2x is x + x
#help-36
shell mountain
charred vigil
x^2
tawdry valve
Hi guys
How do you get the derivative of this
With steps
final saddleBOT
Hi guys
How do you get the derivative of this
With steps
tranquil pine
does anyone know how to make quadratic equation to standard for like
x²+6x+9=0
tawdry valve
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snow kindle
Is $$AA^T$$ necessarily symmetric?
final saddleBOT
Is $$AA^T$$ necessarily symmetric?
soft zealotBOT
THEBIGTHREE
shell mountain
What does it mean for a matrix to be symmetric?
snow kindle
Its transpose equals itself
So that’s only true if it’s also commutative?
*AT and A are commutative
shell mountain
Well, what's the transpose of AA^T?
snow kindle
A^T * A
snow kindle
Ohh right it swaps oml
A^T^T * A^T = AA^T so yeah
Then if it was commutative as well wouldn’t that mean A must be symmetric as well?
shell mountain
A^T^T * A^T = AA^T so yeah
Based on this, it's symmetric regardless of if it's commutative or not
snow kindle
Then if it was commutative as well wouldn’t that mean A must be symmetric as wel...
AA^T is symmetric yes, but I mean the matrix A
shell mountain
Well, there's only a small subset of matrices that commute with all others
Not finite
But small
Relatively speaking
snow kindle
Well I know if A and B are commutative and symmetric their product is symmetric
So would it work in reverse?
If their product is symmetric and they’re commutative then they’re both symmetric
Or at least maybe in the special case where B = A^T
final saddleBOT
@snow kindle Has your question been resolved?
final saddleBOT
@snow kindle Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
lost stump
If a bacteria is multiplied by 2,6 times a hour, and there starting count is at 5000. We want to know how much bacteria is after 9 hours, so don't you do 5000*2.6^9?
final saddleBOT
If a bacteria is multiplied by 2,6 times a hour, and there starting count is at ...
lost stump
vital crag
yes
fast grotto
ur book isnt even using the right given values 💀
vital crag
books have erratas for their corrections
brave olive
Why these two d-dimensional vectors multiple together would becomes a 1 dimensional answer? Thank you
final saddleBOT
Why these two d-dimensional vectors multiple together would becomes a 1 dimensio...
vital crag
Why these two d-dimensional vectors multiple together would becomes a 1 dimensio...
do you know dot product?
also which two vectors?
there's like 20 variables
brave olive
do you know dot product?
yes. dot product means one row element of one matrix multiples one column elements of another matrix. and the size of the matrix would depends on the #row of one matrix, and #column of another matrix
brave olive
also which two vectors?
E and A are the nodes and each node contains d variables that aims to differentiate themselves from other nodes
vital crag
E and A are the nodes and each node contains d variables that aims to differenti...
E and A are d-dimensional vectors?
where in that image does their dot product become one dimensional?
brave olive
yes, the descriptor (embedding) of E and A are d-dimensional vectors
vital crag
or any type of operation.
vital crag
there's no description of $f_r$ so how can we know?
soft zealotBOT
riemann (eric tao for honorable)
vital crag
dot product is one such example
brave olive
what is the meaning of /rightarrow?
vital crag
or are you asking about $f_{r_1}$?
soft zealotBOT
riemann (eric tao for honorable)
brave olive
yes. That LHS to RHS is weird
vital crag
for three sets $X, Y, Z$, $f: X \times Y \mapsto Z$ means a function $f(x,y)$ takes elements from $X$ and $Y$ and output to $Z$
soft zealotBOT
riemann (eric tao for honorable)
brave olive
for three sets $X, Y, Z$, $f: X \times Y \mapsto Z$ means a function $f(x,y)$ ta...
