mystic nebula
shouldnt it be decreasing on (-inf, -4]
#help-0
lone heartBOT
@mystic nebula Has your question been resolved?
lone heartBOT
@mystic nebula Has your question been resolved?
unkempt birch
This is about UN Logic:
lone heartBOT
This is about UN Logic:
unkempt birch
I'm mostly lost about how these models work
i get the general idea but if someone could explain it thoroughly i would appreciate it
lone heartBOT
@unkempt birch Has your question been resolved?
summer dirge
lone heartBOT
summer dirge
so, am I going row by row here? I want to use row operations to go from A to B, which changes detA along the way, yes?
when I multiply r1 by 3 to go from A to A', then detA' = 3detA, yes?
but then I add the new "r1", which is 3r1, to 2*r2, which just multiplies the determinant by 2, or is that not right?
ocean hawk
no, adding a multiple of one row to another doesn't affect the determinant
summer dirge
no, adding a multiple of one row to another doesn't affect the determinant
but i have multiplied r2 by 2
which scales it by 2
no?
summer dirge
but then I add the new "r1", which is 3r1, to 2*r2, which just multiplies the de...
here
my main concern isnt about rows 1 and 2, anyhow tbh
its rows 3 and 4
which i am a bit confused about
ocean hawk
it just doesn't. your class or textbook should show that it doesn't. I don't know the proof offhand. this answer shows what elementary row ops does to the determinant: https://math.stackexchange.com/a/1904429/993372
actually this answer shows why: https://math.stackexchange.com/a/1904430/993372
summer dirge
it just doesn't. your class or textbook should show that it doesn't. I don't kno...
but am i not multiplying a row by 2?
row 2 is being scaled by 2, then having 3*row1 added it it which doesnt change the det
but the scaling by 2 should, no?
ocean hawk
just read the link
summer dirge
its rows 3 and 4
this is still my main concern
lone heartBOT
@summer dirge Has your question been resolved?
ocean hawk
if you first multiply r2 by 2, then yes it scales it. if you're just adding a multiple of it to another, doesn't change the determinant
whole monolith
How would I go at this?
lone heartBOT
How would I go at this?
Show your work, and if possible, explain where you are stuck.
lone heartBOT
whole monolith
.close
lone heartBOT
Available help channel!
alpine sable
Let A be a random value in some range [u, l]. Let B be a sequence of n values taken randomly from range [u, l]. Given n, what is the probability that A is less than the sum of all elements in B?
lone heartBOT
Let A be a random value in some range [u, l]. Let B be a sequence of n values ta...
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
@alpine sable Has your question been resolved?
obtuse folio
lone heartBOT
obtuse folio
.close
waxen turtle
lone heartBOT
little star
substitute values of c and plot
waxen turtle
have you read the axes titles properly, the units specifically
Oh it's like flipped
Inside the parenthesis
waxen turtle
So c and d
proud belfry
I need to prove these numbers are coprime integers
lone heartBOT
I need to prove these numbers are coprime integers
lone heartBOT
@proud belfry Has your question been resolved?
proud belfry
No
stark scroll
I need to prove these numbers are coprime integers
you could probably use the euclidean algorithm to solve this problem
if you factor out n(3n+1) you can prove that n is comprime to 4n+1 and 3n+1 is coprime to 4n+1 by the euclidian algorithm
lone heartBOT
@proud belfry Has your question been resolved?
dark hearth
How do you find change of basis matrix?
lone heartBOT
How do you find change of basis matrix?
dark hearth
Doing a linear map $T$ mapping $\mathbb{P}^3 -> \mathbb{P}^3$
ocean sealBOT
KAVA
ocean sealBOT
Ann
vale wigeon
(just fixing your tex)
dark hearth
whoa
good to know
Need change basis matrix of $P_{\mathcal{B} \gets \mathcal{E}}$ to find matrix $T$ relative to $\mathcal{E}$
ocean sealBOT
KAVA
vale wigeon
what are B and E
dark hearth
B gonna be hard to type
E is standard polynomial
$\mathcal{E} = { 1, t, t^2, t^3}$
$\mathcal{B} = {2t^2 + t^3, 1+4t + t^2,1+3t + 2t^3,1-t+t^2-t^3}$
dark hearth
Im just having a hard time even knowing where to tackle the issue because I dont understand change of basis matrix
vale wigeon
you're not alone. i also find change of basis matrices confusing as to what exactly goes where
but presumably...
