part ii) is what I need help with
#help-13
worthy ruin
I found the minimum point to be ( sin^-1 (-2/3) , -13/3)
but I dont know how to find the maximum
I tried setting dy/dx = 0 but that gave me the minimum too
dire geode
I found the minimum point to be ( sin^-1 (-2/3) , -13/3)
share your work here and someone can help
worthy ruin
I mean I typed out what I know and what I don't know
wdym
I need help finding the maximum of point of 4sinx -3cos^2
worthy ruin
oh ok
srry
@dire geode idk if that helps
but thats pretty much where im up to
with finding the maximum
I have that equation and I don't know what to do to find the maximum as my attempts only found the minimum point
worthy ruin
me neither I just thought that might be a way to find it
trig
but we've been taught calculus so I thought maybe
dire geode
you were taught calculus in a trig class?
worthy ruin
no
we're been taught both recently
as it's a maximum point of a graph I thought it could involve calc but it probs doesn't
it was just a method I thought could work and didn't
it's trig
the lesson is titled trig
dire geode
well that's cuz you didn't find all solutions when you set the derivative to zero
dire geode
there are infinite solutions to where the sine function has derivative equal to zero
dire geode
you just need to use the quadratic formula here
worthy ruin
you just need to use the quadratic formula here
why would I want to find the roots of the equation
delicate perch
worthy ruin
i want to find when the gradient is 0
dire geode
why would I want to find the roots of the equation
is this not the derivative?
worthy ruin
bro this help channel is taken please delete your msg
dire geode
why would I want to find the roots of the equation
ah ok, my bad. what did you get for the derivative
worthy ruin
4sin(x) - 3 + 3sin^2(x) is the equation
6sin(x) + 4 is the derivative
oh srry
i didn't put it in my workings
my bad
but 6sin(x) = -4 only have on value
one value*
thats why I can only find the minimum
and not the max
dire geode
4sin(x) - 3 + 3sin^2(x) is the equation
6sin(x) + 4 is the derivative
this derivative is wrong
dire geode
,w derivative 4sin(x) - 3 + 3sin^2(x)
wraith daggerBOT
dire geode
chain rule / product rule, etc.
worthy ruin
what
dire geode
if you haven't learned those, i don't think you can use calculus to solve it
worthy ruin
why is there a cos(x) in the derivative
how do I solve it the other way then because I haven't learnt that yet
srry
dire geode
just start back here
dire geode
$A(sinx + B)^2 + C$ is maximized when the $sin(x)+ B$ is maximized
wraith daggerBOT
riemann
dire geode
do you see why?
dire geode
and since $(sin(x) + B)^2$ is always greater than or equal to zero, then your function is minimized when $\sin(x) + B$ is zero
wraith daggerBOT
riemann
dire geode
or in general, when the square is minimized. in this case $B \leq 1$ so the minimum can be zero.
wraith daggerBOT
riemann
dire geode
๐๐ป
glad kestrel
i'll give you one better: why is the gravity
south tundra
No one answered on the physics channel?
vast trellis
@dire geode so how do i get help
cedar kilnBOT
<@!261933205387477002> so how do i get help
glad kestrel
you... ask
vast trellis
Consider the universe U = {๐ฅ โ๐
| 0โค๐ฅ โค40}
Within this universe, determine each set by listing their elements:
๐ด={๐ฅ โ๐ | ๐ฅ =12๐ ,๐ ๐๐ ๐๐๐ก}
๐ต ={๐ฅโ๐,11<๐ฅ โค20}
๐ถ ={๐ฅ โ๐ต | ๐ฅ =4๐+1 ,๐ ๐๐ ๐๐๐ก}
We have this in our labs papers , i dont know how to answer it
balmy apex
what have you done/tried so far
vast trellis
this question nothing , i did the others @balmy apex
balmy apex
at least try to do it yourself before you ask here
vast trellis
Okey , just thought i could get help in that one , as i have 2 hours to post my paper lab
dire geode
Consider the universe U = {๐ฅ โ๐
| 0โค๐ฅ โค40}
Within this universe, determine ...
do you know what integers are?
vast trellis
yes ofc
dire geode
do you know what $12k$ where $k$ is an integer means?
wraith daggerBOT
riemann
cedar kilnBOT
@vast trellis Has your question been resolved?
vast trellis
@dire geode ?
dire geode
it means that k can be inserted by a number
what kind of number, specifically?
can you write it?