R means one-dimensional real number isn't it. Then I suspect R^d \times R^d --> R^1? which is not make sense for me
vital crag
R means one-dimensional real number isn't it. Then I suspect R^d \times R^d --> ...
the dot product does exactly this
e.g. $X=Y=\R^d$ and $Z = \R$.
soft zealotBOT
riemann (eric tao for honorable)
vital crag
then if $x = (x_1, x_2, ..., x_d)$ and $y=(y_1,y_2, ..., y_d)$
soft zealotBOT
riemann (eric tao for honorable)
vital crag
$f(x,y) = x\cdot y = x_1 y_1 + x_2 y_2 + \ldots +x_d y_d \in \R$
soft zealotBOT
riemann (eric tao for honorable)
brave olive
$f(x,y) = x\cdot y = x_1 y_1 + x_2 y_2 + \ldots +x_d y_d \in \R$
The result is d \times d dimension isn't it
vital crag
no
i encourage you to read these examples
https://tutorial.math.lamar.edu/classes/calcii/dotproduct.aspx
Examples 1 and 3
brave olive
oh, so after vector takes dot product, it becomes scalar. @vital crag
vital crag
yes. dot product means one row element of one matrix multiples one column elemen...
yea your understanding of dot product here is slightly misguided. dot products are defined independent of matrices.
brave olive
i am not sure R^d \times R^d is a dot product. Maybe it is more like a cross product by looking its cross symbol
vital crag
i encourage you to read these examples
https://tutorial.math.lamar.edu/classes/c...
just forget matrices and read this
vital crag
**riemann (eric tao for honorable)**
read this
brave olive
yea your understanding of dot product here is slightly misguided. dot products a...
so after vector takes dot product, it becomes scalar. so that's why R^d x R^d --> R ?
It has a formula like that
final saddleBOT
@brave olive Has your question been resolved?
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ruby quarry
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ruby quarry
I've started of with the left hand side of the equation
tan^2(A+pi/4) = (tan(A)+tan(pi/4)/1-tan(A)tan(pi/4))^2
carmine hull
scarlet sequoia
there are 2 ways to do this, the tideous but safe way and the dangerous but efficient way
ruby quarry
ooh interesting
if the tedious way expanding it because I really dont want to do that
scarlet sequoia
The tideous way involves starting from the RHS and use formulas on sin = sqrt(1-cos^2) and sign issues and blablabla...
the quicker way :
start from the LHS
tan = sin/cos
ruby quarry
tan^2(A+pi/4) = (tan(A)+tan(pi/4)/1-tan(A)tan(pi/4))^2
replace each tan with sin/cos?
rare cradle
i would now expand
rare cradle
yea now get it in terms of sin and cos
rare cradle
tan^2 + 1 = sec^2 btw
ruby quarry
ohhhh thats where this question was going
rare cradle
tan^2 + 1 = sec^2 btw
this isn't necessary to use tho
ruby quarry
it makes it much quicker tho right?
rare cradle
sure a bit quicker
ruby quarry
= (1/cos^2A + 2sinA/cosA)/(1/cos^2A - 2sinA/cosA)
I need to get rid of the cos now somehow
rare cradle
get rid of nested fractions
rare cradle
yes
ruby quarry
what do I replace the cosA with?
rare cradle
= 1+2sinAcosA/1-2sinAcosA
compare this with the rhs
do you know a double angle formula for sin?
ruby quarry
back with another one
final saddleBOT
back with another one
ruby quarry
this one is harder I think because I can't use the compound angle identity I used before
I'm thinking of changing the tan(3A) into tan(A+2A)?
scarlet sequoia
how about sin(4A) into sin(A + 3A)
ruby quarry
sure, I'll work with the RHS then
= sin3AcosA + cos3AsinA/cosAcos3A
factor out cosA?
oh wait u can't do that
ruby quarry
ok
= sin3AcosA/cosAcos3A + cos3AsinA/cosAcos3A
= tan3A + tanA
wow
it was that simple...
rare cradle
indeed
rare cradle
how about sin(4A) into sin(A + 3A)
main trick was this
ruby quarry
main trick was this
yeah thanks @scarlet sequoia
scarlet sequoia
you're welcome
ruby quarry
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tranquil pine
how would i express the end statement with the following predicates
final saddleBOT
how would i express the end statement with the following predicates
rare cradle
is there some kind of set for metal spheres and cubes?