$[T]{\mathcal{B}} P{\mathcal{B}\gets\mathcal{E}} [x]{\mathcal{E}} = P{\mathcal{B}\gets\mathcal{E}} [Tx]_{\mathcal{E}}$
ocean sealBOT
Ann
dark hearth
This is why I hate linear algebra 😭
vale wigeon
eh the rest of it's fine
dark hearth
So many symbols I get lost in the sauce
vale wigeon
this change of basis matrix stuff is the worst of it
dark hearth
This is by far what Im struggling to understand the most
Not that Im not struggling in other areas
But this the most
Im confused how that helps me get proper results
vale wigeon
dark hearth
I will try mr sanderson video
lone heartBOT
@dark hearth Has your question been resolved?
dark hearth
Independent work required
long sorrel
can someone solve this
lone heartBOT
can someone solve this
nimble fern
can someone solve this
I bet someone can solve this
nimble fern
can someone solve this
what do you need help with?
long sorrel
Idk how to solve lmao
nimble fern
Idk how to solve lmao
did you try and draw it out
long sorrel
no
lone heartBOT
Show your work, and if possible, explain where you are stuck.
long sorrel
equations that dont work
nimble fern
i see
you can try thinking as:
there are 7 points, we randomly choose 2 and draw a line on them
how many ways can we draw these lines
long sorrel
49?
nimble fern
nah, it's 7 choose 2
nimble fern
first, we pick 1 point, there are 7 ways to choose 1 point
7
long sorrel
yes
nimble fern
secondly we pick 2nd point, there are only 6 ways to choose that point
6
finally, these two points has 2 situations that will be overlapping
e.g.
AB and BA
2
long sorrel
ok
long sorrel
7*6-2?
nimble fern
close
nimble fern
finally, these two points has 2 situations that will be overlapping
e.g.
AB and...
hint: every 2 points we choose has this situation
solar crown
how do you do trinomials again?
lone heartBOT
how do you do trinomials again?
gray isle
trinomial theorem, though i'd just apply binomial theorem twice
solar crown
like i would know how to solve it if it didnt have the 1 in there
gray isle
$(2x+y+1)^5 = ((2x+1) + y)^5$
ocean sealBOT
ℝαμΩℕωⅤ
solar crown
but that wouldn't really change anything, you'd still have to do it manually
gray isle
though i'd just apply binomial theorem twice
since the other factor doesn't have y, and you want y^3
you have less things to consider
solar crown
huh?
gray isle
what's your issue with this
solar crown
nvm i figured it out, its ok
i understand what ur saying now i just was confused on how to binomial that
lone heartBOT
@solar crown Has your question been resolved?
viral musk
F= XY+X'Y'+Y'Z simplify with OR and inverter gate
lone heartBOT
F= XY+X'Y'+Y'Z simplify with OR and inverter gate
alpine sable
what have u tried
also easiest way out is always a kmap, but I'm guessing that's not possible?
viral musk
what have u tried
uh i tried absorption but theres still AND present
alpine sable
I mean wait
the question seems a bit weird to me
when they say simplify with OR and inverter gates" they want you to implement an equivalent function using OR and inverter gates
meaning
viral musk
like uh, youre gonna implement the function without the AND gate
alpine sable
[
F = XY + X' Y' + Y' Z = \p{X' + Y'}' + \p{X+Y}' + \p{Y+Z'}'
]
ocean sealBOT
alpine sable
oh woops okay then that is like the answer
anyways it's just using the fact that [
\p{xyz}' = x' + y' + z'
]
ocean sealBOT
alpine sable
De morgan
viral musk
ohhhh i see
ohhhhhhhhh
i think i get it now though im finding de morgan a bit tricky to implement
thank you very much
alpine sable
i think i get it now though im finding de morgan a bit tricky to implement
mm in what sense?
viral musk
i understood how it works but i can't determine if it can be used it a function
alpine sable
well it's always a good idea if they want you to turn something from a minterm to a maxterm or vice versa
and in a situation similar to yours
viral musk
mhm but im not sure if we'll get to focus on simplifying them using certain conditions because its only just one part of the paper given
alpine sable
yeah later on you will be using k-maps either way
k-maps are a much more standardized method of simplifying Boolean expressions
viral musk
mhm but im not sure if we'll get to focus on simplifying them using certain cond...
the rest have either the expression or the diagram then we'll either make an actual circuit diagram that follows that expression, so most of my classmates and i are having trouble answering this part
viral musk
yeah later on you will be using k-maps either way
ohhhh i see
how does kmaps work?