Do the same for C as well
B is the easier one
You should be able to list all the elements of all 3 sets
cedar kilnBOT
@vast trellis Has your question been resolved?
vast trellis
What do you mean
Can you choose one and answer for me with explaining that would be really good for me
I can follow the steps
dire geode
can you write the first 4 positive numbers of the form $12k$ where $k$ is an integer?
wraith daggerBOT
riemann
cedar kilnBOT
cedar kilnBOT
Available help channel!
young sundial
what are the coordinates of the midpoint of the segment connecting these points (1,-2) (-5,6)
young sundial
forgot how to do midpoint
tight herald
You take the average of the x and y I believe
patent flame
yeah
so add the 2 x values and divide them by 2 to get the x midpoint and then do the same for the y values (add them together and divide by 2)
tight herald
Yep
young sundial
.close
tidal quest
Hi so I have this generating function $G(x) = \frac{x^3+x^2+2x+1}{-x^3-x^2+1}$ and now I want to perform coefficient extraction on this. So i thought of converting this to recurrence relation instead. I listed some the coefficients for $2x^{16}+12x^{15}+30x^{14}+42x^{13}+40x^{12}+32x^{11}+24x^{10}+18x^9+14x^8+10x^7+8x^6+6x^5+4x^4+4x^3+2x^2+2x+1$ but how would I go about finding the recurrence relation
wraith daggerBOT
meguuuuu
glad kestrel
hmm that looks like not fun
dire geode
is it useful to maybe simplify G first
dire geode
,w plot -x^3 - x^2 +1
wraith daggerBOT
tidal quest
$-1+\frac{2x+2}{-x^3-x^2+1}$
wraith daggerBOT
meguuuuu
wraith crypt
usually, one goes from a recurrence to a generating function, not the other way around y'know?
dire geode
well this problem's officially the hardest one i've seen today
oh wait that theorem is backwards
You have a P, Q and you want to calculate A
tidal quest
yeah i just want to determine the coefficients of generating function
since i cant perform partial fractions i thought maybe other ways exist
dire geode
well that's just an ugly root
tidal quest
uh
wraith crypt
no you probably have to be a bit smart about this
dire geode
i was thinking since you can have complex coefficients, the complex roots might be useful
or wait is this over reals?
tidal quest
yeah reals
wraith crypt
maybe a binomial expansion
tidal quest
how would that be used here though
wraith crypt
actually, a binomial looks promising
maybe
you could also treat it as a geometric in x^3 + x^2
tidal quest
actually maybe if i provide the context of question this part might be easier? Maybe we dont need to use generating function
So basically we have S which is a set of binary string
S has some restrictions such that S can only contain blocks of length 1 or 2
So $S = emptyString \cup S_0 \cup S_1 \cup S_{00} \cup S_{11}$ is defined like this. And
$S_{0} = {emptyString \cup S_{11}}0$\
$S_{1} = {emptyString \cup S_{00}}1$\
$S_{00} = {emptyString \cup S_1\cup S_{11}}00$\
$S_{11} = {emptyString \cup S_0 \cup S_{00}}11$\
ops
wraith daggerBOT
meguuuuu
tidal quest
and so we want to find recurrence relation for S which will tell us how many binary strings are in S for length n
is the context better?
wraith crypt
so basically S is the set of all strings with blocks at most length 2?
tidal quest
yeah so some examples are 0.11.00.1
wraith crypt
ignoring all that weird things which i don't know how to make sense of
tidal quest
. divides it into blocks
wraith crypt
it's the set of all strings with blocks of length at most 2
tidal quest
here are the all possible examples of S until n=6
n=0, we just have empty binary string,
n=1, we just have {0, 1}
n=2, we have {00, 11}
n=3, we have {001, 100, 110, 011}
n=4, we have {1001, 1100, 0011, 0110}
n=5, we have {11001, 00110, 10011, 01100, 11011, 00100}
n=6, we have {011001, 011011, 100110, 100100, 001100, 001001, 110011, 110110}
tidal quest
because we have restriction in S_0 and S_1. If you look closely, when We have block of length 1, it must have block of length 2 before and after it
wraith crypt
can you define it clearly: $S$ is the set of all binary strings such that ...
wraith daggerBOT
Camilleone
tidal quest
so S is set of all binary strings such that S can be one of empty string S_0, S_1, S_{00}, or S_{11} right, so lets define each of them individually
wraith crypt
no, don't say S can be one of five different sets
tidal quest
hm? wdym
wraith crypt
so S is set of all binary strings such that S can be one of empty string `S_0, S...
