#help-17
vocal sleetBOT
night beacon
can you explain how?
proven garden
explain what?
night beacon
oh i mean how cani tell to use
like those sum of two cubes or difference of two cubes
proven garden
I've rewritten them to squares
night beacon
x^4=(x^2)^2
it's not (x^2+1) (x-1)^2?
twin meteorBOT
WhereWolf(ping if needed)
proven garden
just use difference of squares
tidal dock
yes
proven garden
what's your final answer?
night beacon
(x^2 + 1), (x + 1), and (x - 1).
night beacon
it's wrong?
proven garden
x^4-1=(x^2+1)(x+1)(x-1)
night beacon
x^4-1=(x^2+1)(x+1)(x-1)
oh so it was right?
proven garden
(x^2 + 1), (x + 1), and (x - 1).
this is not a good way to write your answer
night beacon
this is not a good way to write your answer
oh sorry
but it was right?
sorry for the "and"
proven garden
yeah it's right
night beacon
can you help me with another question?
proven garden
sure
night beacon
still the same guide?
proven garden
yea
proven garden
yeah
night beacon
it's correct?
vocal sleetBOT
@night beacon Has your question been resolved?
night beacon
.close
tidal dock
$\left(\frac{a}{b}\right)^3 = \frac{a^3}{b^3}$
twin meteorBOT
artemetra
tidal dock
so it's $-\frac{27x^6}{8y^9}$
twin meteorBOT
artemetra
tidal dock
which is the final answer
amber star
the negetive is confusing me, idk where to start from
vocal sleetBOT
the negetive is confusing me, idk where to start from
outer warren
identify like terms and combine them
consider what you'd do if you had something like
-7 + 13
amber star
12x + 1 - 10y?
outer warren
no
consider what you'd do if you had something like
-7 + 13
how would you simplify that
amber star
six
outer warren
same idea applies here
amber star
same idea applies here
they arnt all likes terms
amber star
12x
outer warren
not quite
amber star
8x
outer warren
the x terms are
-2x
10x
their sum is 8x, yes
amber star
8x+10y+1
outer warren
yes
amber star
amber star
but i dont get it how you know if its 6y+ or +7x2
outer warren
you want to combine apples with apples
oranges with oranges
you don't want to try combining those with alien apple orange hybrids
amber star
ok so, with all the y you get 8y
amber star
outer warren
no
amber star
bro why did the greeks made math so harddd
outer warren
your terms here are:
6y
7x^2
-10x^2y
9x^2
-8x^2y
which of those is some constant being multiplied to y?
amber star
6y
-10x^2y
-8x^2y
amber star
2
outer warren
no
amber star
the power
twin meteorBOT
ℝαμΩℕωⅤ
amber star
-10x2y
outer warren
no
amber star
2 is a power
outer warren
use ^ to denote exponentiation
also if you meant that, you just retyped out the whole term
which isn't what i asked for
don't overthink what i'm asking for
amber star
-10x2^
outer warren
^ before the power
amber star
-10x^2
outer warren
is -10x^2 a constant?
amber star
no
outer warren
which of those is some constant being multiplied to y?
so its not what i wanted from you
other than 6y, were there any that is some constant being multiplied to y
amber star
-8x^2y
amber star
-8x^2
outer warren
why do you think that's a constant?
what?
what y? what repetition?
is
-8x^2
a constant?
outer warren
cause it changes
(or can change)
by definition is not constant
amber star
ok
outer warren
if you answered no to
is -10x^2 a constant?
it should also have been a clear no for this
anyway going back
other than 6y, were there any that is some constant being multiplied to y
amber star
bro idk this is confusing
outer warren
these are not supposed to be trick questions
which of those terms is some numerical value being multiplied to y
amber star
amber star
apart for those 3 there isnt
outer warren
why are you selecting -10x^2y
and -8x^2y
outer warren
-10x^2 and -8x^2 aren't constants, "some number"
amber star
outer warren
the variable part of the whole term arent the same
flat whale
well its depends what x is
.