if its alright
alpine sable
if its alright
erm that's going to take a bit to explain
hm
I can explain to you later since it's pretty hard for me to do so on phone
viral musk
mmm sure sure
alpine sable
there are some good websites online that explain it as well
also are u doing digital systems
out of curiosity
viral musk
would that be the same as digital logic? that's what our subject is about
alpine sable
would that be the same as digital logic? that's what our subject is about
do you do on-hands stuff
like coding stuff for FPGAs and such
or constructing the Boolean circuits on a breadboard
viral musk
just contructing on a breadboard, pretty fun to be honest
viral musk
are u in highschool or something
kinda
alpine sable
kinda
oh I see that's cool
nice they are teaching u this stuff early on
also sorry you can close this channel since your original question is answered and we are off topic now
Can I add you though, not often I see EEE aspirants around here lmao
viral musk
oh uh sure you can add me, but i'm not entirely an "aspirant" i just find this interesting but i'm not sure on whether i would actually take this course or not
viral musk
also sorry you can close this channel since your original question is answered a...
its alright i actually have another problem here that im currently solving
alpine sable
oh uh sure you can add me, but i'm not entirely an "aspirant" i just find this i...
ah I see yeah fair
alpine sable
its alright i actually have another problem here that im currently solving
okay no worries. still good etiquette in this server to send one question at a time in a channel for newcomers
so you can still open a new channel after Ur original question was done
lone heartBOT
Available help channel!
@alpine sable Has your question been resolved?
Available help channel!
alpine sable
help please
lone heartBOT
help please
vale wigeon
!status
lone heartBOT
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
ok then tell
alpine sable
first multilpied 4/sinx inside the bracket,
then,wrote it as e^ln( the whole thing )
then simplified it a bit ...
didnt got the answer
i did this just because i know when x approaches 0 in [ln (1+x)] /x = 1
so i did multiplied and divided by x, i am getting ans 1
vale wigeon
first multilpied 4/sinx inside the bracket,
what?
isn't 4/sin(x) the exponent on this thing??
vale wigeon
anyway, it is a good idea to look at the logarithm of your function instead of the function itself.
so you'll have $\ln(f(x)) = \frac{4}{\sin(x)} \ln\paren{\frac{(1+x)^{2/x}}{e^2}}$
ocean sealBOT
Ann
alpine sable
mhm
vale wigeon
which in turn can be simplified as $\frac{4}{\sin(x)} \paren{\frac{2\ln(1+x)}{x} - 2}$
ocean sealBOT
Ann
alpine sable
yeah
vale wigeon
do you see how to proceed from here
vale wigeon
at this point i would factor out 2 from the parentheses and combine the stuff inside into one fraction
which gives you $\frac{8}{\sin(x)} \cdot \frac{\ln(1+x)-x}{x}$
ocean sealBOT
Ann
alpine sable
alr
vale wigeon
and then taylor series
alpine sable
yeah i thought so
without using the expansion its not quite possible
hmm
yeah then i am good to go
thanks ann!
have a wonderful day
.close
tight pawn
Hi I don't know how to transform this
lone heartBOT
Hi I don't know how to transform this
remote escarp
try using $1-\cos(x)=2\sin^{2}(\frac{x}{2})$ and first remarkable limit
ocean sealBOT
Alisia
tight pawn
oh thanks i had forgot this one @remote escarp
tired mortar
where is the sihypn adj and opp in this triangle?
lone heartBOT
where is the sihypn adj and opp in this triangle?
kind egret
16 is opposite 7 is adjacent
vale wigeon
the hypotenuse is the side across from the right angle. the other two sides are called legs.
the opposite is the leg that's opposite the angle you're looking at
the adjacent is the leg that's touching the angle you're looking at
tired mortar
so basically like the normal one but flipped?
vale wigeon
yes. triangles can and do appear in any orientation whatsoever.
tired mortar
where is the sihypn adj and opp in this triangle?
the opposite of x is the opp?
vale wigeon
yes
tired mortar
x degrees
vale wigeon
the opposite is the opposite
tired mortar
alr
tough lintel
the opposite of x is the opp?