.
those look like five different sets to me
jaunty mural
n=0, we just have empty binary string,
n=1, we just have {0, 1}
n=2, we have {00...
im tryna spot the pattern and 
wraith crypt
im tryna spot the pattern and <:pandaOhNo:513070260471988226>
if you spot it lemme know lol
tidal quest
oh i guess i should have said S is union of those 5 sets
wraith crypt
i don't understand what seems to look like a recursive definition, so i'd prefer it in a single concise definition
tidal quest
can I move on to expalin those 5 sets now? Or are you still confused about S?
tidal quest
So uh, $S_0$ writes $S_0 = {{\epsilon}, S_{11}}0$. What this means is that whenever we see an occurence of $0$ as a single block. So $\cdots0 \cdots$, then it must be the case that before that $0$, there can only be block of length 2, or empty string. So there can only be $11$ or $\epsilon$ before $0$
Similarly for $S_1$ when we see a block of length 1 such that it is $1$, then it must be the case that before that $1$, there can only be $00$ or $\epsilon$ before $1$.
For $S_{00}$, there can only be $\epsilon$, $1$, $11$ before $00$
For $S_{11}$, there can only be $\epsilon$, $0$, $00$, before $11$
Is this better?
wraith daggerBOT
meguuuuu
tidal quest
This means that something like 1.0.1.0 is not valid
there cannot be consecutive blocks of length 1
similarly, 00.00 is not valid
wraith crypt
what the heck is $\epsilon$
wraith daggerBOT
Camilleone
tidal quest
there can be continuous blocks of length 2 but they must be different, so 00.11
epsilon is empty string
which means there is nothing before it
so $\epsilon 0 = 0$
wraith daggerBOT
meguuuuu
tidal quest
yeah
tidal quest
so 00.0 can be "merged" into block right, which is why this is not possible
wraith crypt
okay so
tidal quest
because "00.0" = "0.00" so we cant tell the difference
but if we have "11.0" then we know exactly where the block ends and begins
wraith crypt
S is the set of strings such that:
- a single block is preceded by a double block (unless it's the first element)
- a double block has no restrictions on what precedes it
can you confirm this is exactly the definition of S?
tidal quest
there is one more restriction, every block of 0s must be followed by block of 1s. So 00.00 is not valid, only 00.11 is valid
wraith crypt
obviously, because 0000 counts as a 4-block
tidal quest
yeah
and 00.0 counts as 3 block thats the reason yeah
but yeah thats the definition of S
wraith crypt
when i say preceded by, it's implicit that the blocks will be filled differently
so can i confirm that is the exact description of S?
tidal quest
S be the set of binary strings that contain only blocks of length one or two and that have no two consecutive blocks of length one yeah
wraith crypt
S be the set of binary strings that contain only blocks of length one or two and...
see, that's a much easier definition to work with
and the question is?
tidal quest
to find linear recurrence with initial conditions for the number of binary strings in S of length n
this is just the coefficient in the generating function which was why i was going that approach
wraith crypt
it sounds like you could just consider cases tbh
on the last...two digits of a string of length n
last digit or two digits maybe
tidal quest
why only last two digit?
wraith crypt
because what precedes it will also be a string
if for example the last two digits is a 00
everything that precedes it will be a string of length n-2, and all such strings ending with 1 will be valid
tidal quest
oh
wraith crypt
n=0, we just have empty binary string,
n=1, we just have {0, 1}
n=2, we have {00...
e.g. take n=5, then the two strings ending in 00 have everything before that 011 and 001 - these are the n=3 strings ending with 1
tidal quest
hmm i see so for this case a_n = a_(n-2) for 00 + a(n-2) for 11 + a(n-1) for 0 + a(n-1) for 1?
no wait that doesnt work
wraith crypt
you're right, i think you may want to look at the last three digits instead for the end-with-one-block case
and also, not the entire set of n-2 strings are used in the end-with-two-block case (but there's a simple way to get around this)
tidal quest
yeah
the only way we can count properly is if we mention explicitly that we are getting from $a_{0}, a_{1}, a_{00}, a_{11}$
wraith daggerBOT
meguuuuu
wraith crypt
okay, so
the idea is
anything prior to a 2-block is going to be dead easy to count
so let's do that first
let's say our n-string ends with 00
everything before that is an n-2 string ending with digit 1
how many of them are there?