amber star
alr
outer warren
a chicken and turducken aren't considered to be like terms
even though turduckens have chicken in them
amber star
well the chicken is dead
outer warren
anyway what i'm heavily hinting towards is that
6y is the only "y-term here", to only term that's some constant being multiplied to y
now moving on to the next type of term:
7x^2, some constant being multiplied to x^2
are there any other terms here that is some constant being multiplied to x^2?
outer warren
why are you circling only parts of terms
"terms" are expressions separated by addition/subtraction
6y
7x^2
-10x^2y
9x^2
-8x^2y
outer warren
stuff like x and x^2 (even though they both have x in it aren't like terms)
just because certain components are present doesn't necessarily make things like terms
amber star
oh yeah right the power
amber star
but they all have the power of 2 and has x
outer warren
yes, but some terms have y latched on
y and xy
similar to how there's also an x there for the xy
amber star
just means its timed
outer warren
and similarly in your question
y and x^2y aren't like terms
x^2 and x^2y aren't like terms
amber star
> 6y
> 7x^2
> -10x^2y
> 9x^2
> -8x^2y
how did u make different sections like that
outer warren
i just typed a new line
amber star
.
amber star
.
outer warren
it seems like x^2y is confusing you since both x^2 and y are present in that,
so just treat that like an entirely different object
$6y + 7x^2 - 10k + 9x^2 - 8k$
amber star
like how do u know its -10x^2 but not -10x^2y
twin meteorBOT
ℝαμΩℕωⅤ
outer warren
like how do u know its `-10x^2` but not `-10x^2y`
wdym?
its NOT -10x^2
the term you have is -10x^2y
outer warren
because that's what's printed on the page
amber star
can we vc
outer warren
no
refer to the modified expression i posted above
would you be able to simplify that?
amber star
**ℝαμΩℕωⅤ**
this?
outer warren
yes
amber star
16y^2 - 2k + 6y
sage panther
A term is only separated by addition/subtraction. Not multiplication. So the entire term is -10x^2y. You don't need to break anything apart.
Basically what you're trying to do is add constants (which are the numbers in the terms) if and only if, they have the same variables and powers attached
For example, you can add x and 2x together, because they both have an 'x' in them. So your final answer would be 3x
On the other hand, you can't add 3x and 4xy together, because while they both have x's in them, one of them has a y, and the rule is that both terms have to have the same variables and exponents on those variables in order to add them together
amber star
-18k
outer warren
the combined result isn't -2k
amber star
A term is only separated by addition/subtraction. Not multiplication. So the ent...
even if there is a power between the x and y?
(4nd paragraph)
outer warren
5 * (something)
7 * (is this the same as that something?)
if they are the same or equivalent, they're like terms
amber star
depends if something is the same or not
outer warren
if they're different, they aren't
outer warren
is $x^2$ the same as $x^2y$ for all values of $x,y$
twin meteorBOT
ℝαμΩℕωⅤ
amber star
no
outer warren
thus $5x^2$ and $7x^2y$ aren't considered to be like terms
twin meteorBOT
ℝαμΩℕωⅤ
outer warren
just like how you identifed that x,y,k are all different
and that you didn't have like terms there
sage panther
even if there is a power between the x and y?
I think I know what you mean
Basically, you can't add xy and x^2y, because you can't add terms with unlike powers on the variables
amber star
so if i cant add them, what do i do with them?
outer warren
nothing
keep them separate
just like you did with my modified example
just treat that like an entirely different object
amber star
sage panther
You just add the ones that have the same variables and powers.
The original questions only asks you to simplify, which in this example, means that you're just adding the terms with like variables and exponents
sage panther
Yes! That
wet sierra
Ya
outer warren
4x + 5y
x and y aren't like terms
don't forcibly combine, nothing to do there, so just leave it
amber star
do i add them?
outer warren
the whole term would be
-10x^2y
not just the 10x^2y you underlined
amber star
-18x^4y
outer warren
no
amber star
-18x^2y
outer warren
yes
amber star
that what i said
outer warren
wet sierra
💀
amber star
what next?