The opposite is opposite of the angle theta
the adjacent is adjacent to it IE its on the angles side
vale wigeon
this looks like a very badly written letter x
tired mortar
where tf did he get 66 degrees
lone heartBOT
@tired mortar Has your question been resolved?
tired mortar
i know
lone heartBOT
tired mortar
.reopen
lone heartBOT
✅
tired mortar
how do i know if i need to use sin cos or tan
snow cobalt
how do i know if i need to use sin cos or tan
do you know how to differentiate between what the hypotenuse is as compared to the base and hypotenuse?
tired mortar
i have no idea what u just said
snow cobalt
do you know what the hypotenuse is?
tired mortar
yeah
snow cobalt
in any given triangle, can you make out which is the hypotenuse?
frozen tree
hi
tired mortar
in any given triangle, can you make out which is the hypotenuse?
is the hypotenuse the one the part of the triangle that doesnt have anything written on it
because for 2 questions
snow cobalt
no- 😭
tired mortar
ive only seen opp and adj
snow cobalt
hypotenuse is the longest side of the triangle which is opposite to the right angle
tired mortar
so basically what i said
in all those questions the longest angle doesnt have anything written next to it
frozen tree
in all those questions the longest angle doesnt have anything written next to it
wrong
snow cobalt
in all those questions the longest angle doesnt have anything written next to it
really?
tired mortar
yeah
snow cobalt
could you reverify your statement?
tired mortar
16 is opposite 7 is adj
snow cobalt
both of these have 19.5 and 7.8ft written next to the hypotenuse respectively
frozen tree
you should know that the hypotenuse is opposite to the right angle
frozen tree
right
this is how you should label the sides
Hypotenuse side = Opposite to the right angle
Opposite side = Opposite to the angle given/angle you want to find
Adjacent = The remainding side
tired mortar
huh
frozen tree
Now try and reverify which is which
frozen tree
pardon?
dull dove
lone heartBOT
dull dove
No this isn’t an exam. I know what to do, just want to cross check my answers in case I’ve made a mistake. For the second one
For the one that says two different marbles I just need to find the probability for RB BR BY YB RY YR and add them up yeah?
Those two letters signify colors
arctic lintel
well there is a 5/16 chance of picking a blue marble on the first draw, since there are no replacements we can redraw with another 4/16 probability of getting a blue marble
tribal haven
well there is a 5/16 chance of picking a blue marble on the first draw, since th...
that’s with replacement
arctic lintel
For the one that says two different marbles I just need to find the probability ...
yeah you could, but sometimes its easier to find the probability that isn't happening then subtract that from 1
so in ur case find 1 - probability of getting 2 of the same marbles
which is easier as there are only 3 ways you could get the same marbles, RR, BB, YY
lone heartBOT
@dull dove Has your question been resolved?
dull dove
yeah you could, but sometimes its easier to find the probability that isn't happ...
So probability of picking of getting 3 of the same marbles, for red blue and yellow, add them together then subtract from 1?
dull dove
Does this to apply other things as well?
Where I just subtract from one
@arctic lintel
arctic lintel
yes
dull dove
Like?
arctic lintel
like flipping a coin 100 times, if u wanted to know the probability of not getting all the same face you could find the probability of getting only the same face then subtract it from one, as its much faster
lone heartBOT
@dull dove Has your question been resolved?
dull dove
like flipping a coin 100 times, if u wanted to know the probability of not getti...
Oh I see
Thanks
.close
smoky fulcrum
how did they turn the left side to right side?
lone heartBOT
how did they turn the left side to right side?
keen pasture
Throw a exp on each inequality and use that exp is strictly increasing
smoky fulcrum
Throw a exp on each inequality and use that exp is strictly increasing
so you mean like that?
keen pasture
so you mean like that?
The other way around e^0 and so on
hasty parcel
What is done in the last step? How do we get x(lnx-1)+c ? I think I get the constant, but why does -1 "transfer" into the logarithm?
lone heartBOT
What is done in the last step? How do we get x(lnx-1)+c ? I think I get the cons...
@hasty parcel Has your question been resolved?
brittle sequoia
What is done in the last step? How do we get x(lnx-1)+c ? I think I get the cons...
They just factorised
xlnx-x+c=x(lnx-1)+c
cosmic imp
3 = 2x^2 - 5x what do i do with the square i forgor 💀?
lone heartBOT
3 = 2x^2 - 5x what do i do with the square i forgor 💀?
gray isle
rearrange to general form
then proceed with factorisation or apply quadratic formula
cosmic imp
.close
amber quail
lone heartBOT
amber quail
hey im really lost
i figured you cant find out the angle under 20 degrees because you dont have the angle under C
i cant figure out what the next step would be
@craggy dagger
gray isle
!15m
lone heartBOT
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.
gray isle
also, read the second line in the question
amber quail
also, read the second line in the question
i dont know how that can help me
to what rules bisectors are connected
gray isle
do you know what bisect means?
amber quail
well that theres a line in the triangle which makes another triangle ?
gray isle
do you know what congruent mens
amber quail
no way omg
so the angle under 20 is also 20 and the length AD is also 27
cm
DB will also be the same on both right ?