(hint: if i have a binary string in the set, i can flip every digit to form another binary string in the set)
tidal quest
n/2 strings?
wraith crypt
not n-2
wraith crypt
hmm i see so for this case `a_n = a_(n-2) for 00 + a(n-2) for 11 + a(n-1) for 0 ...
see this notation
tidal quest
you mean a_(n-2)/2?
wraith crypt
yes!
tidal quest
we divide by two because a_(n-2) includes for n-strings ending with 11 right?
but in our case we only are considering 00 for now
wraith crypt
yes, so between 00 and 11 endings, there are a_{n-2} string possibilities total
now let's look at 0 endings, as a single block
tidal quest
yes
wraith crypt
it must have some amount of strings ending with 11 before it
note that this is not quite so easy to count
but there is a trick, and that's to see that the n-string ends in 110
and 11 is a 2-string, so everything before 110 is easy to count
tidal quest
so that means a_(n-3)/2
tidal quest
um wait one sec
let me test out before uh
so that means we need inital conditions for a_1, a_2, and a_3 right
wraith crypt
yes
tidal quest
wait i meant to say a_0, a_1, a_2 but now im confused if it is a_1, a_2, a_3
if we have empty string it still belongs to S so wouldn it be 1
so a_0 = 1
wraith crypt
well, if you include the empty string then start from 0
tidal quest
so that means our final ans is a_n = a_(n-2) + a_(n-3)/2 + a_(n-3)/2, with a_0 = 1, a_1, =2, a_2, =2?
wraith crypt
you can simplify it a bit further
tidal quest
which means a_n = a_(n-2) + a_(n-3)
wraith crypt
^ that, yeah
wraith crypt
well, that's more down to the fact that the empty string is a bit of a special case
tidal quest
oh so start from a_4
tidal quest
yeah let me try some out to confirm
YES! it works
wow
thank you so much
i cant believe i tried to convert generating function to recursive relation
wraith crypt
generating functions are powerful but it's a pain to calculate properly
so finding simple solutions like this is a better first attempt
cedar kilnBOT
cedar kilnBOT
Available help channel!
nova inlet
trying to find the general solution to this diff eq
cedar kilnBOT
trying to find the general solution to this diff eq
wraith daggerBOT
Shuri2060
jaunty mural
If you can write it in this form, then you can sub v = y/x and it becomes separable
nova inlet
is y x and x t?
gaunt hamlet
Yes
nova inlet
ok so i have
dy/dt t + y = (y-4)(1-y)
ill just tell you my final answer if you can check that bc i did this before i j dont know if its right
(1)/((((x/t)-2)^(1/4))(((x/t)+2)^(3/4)))=Ct
cedar kilnBOT
@nova inlet Has your question been resolved?
cedar kilnBOT
@nova inlet Has your question been resolved?
cedar kilnBOT
@nova inlet Has your question been resolved?
drifting matrix
,wolf dx/dt = (x - 4t)/(t - x)
wraith daggerBOT
drifting matrix
huh what is Wolfram Alpha doing here.
nova inlet
<@&286206848099549185> why dont online calcs give me the right answer
crimson sedge
huh what is Wolfram Alpha doing here.
dieing
nova inlet
,wolf xโโ=-2txโ^2
wraith daggerBOT
nova inlet
this shit too
drifting matrix
Try differentiating your solutiion.
nova inlet
,wolf xโโ=-2txโ^2, x(0)=1, xโ(0)=-1
wraith daggerBOT
drifting matrix
dieing
Oh I think I see it now. It's a fourth order equation so solving for x is... messy.