outer warren
once you've combined all like terms, you have your end result
sage panther
Now that term is done, and you can look at the other ones. You're again looking at which terms have the same variables and powers, and adding them together. Your final answer isn't 1 term, it'll still be more than one, but that's okay. You're not looking for an "answer", you just want to simplify
wet sierra
Remember it's negative
wet sierra
I'd say so
amber star
are you sure
wet sierra
But don't take my word
amber star
cause that my last try
wet sierra
I'm not that great at math
amber star
so am i
amber star
@outer warren
sage panther
Yep, that looks right to me
vocal sleetBOT
amber star
just took 1 hour of my life
vocal sleetBOT
Available help channel!
grave delta
Can someone help me with (iv) please
vocal sleetBOT
Can someone help me with (iv) please
opal obsidian
What have you tried?
i) Can you express every natural number of the form a+b \sqrt{2}?
grave delta
No
grave delta
Oh right
opal obsidian
clearly 1, 0 belongs to Z
essentially pick any integer a,b from Z and see if you can represent all of N
opal obsidian
my bad, I didn’t see
median crane
which direction do you need help with
grave delta
Both if you can
I’ve tried doing contradiction for left to right but idk if I’m getting anywhere
grave delta
For both directions?
median crane
,, P \leftrightarrow Q \iff \neg P \leftrightarrow \neg Q
twin meteorBOT
Pure
grave delta
How would I prove it from right to left so if x^2 is a member of G then x is a member of G
vocal sleetBOT
@grave delta Has your question been resolved?
vocal sleetBOT
@grave delta Has your question been resolved?
old niche
I might not actually be. very clear about what an inductive hypothesis is
regal bane
Something we assume to be true, so that we might use it to prove the inductive step
old niche
Something we assume to be true, so that we might use it to prove the inductive s...
the inductive step is always + 1
right
lean forge
nope
If you assume n-1 you can show that the property is hereditary for n
Depends on where you initialized
and how easy it is to show
But in general it's n+1
old niche
But in general it's n+1
because when you do the inductive step, you cite the inductive hypothesis
but that part confuses me
because if the IH is that its true for some n, and you want to show its true for some n + 1
then...
lean forge
Idk but here's an dumb exemple : Show that every even number is divisible by two
You can either talk about P(2n)
Then it's +1
Or if you use P(n) you'd use +2
Idk if you see why
lean forge
then...
Then it's true for all n if it's true for the first one
If you have a number for which the property is true, and it happens to be also true for the next one
And that it's also true for the first number
Then it's going to be true for the second number
3rd one
etc... for all number
lean forge
there's no set case
in reality you can use strong induction everytime
But basically
If you notice that you need a number that's smaller than n to continue with your proof
switch to strong induction
old niche
in reality you can use strong induction everytime
why?
old niche
If you notice that you need a number that's smaller than n to continue with your...
can you give an example
lean forge
why?
because with weak induction you suppose n and show n+1
with strong induction you suppose all k <= n then show n+1
So if you end up just using n
your strong induction will still be correct
old niche
what if the induction only works from n = 3 then n = 7, how would i state my proof is what i want to ask avoyt
about
lean forge
You'd simplet write
Let $n \in A$
twin meteorBOT
Azenx
old niche
like in strong induction, sometimes they use 2 letters in the like assume whatevr whatever
like what does it mean to induct on something
i gues
guess
like i dont think induction is supposed to be hard, but there is some correct template
which im not fully understanding
lean forge
Finite induction is very rare
Actually i've never seen one
Even in my course there were no exemples for it lol
old niche
i can show you something im trying to do
what im referring to
for instance, this only works for like 0, 1, 2, 3, 4, 5
i think
lean forge
Hmm
Then you wouldn't show it by induction for n between 0 and 5
Either use induction to show the negation for n>=6
ie t_n<2^(n-2)
old niche
Then you wouldn't show it by induction for n between 0 and 5
ahhh so this is were strong induction comes in
to prove the negation
lean forge
Either directly use linear progressions to find the general expression of tn
lean forge
to prove the negation
Yes
old niche
so like it would be: Assume tn < 2^n-2 for all n >= 6
wts this holds for tn + 1 < 2^n-2-1 for all n >= 6
lean forge
well yea
but first
hollup let me make sure there arent any other ns for which this is true lol
lean forge
wym ?
old niche
statement wont be frue when n is 6, 7, 8
lean forge
Ho
old niche
?
lean forge
statement wont be frue when n is 6, 7, 8
It does no ?