CD = DB ?
gray isle
<DAB will be 20°
that's all you get from that
AD wil not be 27cm
CD will not be congruent to DB
determine the rest using trig
amber quail
okay i get it though so the triangle ABC has the angles 40 degrees and 90 degrees thats 130.
I do 180 - 130 to get the top angle which is 50
now I have the adjacent of ABC which is 27 cm, and the angle 40. I want the opposite so I use tan and divide the result by two to get the lenght x
@gray isle correct ?
it wasnt nevermind
.close
thick lynx
How would we get
lone heartBOT
How would we get
tacit arch
divide second row by a constant
thick lynx
divide second row by a constant
By d - c/a?
tacit arch
If you have the solution just show the whole thing
thick lynx
If you have the solution just show the whole thing
I'm writing it currently
thick lynx
Yeah
thick lynx
And 0 divided by anything is 0
yep
tacit arch
try it
thick lynx
try it
So that's the inverse
lol
is that correct?
This is basically what we did with @tall topaz and @fickle heath but now with arbitrary constants
fickle heath
I don't understand your first step
thick lynx
I don't understand your first step
c/a times the first row subtracted from the second row
Oh.
b is missing there
fickle heath
Not just that I'm afraid
deep pike
Im having a struggle with this derivative maybe because of the chain rule, can someone help me to solve it?
deep pike
i have an exam in 2 days and this is what i struggle the most because i can see how to solve most of derivatives of this level but i cant when it comes to chain rule i just dont get what i need to derivate
celest terrace
logarithmic differentiation
deep pike
logarithmic differentiation
how do i know that i should apply logarithmic differentiation
frigid snow
how do i know that i should apply logarithmic differentiation
when one variable is raised to another
frigid snow
i dont know the formula but i can explain how it works
deep pike
well i would appreciate a lot
because im messing up when its a avriable raised to another
and
frigid snow
okay
lets take an easier example
y=x^x
take log on both sides
log y = log(x^x)
now by using properties of log the x in the power can come outside
so log y = xlogx
now differentiate wrt x
and when everything is done put back the value of y
deep pike
i see
frigid snow
if you follow this method for g(x)^h(x), you should get the formula you mentioned above
deep pike
and lets say
that i have
a variable inside another variable and its raised to another variable
what method
frigid snow
a variable inside another variable and its raised to another variable
can you give an example
frigid snow
Im having a struggle with this derivative maybe because of the chain rule, can s...
something like this?
deep pike
or maybe (2x^3 + 5x^2)^4x+1
deep pike
something like this?
yes
frigid snow
i think you can still follow the same method
but
on the rhs you get log(a.b) change it to log a + log b
frigid snow
or maybe (2x^3 + 5x^2)^4x+1
hmm for addition inside
lemme think
oh yea you can still do the same thing
just differentiate using chain rule
for log(2x3 + 5x2)
deep pike
okok do you know the basics of the chain rule?
frigid snow
kindof yea
deep pike
im trying to find info that I can understand
because i know how to detect but i dont know how to apply
frigid snow
oh
okay
so
lets take the same example
d(log (2x^3 + 5x^2) )/dx
ignore the inner function
and just differentiate the log
differentiation of log(x) is 1/x
frigid snow
d(log (2x^3 + 5x^2) )/dx
so this becomes 1/(2x^3 + 5x^2)
now multiply this by the differentiation of the inner function
i.e. 6x^2 + 10x
deep pike
its only that i thought that it was more difficult
i understand it
thank you very much my friend
saving my maths
frigid snow
no probs
lone heartBOT
@deep pike Has your question been resolved?
orchid reef
Hello i get f(x)=x^4 -8x²+10
I have to proove that the derivative is 4x(x-2)(x+2)
tall topaz
First principle?
snow cobalt
did you try doing it?
orchid reef
did you try doing it?
Yes
snow cobalt
what did you get?
orchid reef
what did you get?
Wait do i have to factorise before derivate it ?
snow cobalt
Wait do i have to factorise before derivate it ?
no
take the derivative and tell me what you get
you don't see how -16x gives (x-2)(x+2) because you didn't try taking the derivative and factorizing it
orchid reef
you don't see how -16x gives (x-2)(x+2) because you didn't try taking the deriva...