tranquil pine
nah
you have to use univeral/existential quantifiers
this is what im thinking so far but i dont know which if either of them is correct
desert mantle
so far you have (more or less) "for every cube there is a heavier metal sphere"
that's the wrong way around
scarlet sequoia
Yes, your statement begins with "there is" so your mathematical statement should begin with there exists
I'll write A and E instead of "for every" and "there exists"
it gives : ExAy sphere(x)^metal(x)^cube(y)=>heavier(x,y)
tranquil pine
it gives : ExAy sphere(x)^metal(x)^cube(y)=>heavier(x,y)
how would this compare to the statement ExAy sphere(x)^metal(x)^cube(y)=>heavier(x,y)
scarlet sequoia
oh right sorry
tranquil pine
also i am slightly confused about quantifier terminology
scarlet sequoia
you have the correct terminology
scarlet sequoia
how would this compare to the statement ExAy sphere(x)^metal(x)^cube(y)=>heavier...
this is the correct statement
tranquil pine
from what i understand the universal quantifier includes every single element of a set
but then how could every single element of the set is a cube while a y being a sphere existing as well
scarlet sequoia
But the problem is you have to put things in brackets
tranquil pine
this is the correct statement
waht deems this correct and not the original with the second and statement?
scarlet sequoia
ExAy sphere(x)^metal(x)^(cube(y)=>heavier(x,y))
This is correct
or rather, the order of your statements matter as well
Scratch every statement i have written beforehand
tranquil pine
ExAy sphere(x)^metal(x)^(cube(y)=>heavier(x,y))
i can see how that is more "proper" but is that just to improve the flow of the statement or does it have a difference in meaning too
scarlet sequoia
Ex sphere(x)^metal(x) Ay cube(y)=>heavier(x,y)
This last statement reads : "There exists something that is a metal sphere, such that for everything that exists, IF it is a cube THEN it weighs less than the metal sphere"
tranquil pine
hmm
scarlet sequoia
ExAy sphere(x)^metal(x)^(cube(y)=>heavier(x,y))
this statement is also correct, but it is put in a different way
tranquil pine
how come the statement without the parentheses around cube and heavier is incorrect?
scarlet sequoia
It is not incorrect, it is just not well-defined
tranquil pine
I see
I appreciate the help
one last thing
why is it necessary to replace the and statement with an if then
scarlet sequoia
So you're asking to compare to this : ExAy sphere(x)^metal(x)^cube(y)^heavier(x,y)
tranquil pine
So you're asking to compare to this : ExAy sphere(x)^metal(x)^cube(y)^heavier(x,...
yeah
scarlet sequoia
So you're asking to compare to this : ExAy sphere(x)^metal(x)^cube(y)^heavier(x,...
remember that A^B implies A
scarlet sequoia
So you're asking to compare to this : ExAy sphere(x)^metal(x)^cube(y)^heavier(x,...
in particular, this statement implies that ExAy cube(y)
tranquil pine
So you're asking to compare to this : ExAy sphere(x)^metal(x)^cube(y)^heavier(x,...
oh
is it just that this implying that everything A is a cube is why this is wrong
y*
everything y is a cube
scarlet sequoia
yeah basically it implies everything is a cube
tranquil pine
which consequently leaves no room for x to be a sphere
correct?
which would be a logical inconsistency
scarlet sequoia
Yeah the logical inconsitency is ExAy sphere(x)^cube(y)
There can't exist a sphere if everything that exists is a cube
tranquil pine
oh i get it now
so regardless the universal quantifer includes everything in the set?
scarlet sequoia
yes
tranquil pine
which is why this is incorrect because x HAS to be in y
right
because y is the universal set
and no element can exist outside of it
scarlet sequoia
yes
snow nacelle
soo
snow nacelle
i have the problem down to
lim x->infinity of x-2/x(x-1)
what do i do from here ?