Actually 5 6 and 7 work as well
vocal sleetBOT
@old niche Has your question been resolved?
vocal sleetBOT
old niche
.reopen
vocal sleetBOT
✅
vocal sleetBOT
@old niche Has your question been resolved?
vocal sleetBOT
crude arrow
first f(1) = 1 - 7 = -6
so we must prove that lim x-> c f(x) = -6
so we need to show $\forall \epsilon > 0$, $\exists \delta$ s.t if $|x-1| < \delta \in R$, then $|x^2 - 7 -(-6)| < \epsilon$
@vast shale
SO WHAT IS |x^2-1| SIMPLIFIED
you should know this....
so just let delta be less than $\frac{\epsilon}{|x+1|}$
and ur done
pls ".close" when ur done
I mean delta
what the actual hell
twin meteorBOT
nosqldb
crude arrow
@vast shale I gave you the proof basically
twin meteorBOT
nosqldb
hushed pewter
what the actual hell
You need to calm down with the hostility.
crude arrow
You need to calm down with the hostility.
I'm sorry
hushed pewter
pls ".close" when ur done
And this isn't helpful. You're assuming they instantly get what you wrote, which is a pretty high opinion of yourself.
crude arrow
And this isn't helpful. You're assuming they instantly get what you wrote, which...
but they did understand
?
hushed pewter
<@456226577798135808> I gave you the proof basically
And if you're doing this, then you need..
!nosols
crude arrow
And if you're doing this, then you need..
!nosols
I walked them through it
and they provided answers too
but at the end I helped them complete it
we just need delta to be less than epsilon / |x+1|
we define the delta
pls read the statement
we want to show there exist a delta
in
fervent tulip
Am I going crazy or does this have no solution?
vocal sleetBOT
Am I going crazy or does this have no solution?
fervent tulip
@cyan shadow I just did reduced row echilon to see if its possible and always end up with 0001, put it through symbalab too
yes
cyan shadow
did you do it by hand as well?
fervent tulip
Yes, let me pull out my ipad
cyan shadow
one of the answer choices is correct
cyan shadow
you should not have gotten the same result as symbolab if you did it by hand
well like okay maybe you would
but you should have stopped at an earlier point
if you send your work I can point it out then you can understand
i think I know your exact mistake
fervent tulip
I didnt get the exact one, I stopped here:
cyan shadow
I didnt get the exact one, I stopped here:
this was the correct place to stop
so why do you think this has no solutions?
fervent tulip
Because if you solve it out it ends up being 0001 on the bottom no?
cyan shadow
why is the last element 1?
fervent tulip
for this one I just trusted symbalab during the end because I got stuck, but where else would you go?
because u get9b_1+6b_2+b_3 = 0
cyan shadow
because u get9b_1+6b_2+b_3 = 0
oh so its consistent when $9b_1+6b_2+b_3 = 0$?
twin meteorBOT
cyan shadow
then the bottom row is all 0, which is fine
fervent tulip
I mean yes, but it doesnt take the rest into account no? its an answer choice but does just having it at one point make it consistant or is it only consistant with the upper two equations as well?
Like can we take these as seperate equations or are they conditional to one another
cyan shadow
its fully consistent, i.e. there are no [0 0 0 x] x neq 0 rows when that constraint is met
you could just say let $b_3 = -9b_1 -6b_2$ and it would have no impact on the top two rows
twin meteorBOT
fervent tulip
Im sorry im a little new to lin alg, does this mean each equation at every point is all consistant?
ah
ok I think thats making more sense
so I could have just stopped working there as soon as I saw something was consistant?