4x -4x*4
snow cobalt
that's your derivative?
orchid reef
that's your derivative?
before i factorise my derivative is 4x-16x
snow cobalt
before i factorise my derivative is 4x-16x
Ok
Wrong
Your derivative of x⁴ came out to be 4x?
lone heartBOT
@orchid reef Has your question been resolved?
rocky summit
Can someone please guide me on how to solve this one?
I stopped halfway because I didn't feel that I was heading in the right direction
Also, I think one should be able to solve the exercise (the book doesn't have a solution unfortunately) without writing out all the terms of the conjugate expression (tho probably still w/ the help of Equation 2, since it was right before that problem)
lone heartBOT
Can someone please guide me on how to solve this one?
I stopped halfway because...
@rocky summit Has your question been resolved?
lavish cave
Can someone please guide me on how to solve this one?
I stopped halfway because...
are you allowed to use Taylor series or L'Hopitals rule?
rocky summit
are you allowed to use Taylor series or L'Hopitals rule?
hm, I think it's ok to use L'H in this particular exercise, but probably not Taylor series, since we didn't even cover it yet
but won't it be a mess if we use L'H?
lavish cave
but won't it be a mess if we use L'H?
nope
you only need to differentiate once as d/dx (x - 1) = 1
ah wait it's not in 0/0 form
rocky summit
why, it is indeed
lavish cave
why, it is indeed
do you mean sqrt(3 - x) instead
cause 8^(1/3) - sqrt(4) is clearly not 0
rocky summit
but $(8)^{1/3}={2^3}^{1/3}=2$
ocean sealBOT
Sweet Tea 🧋
dull dove
How do I determine a binary operation has no inverse/identity element?
near lagoon
Are you studying a specific operation?
near lagoon
What is it?
ivory pivot
near lagoon
Mm, I agree it has no identity element
dull dove
Why
near lagoon
I mean because if there was such an element e, we would have for instance a = a*e = (3a+e)/5-1 for any a in R, that is 2a+5=e for any a in R, which is impossible
So either I'm wrong or I don't see the point of the exercise last question
dull dove
Could you explain further
near lagoon
I am very sorry, but I have to go now, surely someone else will be able to help you quite soon though
dull dove
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cold trench
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glass lake
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glass lake
Can someone solve this please? Thanks
cinder egret
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twin nimbus
hearty coral
The number of fish in a lake decreases by x% each year. Given that the number of fish halves in 8 years, work out the value of x . Give your answer correct to 1 decimal place.
vale wigeon
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lone heartBOT
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
like how to I even write the equation? I did like (FX)/2 = FX*8 but that was wrong and I mainly just did random cuz I had no clue how to do it
vale wigeon
I did like (FX)/2 = FX*8
yeah this makes no sense
ok, so let's think this through
do you know how to calculate percentage increase/decrease?
hearty coral
do you know how to calculate percentage increase/decrease?
yes
vale wigeon
ok
so then tell me
let's say i give you a number A
how do you decrease it by x%?
tell me your process.
vale wigeon
this notation is either nonsensical or plain wrong
ok
this is not going well
let me try a concrete example
a pair of shoes used to cost 80 euro, but now there is a 7% discount on them. find the new price of the shoes.
hearty coral
isn't it just 80 * 0.93
hearty coral
ye
vale wigeon
decreasing a quantity by x% means multiplying it by (1 - x/100)
hearty coral
right
vale wigeon
what happens if you do that 8 times, once for each of the 8 years it takes for the fish population to halve?
hearty coral
^8 or huh
80 * 0.93^8 or idk if that's correxct it not, then just 80 * 0.93, the answer of that times 0.93 then the answer times that * 0.93 and so on until 8 times
i think there was a formula to make that faster but we haven't gone though that
.close
rigid mesa
lone heartBOT
rigid mesa
so i can find that as lim x->infinity we get -2
but i dont understand how to do the lim x->(-infinity)
buoyant saddle
well the sqrt is always positive
but the x-2 will be negative
and sqrt(x^2+2) is approximately the same as x-2 as x tends to infinity
the difference is x-2 is negative and the sqrt will be positive
so u get negative infinity - infinity
=negative infinity
rigid mesa
so u get negative infinity - infinity
that's one way to do it
but they did it in the following way
and i dont quite understand why they flip the sign in front of the square root in the denominator
like isnt (-infinity)^2 = infinity???