iv been told 2 things
that infity over infity is 1 and that infinity over infinity^2 is 1/infinity
scarlet sequoia
that infity over infity is 1 and that infinity over infinity^2 is 1/infinity
those statements are usually false inducing, take them very lightly
scarlet sequoia
So
x-2 is what we say "equivalent" to x when x->infinity
meaning that lim x->infinity of x-2/x = 1
oh wait
scarlet sequoia
lim x->infinity of x-2/x(x-1)
can you clarify the parentheses and such on this formula ? it could be confusing
silver swan
that infity over infity is 1 and that infinity over infinity^2 is 1/infinity
In the idea of a limit 1/infinity approaches 0
snow nacelle
yea one second lemme pull out the paper again
(x-2)/x(x+7)
thats if i even factored it correctly lol
silver swan
Well for this it’s helpful to distribute the x
silver swan
Yes
As in the case of limits at infinity
The biggest power is essentially all we care about
we ignore everything else
so this would just be 1/x^2
As x^2 is the highest power
And it would be 1/infinity
snow nacelle
okay so the second person was right then lol
silver swan
Think about it as you have a number growing to infinity
It will approach 0
As the denominator blows up
So as the limit goes
It is 0
snow nacelle
oh okay i gotcha
so for
(x+2)/(x+1) as x-->infinity
what would that be ?
cause i had infinity / infinity for that =1
silver swan
Infinity over infinity is undefined
Do you know l’hopital
Rule
This limit does in fact =1
or I should ask do you know derivatives yet or have you only started limits
silver swan
no
snow nacelle
cause thats the answer the teacher wrote is 1 but she didnt write how she got 1
silver swan
for example 3x/x
As it approaches infinity
Is 3
that is infinity over infinity
Well l’hopitals rule let’s us take 2 indeterminate forms
snow nacelle
hmm
silver swan
And take their derivative
Which is equal to the value of the original limit
You’ll learn all this soon
snow nacelle
haha hopefully she made this overly complicated
silver swan
And then the derivative of 3x is 3 and the derivative of x is 1
So we have 3/1
Which is just 3 so our limit is 3.
snow nacelle
this question had 6 parts and i got 2 right and the rest partially right so i was just trying to figure out how to do them correctly
so we just take the derivative of (x+2)/(x+1) so 1/1
thats why the answer is one huh
i hate that this all makes sense hahah i can justify any of these being 1 but knowing which real reason is hard haha
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Available help channel!
young birch
final saddleBOT
young birch
help
livid ice
Do you know how to find an inverse function?
young birch
yes i do
livid ice
Ok start by finding the inverse of f
We'll have to just call k by that name
Nonetheless k is just a number you can still move it around like any other
livid ice
Yes that's correct personally i would have divided by k first
But your expression is equivalent
young birch
ouu yeah thats right
livid ice
So that expression is f inverse of x
They told us something else that you can use to create an equation
final tangle
personally, explicitly finding the inverse function is unnecessary
young birch
im so confused
livid ice
F inverse of -2 is
The inverse function when x = -2
final tangle
considering the definition of inverse,
f^-1(-2) = 3,
when x = -3, f(x) = -2
i.e f(-3) = -2
young birch
do i have to plug in anything 😭😭
young birch
Do you know how inverses work
i learned it like 2days ago so im kinda confused
young birch
yes
lean magnet
you have your inverse equation right?
young birch
yes
lean magnet
and you have the knowledge that inverse f(-2) = -3
meaning that in the inverse equation, when you plug in -2 for x, the result is -3
young birch
OHHH
OMG
wait
the answer is 2
right
how do i close this channel
thank you sat
young birch
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granite shuttle
how do i do this?
final saddleBOT
how do i do this?
granite shuttle
I have F_net = F_down - F_up
ma = 187 - 0.8|v|
a = (1/m)(187 - 0.8|v|
@granite shuttle Has your question been resolved?
granite shuttle
<@&286206848099549185>
tranquil pine
Hi how would I find the next two numbers in this sequence? -1,4,-9,16,-25
sly hare
fibonacci
sly hare
Hi how would I find the next two numbers in this sequence? -1,4,-9,16,-25
I have a file about this if u want.
proven nebula
(-1)^n/(n^2)
tranquil pine
So how would I set up the formula for this problem in particular?
proven nebula
(-1)^n/(n^2)
dont know how to explain how to get that
tranquil pine
What would n be then?
final saddleBOT
@tranquil pine Has your question been resolved?
frail osprey
I need help with this page pls
final saddleBOT
I need help with this page pls
frail osprey
<@&286206848099549185>
final saddleBOT
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.
final saddleBOT
<@&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.