cyan shadow
no you got it to proper rref form
fervent tulip
ah
cyan shadow
the trick for symbolab that you fell for is that it divided the entire last row by $9b_1 + 6b_2+b_3$ then used that to cancel out the last column in the first two rows
twin meteorBOT
cyan shadow
which is perfectly good for rref, but it makes the assumption that$9b_1 + 6b_2+b_3\neq0$ since you cannot divide by 0
twin meteorBOT
cyan shadow
it made that assumption and did not write it anywhere
fervent tulip
so just going back to the symbalab aspect of it, does that still mean that the equation does not have solutions
ah
so the 0001 is with an asumtion, but without it we can still have a soltution?
cyan shadow
so under the assumption that $9b_1 + 6b_2+b_3\neq0$, it is inconsistent, but as we figured out, with $9b_1 + 6b_2+b_3=0$ it is consistent
twin meteorBOT
cyan shadow
(wolfram would have caught this, and is what I used to rref your matrix)
cyan shadow
well it doesn't really catch it but it gives you something that you should realize
it does this
and that assumption is of course wrong
wolfram is great for all math until you get to proofs
then it doesnt work, except for the trivial calculations
fervent tulip
ah yeah im on diff eq rn
mathmatica might be worth the money atp
well tysm for the clarification. this really helped me lmao
.close
wary mantle
Find $z$ s.t. $z^2 = i$. Hint: it can be easier to use polar coordinates.
wary mantle
Why would it be faster to use polar coordinates here
We'd have $z = |z|(cos(\phi) + \sin(\phi)i)$, right?
hybrid flicker
Yes, and you have an easy formula for finding roots in polar form, which comes from De Moivre's formula...
covert python
multiplying by a complex number is equivalent to a rotation around the origin
wary mantle
Yes, and you have an easy formula for finding roots in polar form, which comes f...
My lecture notes haven't covered that yet
And still they say it's easier to use polar coordinates
wary mantle
you should know the polar form of i
$i = 1(\cos(\frac \pi 2) + \sin(\frac \pi 2)i)$
Is that what you mean?
median crane
,, i = \exp \p{i\df{\pi}{2}}
twin meteorBOT
Pure
wary mantle
We haven't covered the exponential form of complex numbers
wary mantle
sqaure rooting means you sqaure root the length and halve the angle
Ok, so the angle will be $\frac \pi 4$.
The length 1
median crane
$z = \pm1\p{\cos \frac \pi 4 + \sin(\frac \pi 4)i}$.
twin meteorBOT
Pure
wary mantle
Thanks
wary mantle
$z = \pm1\p{\cos \frac \pi 4 + \sin(\frac \pi 4)i}$.
By the way, how did you define your command \p
median crane
\newcommand{\p}[1]{\left(#1\right)}
Check the brackets I’m on phone but I think this is right
wary mantle
Check the brackets I’m on phone but I think this is right
Thanks! Do you always use it instead of () or only when you think the brackets need to be larger
median crane
Only when I need it because sometimes it messes up the spacing
empty crane
vocal sleetBOT
empty crane
pls help 😪
empty crane
yurrr
crude arrow
wait so i do 14x250 to get the first bit
What’s the area of a triangle
crude arrow
Yeah
empty crane
1750
empty crane
8050
crude arrow
Otherwise we have a big problem
empty crane
😪
empty crane
14
crude arrow
And height 14
empty crane
8050/14?
empty crane
😼😼😼
lofty escarp
nice pfp
empty crane
me?
lofty escarp
loool i dont mind him
crude arrow
Since he’s dropped something good
Anyway
What’s 250 + 8050/14
This is the hard part ngl
Let me know if you need help
crude arrow
i am abit of an idiot
Btw for future reference
You want to make both numbers into whole numbers
And then add
crude arrow
cheers for the help
Ofc
vocal sleetBOT
@empty crane Has your question been resolved?
wide vector
why is it just u^4? where did the cos go?
vocal sleetBOT
why is it just u^4? where did the cos go?
wide vector
ya
vast shale
yes
magic wasp
woven musk
If I want to know the lenght of the vector v
vocal sleetBOT
If I want to know the lenght of the vector v
woven musk
Is this the right formula to use?