buoyant saddle
it’s wrong
is not infinity lol
i’m not even sure how they got to the second step
look at a graph
it goes to negative infinity
don’t use that solution whoever did it doesn’t know what they’re doing
buoyant saddle
if u substitute negative infinity into x u get negative infinity and into the sqrt u get positive infinity so negative infinity - positive infinity is negative infinity
ahh right
lol ur dumb
it’s right and yes it is
there’s no reason y u can’t substitute in here
u said u cant solve limits that way
u clearly can
any negative number squared is positive and the sqrt of any number is positive
so yes u can
there’s no reason y u can’t
yea u can lol
u have no idea what ur talking about
this scenario is perfectly fine
it isn’t indeterminate or infinity - infinity
it’s negative infinity minus infinity
which is negative infinity lol
NO
🤣
look at the graph
don’t comment when u clearly have no understanding of the question
if they’re both negative
it works
if they’re opposite sign then no
it’s negative infinity minus infinity
which is always negative
rigid mesa
hold on so
because it is determinate
it wont work to try and solve it using the usual method?
yes i undestood that but
if it was infinity
and not -infinity
buoyant saddle
when the plugged in negative infinity
in the numerator
for -4x
or wait
mh
mb
they divided
lemme see again
ahh wait
i think it’s because the sqrt of will always be positive but when they did difference of two squares they got rid of that?
no wait
it’s right
they just forgot that there -4 on top makes it negative
because u get -4/0
which is infinity
but since it’s -4
it’s negative
they did it right just forgot the negatige
rigid mesa
they did it right just forgot the negatige
hold on so on their last step they flip the sign in front of the square root. why do they do that?
buoyant saddle
yea i’m not sure
this is y i’d never do it this way
that doesn’t make much sense
buoyant saddle
no problem
rigid mesa
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alpine sable
how can i do this without trigonometry
lone heartBOT
how can i do this without trigonometry
fallen verge
AO = 2OP and use the special triangle
foggy current
Isn't it OP=2AO?
lone heartBOT
@alpine sable Has your question been resolved?
alpine sable
then?
wicked cape
How should I apply expansions to cos and sin?
lone heartBOT
How should I apply expansions to cos and sin?
@wicked cape Has your question been resolved?
wicked cape
the one for cos is y=-2cospix + 1
but the sin one is tricky
<@&286206848099549185>
wicked cape
<@&286206848099549185>
exotic belfry
but the sin one is tricky
arent sin and cos just a shift of pi/2 to each other?
exotic belfry
so, if you can express something in terms auf cos, you can do it also in terms of sin and vice versa.
wispy ibex
cos( pix) = sin(pi/2 - pix)
wicked cape
so, if you can express something in terms auf cos, you can do it also in terms o...
whagts theta in this case?
exotic belfry
write x instead of theta, if you have trouble with theta.
wicked cape
why do i subtract by pix?
exotic belfry
look at the graph of both and see that they are the same (but shiftd):
wicked cape
ok yes i get that, its just that pix is theta in this case?
i have trouble visualizing that
i understand the concept but you proposed the sin(90-theta) is cos therefore pix is theta but how does that correspond
ok nvm nah im just stupid
i get it lol
thanks
exotic belfry
as sin and cos are peridic you can use different "shift"-formulas between sin and cos. use thsi one you feel comfortable with.
wicked cape
makes sense thanks a lot
marsh horizon
can anyone help me with some math?
lone heartBOT
can anyone help me with some math?
slate jolt
dont ask to ask
just ask your question
this is a help channel in a maths discord dont hesitate to seek for help
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stoic cloud
this is a help channel in a maths discord dont hesitate to seek for help
Hey, would you be able to assist me in channel 32?
hearty coral
Hiro painted his room at a rate of 8 square meters per hour. After 3 hours of painting, he had 28 square meters left to paint. Let A represent the area (in square meters) left to paint after t hours. I don't really understand how to get the answer
hearty coral
one is supposed to use the formula y = kx+m
junior vigil
it would be easier to think of this as A=kt+m
hearty coral
oh yeah okay that makes sense
so like 28 = 8 * t -28
or uh
no that's not right
I kind of don't know how to think
junior vigil
well, it wouldn't be 8...think about it, the area left to paint is decreasing right?