@frail osprey Has your question been resolved?
barren viper
can someone help me with this
final saddleBOT
can someone help me with this
barren viper
im having trouble finding how many prefer chess and taekwondo but not swimming
<@&286206848099549185>
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versed sinew
idk how to do any of this 💀 pls help
final saddleBOT
idk how to do any of this 💀 pls help
versed sinew
I also have to explain all my steps... I don't know where to start, someone please help
final tangle
consider geometric properties related to vertical angles and angle sum on a line
the rest is algebra
versed sinew
IDK WHAT THAT MEANS 😭
<@&286206848099549185> pls idk how to do this stuff
pls I just started geometry and I'm already behind
🙁
dawn elk
So did you look up this?
consider geometric properties related to vertical angles and angle sum on a line
final saddleBOT
@versed sinew Has your question been resolved?
versed sinew
So did you look up this?
> consider geometric properties related to vertical ang...
just did ty!
final saddleBOT
dawn elk
just did ty!
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Available help channel!
calm bone
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frigid sierra
final tangle
ln e^x=x
that looks directly applicable here
calm bone
the anwer is just 6?
final tangle
answer to the whole question, no
calm bone
oh
final tangle
ln e^6 = 6
is just 6 though
calm bone
ln e^6 = 6
is just 6 though
would i just type in
final tangle
type in what
final tangle
yes
final saddleBOT
calm bone
cool
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Available help channel!
pallid spoke
final saddleBOT
pallid spoke
vital crag
it's just geometric series?
vital crag
what's your a, r ?
pallid spoke
got it
just had my a and r mixed up
thanks riemann
@tranquil pine #help-19
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final saddleBOT
final saddleBOT
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clear jacinth
Hello
rare cradle
What's I
clear jacinth
irracional
I don't know what is the letter you use in your country
here we use I
Wait let me organize this
soft zealotBOT
everytimecrusader
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
everytimecrusader
everytimecrusader
clear jacinth
After that i tried applying induction but i was not really sure how to insert that info in to the induction proof...
unique aspen
without going into much detail, why are you using primes
if you only consider primes, aren't you missing out on fractions like 1/6
you should rethink your whole approach
clear jacinth
How would you do it
unique aspen
contradiction
i mean there's very standard proofs online, if you just want a solution
clear jacinth
Nah im trying to learn
Im using primes to proof $\sqrt[]{2}$ is racional, since racional numbers can me writeen as fractions
soft zealotBOT
everytimecrusader
clear jacinth
And try to get a contradiction with that
plain sedge
I had a random thought if X^X < X! has a solution and if yes, then what would be the best method to find it, because ofc you can just make a graph, but that wouldn't be very efficient and would take a long time, especially in case there is no solution. My next idea was to write both sides down using logarithms, but cant think of a way to turn a factorial into a logarithm
final saddleBOT
I had a random thought if X^X < X! has a solution and if yes, then what would be...
plain sedge
I wrote a simple program to calculate the answer, but since i am working with big numbers, its gonna take a long time and again there is a chance there is no answer, meaning it is gonna run forever
unique aspen
I had a random thought if X^X < X! has a solution and if yes, then what would be...
$log(x!) = log\left(\prod_{i=1}^x i \right) = \sum_{i=1}^x log(i)\
log(x^x) = xlog(x) = \sum_{i=1}^x log(x)$
soft zealotBOT
Kaisheng21
unique aspen
maybe this will help
plain sedge
not really
hearty zephyr
x! = x(x-1)(x-2)...(2)(1)
log(MN) = log(M) + log(N)
So your log(x!) is the sum of log(i) where i goes from 1 to x
plain sedge
well yeah,but how do I use that info to solve the inequality
unique aspen
ok
plain sedge
I may just be stupid, but I dont see it
unique aspen
so log(x!) is the sum from i = 1 to x of: log(i)
and log(x^x) is the sum from i = 1 to x of: log(x)
so compare log(i) and log(x)
which one is gonna be bigger
if i is a number between 1 and x, inclusive
plain sedge
yeah that makes sense ig
plain sedge
like?
unique aspen
i know they're equal for x = 1
so i was thinking of differentiating ^-^
if the derivative of x^x was strictly greater than the derivative of x!, then after x = 1, x^x would have to be strictly greater than x!