nova inlet
is 1/2(ln((t+1)/(t-1)))+2 the same as this
drifting matrix
ask wolfy
nova inlet
how
drifting matrix
,wolf simplify 1 - tanh^-1(t) - (1/2(ln((t+1)/(t-1)))+2)
not zero thus not same
tanh^-1 does have a ln-like description though
nova inlet
,wolf xโโ=1.5x^2, x(0)=1, xโ(0)=-1
wraith daggerBOT
nova inlet
,wolf xโโ=-2txโ^2, x(0)=1, xโ(0)=-1
can you help me solve this one then
wraith daggerBOT
nova inlet
,wolf simplify 1 - tanh^-1(t) - (1/2(ln((t-1)/(t+11)))+2)
wraith daggerBOT
nova inlet
,wolf simplify 1 - tanh^-1(t) - (1/2(ln((t-1)/(t+1)))+2)
wraith daggerBOT
drifting matrix
,wolf simplify 1 - tanh^-1(t)
wraith daggerBOT
nova inlet
,wolf xโโ=1.5x^2, x(0)=2, xโ(0)=-1
wraith daggerBOT
nova inlet
what does that mean
i mistyped initial condiition is x(0)=2
,wolf simplify (-2x^(-1/2)-t+2)-(x-(4/((t+2)^2)))
wraith daggerBOT
indigo badge
What would be a good way to go about imagining what these look like?
indigo badge
I know the first one is an equation of a circle as well as the last one, but the last one's radius is sqrt(z)
I rearranged the second one to this:
so to me that looks like a sphere, my guess is this one is E as well
I just realized I'm gonna have to use one of the answers at least twice
.close
trim quail
what do i need to do to turn this into a equivalent expression
solar grail
what do i need to do to turn this into a equivalent expression
wdym?
trim quail
How do I evaluate C: into 16
raven barn
Do you know rules for powers?
raven barn
crimson sedge
use the power rule
raven barn
No worries
trim quail
ngl didn't know it was that easy
cyan grotto
.close
cedar kilnBOT
Available help channel!
hidden epoch
how would you graph -x=3^(y+1)
cedar kilnBOT
how would you graph -x=3^(y+1)
hidden epoch
ping if you get it
cedar kilnBOT
@hidden epoch Has your question been resolved?
hidden epoch
i tried using the log method
i mean you log both sides
but then one side is negative
im a bit confused
<@&286206848099549185>
i know you can't log a negative
upper abyss
Why is -x a negative number?
In fact, it can't be, since the right is strictly positive
upper abyss
Why is -x a negative number?
.
upper abyss
There's nothing wrong with log(-x), because -x is a positive number.
hidden epoch
oh shid
i just notices
noticed
ah my brain
thanks
thank god theres a place i can i go to when my brain doesn't work
upper abyss
Haha yeah see that a lot, it has a negative, so it must be a negative number, right?
cedar kilnBOT
cedar kilnBOT
Available help channel!
warm skiff
Find a formula to calculate the sum of
(1/1x3)+(1/3x5)+(1/5x7)+...
for any number of terms
warm skiff
i have no idea to even approach this
all we did in class was the formula for an geometric sequence and an arithmetic sequence
south tundra
Try decomposing the fractions
warm skiff
I get 1/(4n^2-1) as the formula for any given term
south tundra
Yeah now you probably need to decompose 1/(2n - 1)(2n + 1)
Decomposing means, in this case, rewriting it as A/(2n - 1) + B/(2n + 1)
Where A and B are some constants that you need to find
warm skiff
i dont see how that will help me
what if i do 1/ (<sum formula for 2n-1>)(<sum formula for 2n+1>)
would that give me the sum formula for the original sequence?
warm skiff
.close
cedar kilnBOT
cedar kilnBOT
Available help channel!
sinful vale
can anyone help me with this
cedar kilnBOT
can anyone help me with this
south tundra
In 1st, just like the question states, you need to substitute y = -6x + 5 into 7x + 2y = 10
And in the 2nd one, you need to manipulate equation such that some unknown cancels out when you add the equation (hint: multiply the 2nd equation by 2)
sinful vale
In 1st, just like the question states, you need to substitute y = -6x + 5 into 7...
how do i do that tho
i understand what itโs asking but i donโt know how to answer it
dense wing
if I had 2x+3 and asked what the value was at x=2, what would you do?
sinful vale
substitute x for 2 and solve
sinful vale
idk what to substitute tho
sinful vale
yeah
green jungle
so from the first equation we can say that y = -6x+5 right?
sinful vale
yes
sinful vale
like this?
green jungle
idk show me your working i havent done it
wait no it's not 0
can you show me what you've done?