@hearty coral
hearty coral
oh wait
so since he's painting the arera, it's less to pain after every hour
not more
right?
so it's uh
-8??
lone heartBOT
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Available help channel!
dawn geode
hello
alpine sable
hello
dawn geode
my cousin had an algebra question that i’m too lazy to answer for him
alpine sable
Send it
stark crow
theyre the same thing
stark crow
what's he saying?
dawn geode
he said they are different
he said that’s what his teacher said
tbh idek
i think he just has some hearing problems
.close
lone heartBOT
stark crow
theyre written differently but addition is commutative so no teacher would ever say they are
alpine sable
would the answer be y=-2x+7
Same shit your cousin's a bit stupid
dawn geode
ok so
in the question it says solve the literal equation for y
that’s what makes him think they’re different
alpine sable
can someone help me on mine?
dawn geode
this is occupied for my dumb cousin
go to #help-42 it’s open
alr anyway
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what
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wintry sun
Hey guys, someone knows how to deal with that?
lone heartBOT
Hey guys, someone knows how to deal with that?
wintry sun
Let 𝑀 be a 𝑚 × 𝑛 matrix and let rank(𝑀) = 𝑘. Show that there are then matrices
𝐴 ∈ Mat𝑚×𝑘 (ℝ) and 𝐵 ∈ Mat𝑘×𝑛 (ℝ) such that 𝑀 = 𝐴𝐵.
I have an idea but dont know how to prove it.
You take the first k independent vectors from the row space and k independent vectors from the column space. Then those form the two matrices
and then you just have to scale them to get M.
But how to proof?
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thin hull
Hint: When you multiply matrices AB, the jth column of AB will always be A multiplied by the jth column of B.
Try thinking through how you can choose the columns of B to get what you want.
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toxic mulch
Can anyone help with this proof?
lone heartBOT
Can anyone help with this proof?
rose sigil
Can anyone help with this proof?
!status
lone heartBOT
Can anyone help with this proof?
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
@toxic mulch Has your question been resolved?
celest stump
what does parity mean again?
just means m and n are either both odd or both even
right? @toxic mulch
I think if you want the easiest way of doing this is just breaking it up into two cases
oh i guess not because its an if and only statement
definitely easiest but would take a while
celest stump
i think a contrapositive would be easiest lol
without contrapositive i think you end up with like 3-4 cases lol
toxic mulch
Ohh okay
toxic mulch
i think a contrapositive would be easiest lol
would there only be one case with contrapositive?
celest stump
i think so
toxic mulch
My prof is challenging us with these really hard questions that I have never even seen anything like this before. Soo kinda suffering ngl...
Anyways
celest stump
because you would show that m and n dont have parity if and only if 2 is not a divisor of m+n
oh do you know what the divisor sign means?
| this
celest stump
because I dont think this would be so hard conceptually to just write it out, like even in your head pretty quickly
yes its essentially that
i mean you can pretty quickly see that if m and n are even then obviously 2 divises it
then if its odd
then we have 2c+1 + 2k+1
2c+2k+2
2(c+k+1)
c+k+1 are integers
the reason why so many cases come is because its an if and only statement
which means you need to show that its not true when there is no parity
which idk how true this is but i think that might mean you would have to show when its odd n is odd and when n is even, then conversly when m is odd and when m is even
i might be thinking about that wrong actually
which would mean direct proof is the same efficiency as contrapositive
toxic mulch
Ohh so then should i try with a direct proof then?
celest stump
yeah i think it doesnt matter which you do
im sure one proof method would make it easier
ohh
contradiction i think can skip a step
toxic mulch
This is what I have but idkk
celest stump
cuz if you assume m and n have parity
then assume 2 does not divide m + n
then you just need to show the case where they have even/odd parity
or maybe not i think the whole if and only if part is messing me up
junior vigil
This is what I have but idkk
i would do the direction you're doing by contradiction, then do the other direction by cases, (i.e. both even, both odd)
toxic mulch
i would do the direction you're doing by contradiction, then do the other direct...
Sorry what are the two directions?
junior vigil
iff means you must prove that
- if m and n have same parity, it implies 2|(m+n)
- if 2|(m+n), it implies m and n must have same parity
toxic mulch
Ahh I see will try that thanks!
celest stump
i would do the direction you're doing by contradiction, then do the other direct...
if you did direct proof, when you go through all the cases when you say m and n don't have parity do you have to check when m is odd, and when n is even, and then vise versa?
junior vigil
if you did direct proof, when you go through all the cases when you say m and n ...
yeah, but you can sorta wave that away with a WLOG thing, addition commutative and what not.
toxic mulch
I'm very confused atm
junior vigil
if you did direct proof, when you go through all the cases when you say m and n ...
it would probably be safer to go through those cases though yes
celest stump
I'm very confused atm
with what we're saying or the work
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spice stream
lone heartBOT
spice stream
Quick
west cipher
good luck
spice stream
Menn
zealous lichen
draw a graph first
spice stream
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spice stream
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