but that's way more work
plain sedge
so do we conclude the logarithm is the most effective?
unique aspen
yes
plain sedge
yay
unique aspen
hope it all makes sense
leaden barn
the following statement is about Laplace's expansion
final saddleBOT
the following statement is about Laplace's expansion
final saddleBOT
@leaden barn Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
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shell mountain
We can't do shit if you don't post the question
Unless you need us to call an ambulance or sumn
zenith barn
do u know the point slope formula?
so then what are y x and m
is it?
coordinate planes are (x,y)
...
final saddleBOT
Help on 53
final saddleBOT
@clever marlin Has your question been resolved?
clever marlin
It worked when i converted the measurements to feet but not inches
<@&286206848099549185>
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@clever marlin Has your question been resolved?
high ledge
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@high ledge Has your question been resolved?
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@high ledge Has your question been resolved?
high ledge
<@&286206848099549185>
soft zealotBOT
3317
high ledge
halp pls WAAAA WAAAAAAAAA
ionic moon
I'm not sure if I am doing right
final saddleBOT
I'm not sure if I am doing right
tender raven
u are right
final tangle
its not recommended that you explicitly write the QF with the original variables a,b,c as they conflict with the variables of you question
best to skip writing the formula and jump straight to plugging stuff in
also full formula is unecessary
you only really need to focus on the discriminant
work is also incomplete
final saddleBOT
@ionic moon Has your question been resolved?
ionic moon
work is also incomplete
yes ik, i thought that i went wrong somewhere but u guys are saying its correct so ill continue it
thank you for the help
.close
final saddleBOT
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tranquil pine
I'm never exactly sure where the intuition for questions like this come from. I can solve an Initial Value problem, but in the second image, which contains the solution, how is it obvious that the answer to this question involves knowing there needs to be a rectangle that contains the point (0,1) in which these functions are continuous? Why is the partial a function we must consider? How do we validate these functions are continuous in some arbitrary rectangle? How do they arrive at this soln? I want to get better at the intuition for questions involving intervals and continuity.
final saddleBOT
I'm never exactly sure where the intuition for questions like this come from. I ...
tranquil pine
I see, thank you @hearty zephyr. I will check out Paul's notes and then see if I missed that section when reviewing. (Test is coming up next week). If I have any further questions around the topic after should I create a new question or just DM you?
hearty zephyr
create a new question in case i'm not around
pseudo ibex
Moh wants to color an n × m chess grid with black and white such that
everytime you choose a 2 × 2 square inside you get 2 whites and 2 blacks.
How many ways are there to do this?
final saddleBOT
Moh wants to color an n × m chess grid with black and white such that
everytime ...
pseudo ibex
@silver dew
silver dew
<@826318983413366824>
2^m+2^n-2
Divide into two cases:
First no two adjacent square at the same row having the same color
Then each row color appears alternately, so 2^n ways
Second case there are two adjacent square at one same row
Then color of squares of those two columns are determined by those two blocks
You can easily see that now colors on each column appears alternately
So 2^m-2 ways since you need to rule out the 2 cases where colors of a row is alternate
So in the end 2^n+2^m-2
QED
pseudo ibex
thnk you
silver dew
Np
pseudo ibex
.close
tranquil pine
how to solve this?
final saddleBOT
how to solve this?
amber holly
For the first limit try multiplying the expression by (sqrt(x^2 - 5x) + x)/(sqrt(x^2 - 5x) + x)
For the second limit notice that it doesn't exist
tranquil pine
The second limit doesn't exist
It's the first one
I mean.. I was trying to solv ethe first one
tranquil pine
For the second limit notice that it doesn't exist
.
amber holly
For the first limit try multiplying the expression by (sqrt(x^2 - 5x) + x)/(sqrt...
Yeah just do this
tranquil pine
I'm trying, w8
tranquil pine
For the first limit try multiplying the expression by (sqrt(x^2 - 5x) + x)/(sqrt...
But this is 1
amber holly
Yes, we're multiplying it by 1 so that it doesn't change
tranquil pine
Yes, we're multiplying it by 1 so that it doesn't change
.
amber holly
That's not how you cancel terms out
Now should you have cancelled anything there yet
Use this: (sqrt(x^2 - 5x) - x)(sqrt(x^2 - 5x) + x) = x^2 - 5x + x^2
Because (a - b)(a + b) = a^2 - b^2
The x^2 terms cancel out so the entire expression becomes this
final saddleBOT
@tranquil pine Has your question been resolved?