sinful vale
sinful vale
yeah and now solve for y
y=5?
green jungle
ok so for elimination
the goal is to cancel out a variable completely so that you can work with one variable and get it's value similar to what u did for substitution
so now look at the two equations in the second question
and pick a variable that you want to cancel out
you can pick any of the two just pick one and i'll show you how to do the rest
sinful vale
cancel out y ig
green jungle
ok so now what's the lcm of 10 and 5
sinful vale
ok so now what's the lcm of 10 and 5
the what
sinful vale
no
green jungle
ok so the multiples of 5 are 5,10,15,20,25,30
basically anything that's fully divisible by 5 is a multiple
same goes for 10?
do u get it now?
sinful vale
no
green jungle
ok do you know 5 times table?
green jungle
so these ------> 5,10,15,20,25 you get by multiplying 5 with sth
green jungle
what would the equation look like for elimination tho
we're getting to that hang on
green jungle
so these ------> 5,10,15,20,25 you get by multiplying 5 with sth
hence they are multples of 5
do u get it now?
sinful vale
yeah
green jungle
so what's the lcm of 10 and 5?
sinful vale
10?
green jungle
yes
so in both equations
the thing that's multiplied with y or the coeffecients as they're called
you have to make one of these coeffecients 10 and the other one minus -10
how would you do that?
sinful vale
like this?
green jungle
YEAH
good
now
add these two equations together
the left hand side of one equation with the left hand side of the other equation and the right hand side of one equation to the right hand side of the other
do u understand?
sinful vale
wait can i do this instead?
green jungle
yeah you can
basically eliminate one variable away
that's the elimination method good job
green jungle
yeah it is
green jungle
i think i have the hang of it now
same i think u got it
cedar charm
earlier in #help-21๏ฝ์๋ฆฌ์คํจ์ถฉ1 i asked a question but i still don't get, i'll repost it.
cedar charm
So far I've used
cedar charm
which equations are you talking about?
cedar charm
ohh
Alright so I'm going to be honest, I don't know how to do that. Missed this whole chapter, sorry.
gentle lintel
you know trig identities like compound angle right?
gentle lintel
yes
cedar charm
Yeah
gentle lintel
you need a fair understanding of these
gentle lintel
earlier in <#903481102591750184> i asked a question but i still don't get, i'll ...
to solve this
cedar charm
I kinda do but I'm trying to solve these and reflect back to see how it was done.
gentle lintel
you also need sinยฒx + cosยฒx = 1
cedar charm
Yeah that I know of.
gentle lintel
then add them up
after youโve done this try multiplying the equations together
then repeatedly use compound angle
cedar charm
So should I write out the tan (a + b) and then replace the tan with sin and cos?
gentle lintel
So should I write out the tan (a + b) and then replace the tan with sin and cos?
you canโt really do that at the moment lol
you donโt know sin x cos x sin y cos y
cedar charm
try squaring the first and second eqautions
btw, what do you mean by this?
I don't know English math terms yet.
gentle lintel
for example
sinยฒx + 2 sin x sin y + sinยฒy = 0.09
for the first one
do the same for the 2nd one
then add them
gentle lintel
no
cedar charm
oh
gentle lintel
0.064
cedar charm
oh yeah my bad
wait no isn't 0.8*0.8 equal to 0.64
Could anyone else jump in and help me out <@&286206848099549185>
leaden snow
@cedar charm What's the problem?
cedar charm
earlier in <#903481102591750184> i asked a question but i still don't get, i'll ...
this^
leaden snow
Just add the two (squared) equations as Chromium said and apply sin^2(x) + cos^2(x) = 1
cedar charm
Wait so I have both those equations squared, then what do I do?
leaden snow
You add them together to get another equation
leaden snow
Add the left hand side of the first equation to the left hand side of your second equation and do the same thing for the right hand side
leaden snow
Now if you group similar terms together you'll see
cedar charm
oh okay so like sinยฒx + cosยฒx would become 1?
leaden snow
Yes
cedar charm
alright one sec
leaden snow
same for y
leaden snow
Once you simplified look at this table again and see if you can find a similarity
cedar charm
did i correctly simplify that?
leaden snow
yes
cedar charm
So in the table the cos (a - b) can be found in my equation right?