heavy yoke
is this all of the information you're given? post the full problem
woven musk
It's in swedish, but the only information is the picture and the vectors (v=(4,7) and u=(5,3))
plain aurora
It's in swedish, but the only information is the picture and the vectors (v=(4,7...
yes
tidal umbra
Is this the right formula to use?
if this is the only thing given then yes you have to use this ^
plain aurora
it's just pythag
chilly temple
im having trouble solving this problem
vocal sleetBOT
im having trouble solving this problem
lean forge
Not sure but would h’(x) = reverse delta g ?
chilly temple
not too sure myself
chilly temple
im having trouble solving this problem
for part a i got <2,-1,1> as a my answer for the gradient
since gradient of g at (-1,-1) equals the gradient of f at (-1,1,-1)
<@&286206848099549185>
lean forge
since gradient of g at (-1,-1) equals the gradient of f at (-1,1,-1)
Yes
Then h’ would be equal gradient g
So h’(0) would be the same
chilly temple
Then h’ would be equal gradient g
correct me if im wrong but i thought h'(0) would be the dot product of inner function and the gradient of g at t=0
hybrid flicker
h'(0) should output a real number, not a vector
So no the gradient won't do
The dot product is the correct one
chilly temple
okay got it
hybrid flicker
So write h = g ○ p where p is the function p(t) = (t²-1,-e^t)
And so the derivative of h is given by...
chilly temple
dot product of the graident of g at(-1,-1) and the deriative of p at t=0?
hybrid flicker
Yep
chilly temple
i think i equated the gradient of g at (-1,-1)with the gradient of f at (-1,1,-1)
chilly temple
the inner function ?
hybrid flicker
Yes
Name that inner function j or something
j(x,y) = (x³,x²y²,y³)
And so $\grad g = ?$
twin meteorBOT
rafilou2003
chilly temple
are we supposed to take the deriative of inner function when solving for graident of g ?
hybrid flicker
That's the point of it being a matrix
If you think more about it, you can think about the chain rule
chilly temple
i think im a bit confused. Would it be possible to give an example
hybrid flicker
like here $\grad g = \langle \frac{\partial j}{\partial x} \cdot \grad f, \frac{\partial j}{\partial y} \cdot \grad f\rangle$
twin meteorBOT
rafilou2003
chilly temple
so it would be the derivative with respect to one variable times the gradient within each component?
hybrid flicker
Yeah
chilly temple
okay i think i got it now
so it would be <3x^2,2xy^2,0> dot <2,-1,1> for the first component ?
hybrid flicker
Yes, but don’t forget what's the values of x and y you will use
chilly temple
in this case they would be both -1 right ?
hybrid flicker
Yes
chilly temple
ohhhhh
i got it
thank you so much
i think i can solve it myself from here
.close
fervent tulip
Just for clarification, during this problem as long as AU=0 thats a vector in the nullspace, and if if I get 0 for all sets thats my solution?
vocal sleetBOT
Just for clarification, during this problem as long as AU=0 thats a vector in th...
iron geyser
fervent tulip
its not that bad, im just clarifying but trust me its a lot easier than it looks
at least I hope
vocal sleetBOT
@fervent tulip Has your question been resolved?
dull bear
wait have you done something like rank-nullity theorem before?
But yep, multiplying the vector by A (on the appropriate side) and getting the zero vector means that the vector is in the kernel, and you can test to see if all the vectors are in the space
dark herald
I need some help figuring out how to start this problem:
vocal sleetBOT
I need some help figuring out how to start this problem:
flat whale
I need some help figuring out how to start this problem:
Do you know the definition of injective
brisk moss
T_T
pallid zenith
oh it was right, oh well
dark herald
Do you know the definition of injective
yes
flat whale
Did you try checking it f matches the definition
dark herald
will do that rn
Im fried as fuck i cant do this
bad time to do homework
someone save me
vocal sleetBOT
@dark herald Has your question been resolved?
dim jetty
Please teach me how to solve this problem
vocal sleetBOT
Please teach me how to solve this problem
dim jetty
tysm 🥹
tardy mountain
👍
dim jetty
what about a problem like this?
tardy mountain
,rotate
twin meteorBOT
dim jetty
everytime i try to solve it i dont get real number
tardy mountain
What have you tried?
dim jetty
no this is k12
tardy mountain
okay
So..