Available help channel!
@granite shuttle Has your question been resolved?
granite shuttle
.close
tawdry pawn
Web assign has the correct answer as 7, -2 however I came up with -7, 2
I have foil'ed them back, and still found my answer to be correct. Am I doing something extremely wrong with signs?
final saddleBOT
Web assign has the correct answer as 7, -2 however I came up wit...
wary helm
How did you get to those answers?
tawdry pawn
wary helm
Your answer is that on the right?
tawdry pawn
yes
wary helm
Their factorization is wrong, yours is correct
final saddleBOT
sterile cypress
weird because delta : 81
x1 : (-(-5) - 9)/2 = -2
x2 : (-(-5) + 9)/2 = 7
maybe that's where i'm wrong, if that's the case you saved me 👌
final saddleBOT
Available help channel!
final saddleBOT
zenith barn
what have u tried so far?
thin bay
final saddleBOT
thin bay
Does anyone know what this formula represents?
dawn elk
Not if you give context
tranquil pine
possibly something to do with a difference of normally distributed variables https://en.wikipedia.org/wiki/Sum_of_normally_distributed_random_variables#Independent_random_variables
tranquil pine
Not if you give context
It’s for a lab involving reaction times
final saddleBOT
@thin bay Has your question been resolved?
lavish niche
You have to find the area of the trapezium right?
(a+b/2)h
a and b are the two parallel sides
h is height
Try it
You only have to substitute the values
dawn elk
<@&268886789983436800>
final saddleBOT
@tranquil pine Has your question been resolved?
granite shuttle
final saddleBOT
granite shuttle
i have the magnitude of del f
and i multiplied it with cos(theta) but that was wrong apparently
rain compass
the directional derivative in direction $u$ is $\nabla f \cdot u$
soft zealotBOT
maximo
rain compass
so in your case you want $(\nabla f)(1,3) \cdot (\cos\theta, \sin\theta)$
soft zealotBOT
maximo
granite shuttle
so in your case you want $(\nabla f)(1,3) \cdot (\cos\theta, \sin\theta)$
how did u know that u is cos theta sin theta
what i did is
rain compass
the direction of theta = pi/3 is exactly the vector (cos theta, sin theta)
granite shuttle
$$ \nabla f (x, y) \cdot \vec{u} = |\nabla f (x, y)| |\vec{u}| cos (\theta)$$
soft zealotBOT
ibzi
rain compass
that theta is different from the theta you’re given
the theta in the cosine is the angle between u and delf(x,y)
final saddleBOT
@granite shuttle Has your question been resolved?
granite shuttle
the theta in the cosine is the angle between u and delf(x,y)
oh so so what is this theta exactly?
granite shuttle
the one in the question
rain compass
the direction for the directional derivative
recall that for (r,theta) -> (x,y), we have
x = rcos(theta), y = rsin(theta)
so for theta = pi/3, the direction for the derivative is along (cos(pi/3), sin(pi/3))
in particular, when taking directional derivatives we care about the unit vector in that specific direction, so for an arbitrary theta, the directional derivative is:
$$(\nabla f)(x,y)\cdot(\cos\theta, \sin\theta)$$
soft zealotBOT
maximo
granite shuttle
oh so we're assuming this is a polar coordinates thingie
rain compass
if you’re told “in the direction theta = …” you are assuming the line with slope tan(theta)
granite shuttle
if you’re told “in the direction theta = …” you are assuming the line with slope...
ohh i see!
and r is one because its unit right?
makes sense!
thank u soo muchh!
rain compass
r could be 20, but we only care about the unit vector so we just take (cos theta, sin theta)
like, the directional derivative along (cos theta, sin theta) and (100cos theta, 100sin theta) is the same since we only take the unit vector in that direction
past mesa
is (3^x)^2
9^2x
Or 9^(x²)
final saddleBOT
is (3^x)^2
9^2x
Or 9^(x²)
shy steeple
$(3^x)^2=3^{2x}$
soft zealotBOT
alshfik
shy steeple
wdym
shy steeple
maybe you're thinking of $(3x)^2=3^2x^2$
soft zealotBOT
alshfik
past mesa
Yh
shy steeple
ok, problem is solved?