but I don't see anything that I can do with that
leaden snow
you could factor the 2 and then replace the expression with cos(x - y)
cedar charm
I'm a bit confused with the English terminology again, could you explain?
leaden snow
write it as 2 + 2[sinx siny + cosx cosy] = 0.73
then replace sinx siny + cosx cosy with cos(x - y)
leaden snow
then you get a numeric value for cos(x - y)
now consider what happens if you subtract (instead of adding) the squared equations from before
cedar charm
then i'd get the value for cos(x + y)?
leaden snow
Yup
cedar charm
alright
solid quarry
you can probably solve this geometrically
cedar charm
also is the value for cos(x - y) = (0.73-2)/2?
leaden snow
yes
cedar charm
alright
gonna get the value for cos(x + y) one sec.
wait so for the value of cos(x + y) i'd have to subtract the second equation from the first one and how would that one look?
after it is simplified?
gentle lintel
you know cosine double angle right?
leaden snow
what did you get after subtracting?
cedar charm
iโm kinda stuck on that wait let me show you
did i write it wrong? or how should it be worked out?
patent flame
these formulae may be useful
cedar charm
yeah i know, iโve posted them earlier but iโm stuck now
solid quarry
bahahah
cedar charm
hmm?
solid quarry
i tried using complex numbers
v = e^(iy)
z = u + v = 0.8 + 0.3i
u = z/2 + sqrt(1-|z|^2/4)(iz/|z|)
uv = z^2/4 - (1-|z|^2/4)(-1z^2/|z|^2))
z^2 = 0.8^2 - 0.3^2 + 2*0.8*0.3i
real(uv) = (0.8^2 - 0.3^2)/4 + (1-|z|^2/4)(0.8^2 - 0.3^2)/|z|^2
imaginary(uv) = 0.8*0.3 / 2 + (1-|z|^2/4)(2*0.8*0.3)/|z|^2
tan(x+y) = imaginary(uv)/real(uv)```there's these ones as well (i've never used them but i mean you could try)
cedar charm
iโm just going to start over and see what i can do because iโm just lost
patent flame
ill see if i can do this question then ill share my answer
cedar charm
alright thank you
yeah iโm getting nowhere, iโll wait for you @patent flame to see how you did it
patent flame
im still getting nowhere tbh
cedar charm
hold on iโm going to look at the exercise again
calculate tan(x + y)
if sin x + sin y = 0.3 and cos x + cos y = 0.8
solid quarry
```u = e^(ix)
v = e^(iy)
z = u + v = 0.8 + 0.3i
u = z/2 + sqrt(1-|z|^2/4)(iz/|z...
,w z = 0.8 + 0.3i, l = |z|, compute (0.80.3 / 2 + (1-l^2/4)(20.8*0.3)/l^2)/((0.8^2 - 0.3^2)/4 + (1-l^2/4)(0.8^2 - 0.3^2)/l^2)
oh god
wraith daggerBOT
solid quarry
that might be the answer. nah wolfram wont do what i want
patent flame
well i got to tan(x+y/2) = 0.375
cedar charm
well i got to tan(x+y/2) = 0.375
wait so did you get it?
patent flame
not really because i don't know how to get past to tan(x+y)
solid quarry
do u wanna try understand my answer?
cedar charm
I have to do it using all of this stuff though
patent flame
well actually tbh you could do tan(arctan(0.375)*2)
are you allowed to use a calculator?
patent flame
yeah so i guess you can do that then
arctan means tan^-1 or inverse tan
whatever you know it as
patent flame
do sin(x)+sin(y)/cos(x)+cos(y)
and using these formulae
change the numerator and the denominator
and all of that will be equal to 0.3/0.8 = 0.375
once you've changed the numerator and denominator you can use the identity sin(x)/cos(x) = tan(x)
cedar charm
alright
cedar charm
do sin(x)+sin(y)/cos(x)+cos(y)
can't it be solved using this
and turning those tan into sin/cos
patent flame
it probably could but i think it would take longer
I originally tried to do that but got kind of lost so i used the other formulae
cedar charm
yeah i tried this one earlier and got lost as well
upper garnet
did u do
solid quarry
and all of that will be equal to 0.3/0.8 = 0.375
yess i got the same answer
cedar charm
i'm struggling with getting there though
patent flame
the answer which i got in radians for tan(x+y) is $\frac{48}{55}$
wraith daggerBOT
I can't believe you've done this
cedar charm
i have to use
solid quarry
i got tan(0.358771)
patent flame
yeah you have used the formula in the bottom right and the identity that sin(x)/cos(x) = tan(x)
patent flame
i got tan(0.358771)
I got tan(2*0.358771)
since i got that $\frac{x+y}{2}\approx{0.358771}$
wraith daggerBOT
I can't believe you've done this
solid quarry
nvm im so tired rn
patent flame
me too man
did you get the answer or do you want to see my working?