I'm going off of assumption here (not sure if this is 100% right)
But since it's equilateral
each angle would be 60
dusty mulch
it is equiangular, meaning it is equilateral
tardy mountain
So you could set each equation to 60 and you should get the same answer.
tardy mountain
oh
dusty mulch
since its equilateral the sides equal each other
tardy mountain
so set them equal to each other?
dusty mulch
so set two of the sides equal to each other and solve for x
tardy mountain
@dim jetty if you're following, do 4x-30 = 2x+20 and solve for x.
dim jetty
okay!
tardy mountain
The answer should be ||25||
dim jetty
yayy i was correct
dim jetty
Please teach me how to solve this problem
i’m sorry i don’t wanna sound dumb but after i know the angles are 73 73 34 what do i do 😭
how do i solve for x in this situation
dim jetty
so i solve for x on 6x+4=34?
dusty mulch
yes
tardy mountain
or ||8y-7=34||
tardy mountain
Don't feel sorry.
We all learn differently.
Try using Youtube when you're stuck.
You could always come back here though.
tardy mountain
Yes. 👍
vocal sleetBOT
@dim jetty Has your question been resolved?
split wind
on this one what is the formula for solving?
isosceles triangle?
dim jetty
isosceles triangle?
yes i believe it is
thats what i was thinking but i wasnt sure haha
vocal sleetBOT
@dim jetty Has your question been resolved?
split olive
How to solve
vocal sleetBOT
How to solve
split olive
hint: use implict differentitation
can you explain more
opal obsidian
differentiate both sides with respect to x
let's start with left side
what do you get when you differentiate $e^{xy}$?
twin meteorBOT
.doc
opal obsidian
@split olive
split olive
$ye^{xy}$
twin meteorBOT
Epsilon
split olive
@opal obsidian
split olive
oh
opal obsidian
but remember y is y(x) or a function which depends on x
twin meteorBOT
Epsilon
opal obsidian
\
opal obsidian
$e^{xy}(y+\frac{dy}{dx} x)$
twin meteorBOT
.doc
split olive
$\frac{1}{x} + \frac{1}{y}$
twin meteorBOT
Epsilon
split olive
$\frac{1}{x} + \frac{1}{y} \frac{dy}{dx}$
twin meteorBOT
Epsilon
opal obsidian
so if there is a function which depends on your independent variable x, you have to apply the chain rule
what we are doing is essentially chain rule
split olive
okay
split olive
**Epsilon**
.
opal obsidian
$e^{xy}\left(y+\frac{dy}{dx} x \right) =\frac{1}{x} + \frac{1}{y} \frac{dy}{dx}$
twin meteorBOT
.doc
opal obsidian
right?
split olive
yes
opal obsidian
you are asked to find dy/dx
so your goal is to collect dy/dx from this equation and make it as the subject
write this equation as dy/dx = _____
for that first bring dy/dx terms in left side and all other to right side
@split olive need help ?
twin meteorBOT
Epsilon
split olive
@vast shale
opal obsidian
let me try
I got $\frac{dy}{dx}\left(xe^x -\frac{1}{y} \right)= \frac{1}{x} -ye^{xy}$
twin meteorBOT
.doc
opal obsidian
did you got something close to this?
split olive
exactly this
opal obsidian
so you should get -y/x right?
