the normal force
halcyon yew
So scale is measuring gravity/weight is being applied to it?
acoustic leaf
the scale measures the normal force being applied to it
halcyon yew
Are u able to draw a diagram
I just don’t understand
The normal force of the scale is going up and that is same with person
How do u measure that
@acoustic leaf ?
acoustic leaf
halcyon yew
So the normal force u drew is equal to gravity of person right?
acoustic leaf
not necessarily
halcyon yew
Doesnt it have to be
acoustic leaf
it does not
halcyon yew
If gravity more than scale normal force wont it go through (the person)?
acoustic leaf
you know the force of gravity is m*g downward always, and you can solve for the normal force by the scale using newton's second law
acoustic leaf
the equal and opposite reaction force of the force of gravity that the earth exerts on you, is the force of gravity that you exert on the earth
the equal and opposite reaction force that the scale exerts on you (normal force) is the force that you exert on the scale (which is what it measures)
halcyon yew
Earth exerts gravity up?
acoustic leaf
earth's gravity pulls you down, your gravity pulls earth up
(not very much, but it does)
halcyon yew
the equal and opposite reaction force that the scale exerts on you (normal force...
So dont u exert gravity?
acoustic leaf
all objects with mass exert a gravitational force on each other
it's just so weak that an object has to have a huge amount of mass to make for a big force
so returning to the scenario, we have two forces $F_n$ upwards and $F_g$ downwards. According to newton's second law, the sum of the forces = mass*acceleration: [F_n + F_g = ma]
woven radishBOT
cloud
halcyon yew
I don’t understand how weight is up 😭
acoustic leaf
it's not
acoustic leaf
it's asking for the "apparent weight" meaning the force the scale measures
meaning the normal force
not the actual weight of the person
devout snowBOT
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halcyon yew
.reopen
devout snowBOT
✅
halcyon yew
meaning the normal force
I dont get how its possible to measure normal force when that force is up
And not going towards the scale
Are u able to help with question 7
Maybe i will understand
acoustic leaf
do you know newton's second law? F = ma?
lost laurel
Hint: there's a pseudo force at play here
halcyon yew
?
halcyon yew
We didnt even learn it
My teacher says we gtta do fnet equation and fbd
We dont gtta do that
Im pre sure
So how do u get 660 N which is answer?
Im sooooo confused and lost 😭
Plz help
<@&286206848099549185> @acoustic leaf
<@&286206848099549185> anyone plz
7
<@&286206848099549185>
graceful cosmos
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celest nimbus
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celest nimbus
how did the left get simplified to the right, thanks
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worthy oxide
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worthy oxide
I dont understand why this is incorrect
i just need alittle guidance i am not sure what else to try
any help is appreciated
dense lynx
try differentiating the answer you input
see what happens
worthy oxide
it just becomes the answer from before right
?
i just did it and i got the question did i do something wrong?
dense lynx
it just becomes the answer from before right
what do you get as the derivative?
you get 9e^9x sin(e^9x) ?
worthy oxide
yea
dense lynx
ah ok
so basically since we use chain rule, we would have to "chain" the 9x
meaning we'd actually get 81e^9x sin(e^9x)
if this makes sense, do you see what went wrong?
worthy oxide
how would i get rid of it during the substitution process
also i tried to plug in the same thing with no 9 and it was still the wrong answer is there more to the problem
dense lynx
also i tried to plug in the same thing with no 9 and it was still the wrong answ...
probably
you might need the integration constant +C
worthy oxide
yea
it was that
thanks
all the other ones give c to you
that is why i was consfused
thank you
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cunning roost
devout snowBOT
devout snowBOT
what i do wrong
supple knot
Negative number * positive number = negative number
cunning roost
Negative number * positive number = negative number
the 6?
oh
ohh i see
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reef swift
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reef swift
Is this the correct way of proving limits using epsilon?
patent thistle
did you mean 7n >= n + 6?
reef swift
yes 😢
reef swift
because that statement is the same as 14/n < epsilon?
patent thistle
uhh it's because it's never used again because you go back to 14/n here
patent thistle
yea it's unnecessary there as well
patent thistle
you are welcome 🙏🏼
reef swift
.solved
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lofty egret
hey, are any of these vectors linearly independent?
devout snowBOT
hey, are any of these vectors linearly independent?
lofty egret
<@&286206848099549185>
turbid junco
hey, are any of these vectors linearly independent?
Yes
turbid junco
how can you tell?
I have x-ray vision
lusty sapphire
<@&286206848099549185>
!15m
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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.
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smoky gyro
Something is very wrong here for the height of the second rectangle but I don’t know what? All I did was plug x=4 in
(This is part a btw)
devout snowBOT
Something is very wrong here for the height of the second rectangle but I don’t ...
smoky gyro
I also dk if I even set the rectangles up correctly
smoky gyro
Did I use right?
dense jay
on the first you used x=0, on the second you used x=4, should have used x=2
the first rectangle isnt drawn quite right though
the top of it would be at the y intercept
smoky gyro
on the first you used x=0, on the second you used x=4, should have used x=2
I’m confused so where am I supposed to start
dense jay
youre doing a right?
inner rectangle means the rectangle is below the curve
since this function is increasing, we are using left endpoints
so x=0 and x=2, draw lines up from those points to the curve, then draw across, those will give you your rectangles
when you do outer, youll be using right endpoints, so theyll be over the curve
smoky gyro
Yes I’m doing part a
smoky gyro
inner rectangle means the rectangle is below the curve
since this function is in...
This looks like one rectangle tho
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cedar crane
I've been trying to figure this out but I don't really know the steps involved since I forgot a lot of the factoring process
devout snowBOT
I've been trying to figure this out but I don't really know the steps involved s...
cedar crane
sec^2-tan^2=1 is what I know
ocean yacht
sec^2-tan^2=1 is what I know
add tan^2x to both the sides
cedar crane
add tan^2x to both the sides
tan^2(theta)=3tan^2?
cedar crane
uhhh where did the secant come from
woven radishBOT
Wither
cedar crane
ah
cedar crane
sec^2 = 1+tan^2
and then the final step to that is to bring the sec^2 over to subtract tan^2?
then 1+1
?
ocean yacht
and then the final step to that is to bring the sec^2 over to subtract tan^2?
no
you know tan^2
just plug it in
cedar crane
uhhh
cedar crane
yeah
cedar crane
just subb tan
do you mind giving me a step by step of what we've done so far so i'm at the same part as you
i'm not getting it atm sorry
ocean yacht
do you mind giving me a step by step of what we've done so far so i'm at the sam...
$sec^2\theta - tan^2\theta = 1$
woven radishBOT
Wither
cedar crane
okay
ocean yacht
$sec^2\theta = 1 + tan^2\theta$
woven radishBOT
Wither
ocean yacht
ohh you added the tan^2 with the 1
yes
$\sqrt{sec^2\theta} = \sqrt{1 + tan^2\theta}$
woven radishBOT
Wither
ocean yacht
sqrt of both?
yeah take sqrt both sides
cedar crane
alr
ocean yacht
${sec\theta = \sqrt{1 + tan^2\theta}$
woven radishBOT
Wither
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
ocean yacht
why wasn't tan^2 affected tho?
cos its in addition with 1
cedar crane
oh I see
ocean yacht
do you get it now?
cedar crane
i'm trying to think what the next step would be but I don't really remember much
meager yarrow
I've been trying to figure this out but I don't really know the steps involved s...
.
cedar crane
yeah I really don't know tbh
meager yarrow
Make use of the identity
$sec^2\theta = 1 + tan^2\theta$
woven radishBOT
Afi