neon slate
is (3^x)^2
9^2x
Or 9^(x²)
neither of those is correct
neon slate
but it is equivalent to 9^x
void crest
**alshfik**
like
past mesa
So (3^x)^2 isn't 3^2x ?
neon slate
3^(2x) is right yeah
void crest
$(3^x)^2=(3^x)(3^x) = 3^{2x} = (3^2)^x = 9^x$
grim nebula
$(3^x)^2=(3^x)(3^x) = 3^{2x} = (3^2)^x = 9^x$
D:
shy steeple
huh?
past mesa
I was given
(3^x)²(3^y)=m
(3^x)(3^y)=n
grim nebula
wtf is the second last one
soft zealotBOT
past mesa
Is 3^-x=n-m
void crest
sorry
grim nebula
lol
void crest
shy steeple
oh right is correct
void crest
wtf is the second last one
trick question
neon slate
in short, you can apply the exponent in any order, or both exponents at once multiplied together
past mesa
Is 3^-x=n-m
?
shy steeple
Is 3^-x=n-m
i don't know what n and m is
grim nebula
I was given
(3^x)²(3^y)=m
(3^x)(3^y)=n
they are here
void crest
I was given
(3^x)²(3^y)=m
(3^x)(3^y)=n
(3^x)²(3^y)=m
(3^x)(3^y)=n
past mesa
Yh
grim nebula
thanks goddess
neon slate
I was given
(3^x)²(3^y)=m
(3^x)(3^y)=n
so those are a couple of statements, is there a question here?
void crest
um
void crest
solve in terms of m and n?
past mesa
N is 177147
past mesa
Thats what you're given
void crest
,calc 2187/3
soft zealotBOT
Result:
729
(3^x)(3^y)=2187
(3^x)²(3^y)=177417
void crest
find what it is
past mesa
(3^x)(3^y)=2187
(3^x)²(3^y)=177417
^
past mesa
n equate the powers to powers
Wdym
past mesa
but we have 2 variables
void crest
(3^x)(3^y)=2187
(3^x)²(3^y)=177417
past mesa
In each
past mesa
Id take the top equation away from bottom
past mesa
Add?
void crest
given same base
past mesa
why add
past mesa
So add 3^x and 3^2x
void crest
umm
i think
1 shld b a y
wait how r u
no jut
just
work with the
first eq first
simplify it
(3^x)(3^y)=2187
(3^x)²(3^y)=177417
so the first eq
how can we simplify it
past mesa
how can that be simplified
void crest
try usign
void crest
past mesa
3^7
void crest
,calc 3^7
soft zealotBOT
Result:
2187
Tf is this emoji lol
void crest
Tf is this emoji lol
sadd
past mesa
(3^x)^2(3^y)=177147
3^(2x+y)=177147
past mesa
3^11
void crest
,calc 3^11
soft zealotBOT
Result:
1.77147e+5
Wait 4
void crest
no its wrong
past mesa
cuz 3^4
void crest
yea
void crest
u shld
past mesa
Mad
past mesa
my mental maths is shiz sorry
void crest
no so
3^(x+y)=3^7
3^(2x+y)=3^11
from this
we can get
x+y = 7
2x + y =11
then its easier from here
past mesa
yh
past mesa
Sorry me dumb
void crest
na
past mesa
x=4
void crest
it happens
past mesa
y=3
past mesa
It works with my method too
past mesa
Can I explain how I did it pls
void crest
It works with my method too
omg
actually
ye i
know
but sure
go ahead
hahhaa
past mesa
3^(2x+y)/3^(x+y)=3^11/3^y
3^(x)=3^4
x=4
3^(x+y)=7
so y=3
void crest
OMG
u
r
using the same property
i used
with
3^(x)=3^4
also
this is
wrong
3^(x+y)=7
hahah
past mesa
Lol ik what I mean
past mesa
Yh
grim nebula
algebruh
grim nebula
gj guys