I got $\frac{dy}{dx}= \frac{1-xye^{xy}}{x} * \frac{y}{yxe^x -1}$
twin meteorBOT
.doc
opal obsidian
is this your next step ?
split olive
yup
opal obsidian
now if you factor a negative from the denominator
you can cancel that with the numerator right?
split olive
yup
opal obsidian
ie, you get dy/dx = -y/x?
split olive
yup
opal obsidian
is that what you got aswell ?
split olive
i did
opal obsidian
i guess there must be mistake in your options
opal obsidian
just make sure the work again
split olive
btw, how do i find solutions to such questions online
split olive
maybe we both did the same mistake, nobody knows
ill check again
opal obsidian
let me know if you find any mistakes
i need to know if I should have trust issues with my algebra
split olive
https://www.emathhelp.net/en/calculators/calculus-1/implicit-differentiation-cal...
this also got -y/x
split olive
thank you so much
opal obsidian
good luck
opal obsidian
I don't follow that either, i studied in grade 12, which is typically 17 years old
split olive
in india?
opal obsidian
but yeah we use it all the time
split olive
im indian too
opal obsidian
amazing
split olive
are you doing math in uni
opal obsidian
final year,
split olive
what is your major
opal obsidian
mathematics
split olive
.close
vocal sleetBOT
cedar fjord
uhm trigonometry?
fair compass
it looks like angle b is twice the elevation at point a for q1
is there a way for you to check, im unsure if its right
cedar fjord
is there a way for you to check, im unsure if its right
I'm afraid, none
fair compass
at point a tan(theta) is h/d1
at point b which is 54 meeters closer to the tower the angle of elevation at b is twice that at A so thetaB=20
so tan(thetaB)=h/d2
where d2=d1-54
at point c, which is 21 meeters closer to the tower from point B, the angle of elevation at c is three times that at A, so thetac=30 where d3=d1-54-21
then solve for the last angle
cedar fjord
ah, distance 1 ok ok
cedar fjord
if it's okay, I would be glad!
cedar fjord
the distance between point A and point B, isn't it 54 m? And the distance between point B and point C, isn't it 21 m?
fair compass
oh your right
mb
that would make point point b 54
c would be 54+21
but the angle of elevation at point B is still twice the angle of elevation at point A.
i gotchu
<@&286206848099549185>
👍
cedar fjord
<@&286206848099549185>
vocal sleetBOT
@cedar fjord Has your question been resolved?
cedar fjord
.close
snow path
hello. still unclear on how to reverse the order of integration.
snow path
i think i have it. it's like an upside down triangle, right?
heavy yoke
it is a triangle, yes
heavy yoke
i think you have your x and y mixed up
heavy yoke
yes
snow path
the one on the right, yea?
heavy yoke
yes
so if we imagine traveling from left to right, we first encounter the line x=9y (this is where we enter the region), then we encounter the vertical line x = 9 (this is where we leave the region)
we want to reverse this, so instead imagine traveling from down to up, and describe which functions we encounter entering and leaving the region
snow path
hmm. so x=9y and x=9 first?
or wait
if we're only concerned with the shape
it would be y=0, x=9y and x=9 first, right?
heavy yoke
so if we imagine traveling from left to right, we first encounter the line x=9y ...
so when we do the bounds in x, the diagonal line x = 9y is the "left side" of the triangle and the vertical line x = 9 is the "right side" of the triangle
similarly, we want to find what the "bottom side" and "top side" of the triangle are
snow path
so y=0 and then y=1?
i feel silly lol
but the topside of the triangle
so wouldnt it be y=0 and y=x/9?
heavy yoke
so wouldnt it be y=0 and y=x/9?
yes!
snow path
YEEHAW
heavy yoke
so then we need to find the x-bounds: these are just the smallest and largest (constant) values for x
snow path
so 0<x<9 ?
heavy yoke
yes
snow path
omg
tysm!
i think i got it from here. but if you still have time, i'm wondering what if in the future the function can't be drawn
is there a way to deduce the bounds algebraically?
by can't be drawn i mean maybe something im not familiar with
heavy yoke
you can put it in a graphing calculator if you aren't familiar with it
snow path
thank you. but is there a way that it can be done without a graphing calculator?
if i have some crazy bounds going on
simple yes or no is fine, i understand it would take some explanation beyond what you have time for
it also just might be a stupid question
lol
heavy yoke
if you have y = some weird function of x and need to reverse the bounds then you need to be able to solve for x as a function of y, which puts a limit on how crazy the bounds can be and still be reversible
humble osprey
Can someone explain to me why the highlighted portion is true?
vocal sleetBOT
Can someone explain to me why the highlighted portion is true?
humble osprey