cedar charm
i'd love to see how you got it
wraith daggerBOT
patent flame
sorry if it's a bit messy, i'm not really neat when it comes to working so i had to put a bit of effort in
cedar charm
oh don't worry
patent flame
yeah me too
patent flame
It seems like you have good understanding of most of the things used so i'm sure you'll be able to learn it quickly
cedar charm
Yeah hopefully, going to go over everything one more time to see if I get it.
I'll most likely be asking for help again sometime soon!
cya:)
patent flame
bye, i'll try to help wherever i can
warm hemlock
So I got a task where it says:
โTwo bodies with the same volume are cast from the molten metal of a sphere with a radius of 3.6 cm: a cylinder with a diameter of 6 cm and a cone with a diameter of 6 cm. Calculate the heights of the two bodies and the surface that results when both bodies are glued together at the bases.โ
I tried to solve it myself but got stuck somewhere. Can someone please give me some ideas on how to solve the problem?
leaden snow
Why the hell do you use 13 decimal digits
warm hemlock
just in case I need precise calculation
leaden snow
Anyway. I'd start with the volume. Calculate the sphere's volume. Half of it needs to be the cylinder, the other half the cone.
They have the same base radius, so their heights are uniquely determined
warm hemlock
will do
leaden snow
But I think you already solved it, didnt u?
onyx tapir
Hi, is this correct?
9^x โ 18 โ 3^x = -77 | /(-18)
9^x โ 3^x = 77 / 18 | log()
x โ log(9) + x โ log(3) = log(77 / 18)```So the task is just to calculate x from this equation: 9^x โ 18 โ 3^x + 77 = 0
drifting matrix
the second step is wrong
if you divide by -18 you would get
$-\frac{9^x}{18} + 3^x = -\frac{77}{18}$
wraith daggerBOT
M8732
cedar kilnBOT
cedar kilnBOT
Available help channel!
rare patrol
Local Maxima here, I think it's 0,2
rare patrol
<@&286206848099549185>
dire geode
looks right
dire geode
yea i just said that
rare patrol
.close
low jewel
is it logically sufficient to say that this function is not continuous because it is undefined at (1,1) and (-1,-1)?
low jewel
or just when x=y i guess lol
elfin hemlock
continiutity is only a thing on domain
low jewel
it says "show that f(x) is not continuous at (0,0)"
im assuming this is because it is undefined at that point?
low jewel
at 0
ok
i guess i should say, how can i prove that f(x) is not continuous at (0,0)
or are you saying that it is
solid quarry
show that lim (x,y) -> 0 3xy/(x^2-y^2) is not 0
elfin hemlock
you have to show a path where the limit is not 0
crimson sedge
Eight subtracted from one times a number is -34. What is the number?
twilit radish
cedar kilnBOT
twilit radish
whats the procedure
obsidian coral
n=2
obsidian coral
What's that n?
twilit radish
it doesnt say
i mean n=2
but when i replace the i just get n1 as the exponent
which i dont know
twilit radish
.close
hollow sapphire
Hi, I'm really confused as to how to approach this question. I can't visualise the diagram correctly(as seen by my attempt). Where did I go wrong with interpreting the question?
cedar kilnBOT
Hi, I'm really confused as to how to approach this question. I can't visualise t...
@hollow sapphire Has your question been resolved?
hollow sapphire
<@&286206848099549185>
hollow sapphire
I'm not native english speaker so I hope i translated it correctly ๐
why did you not draw the tower to be on the bottom? is there are a reason you put it there
hot garden
I'm not sure , what do they mean at the base of a hill?
on the ground? on the start of the hill?
I'll try solving both and see which makes more sense
hollow sapphire
ok
hot garden
@hollow sapphire do you have the solutions to check? I solved it placed it on the ground and got a height value in meters
I can explain to you
hot garden
ok im checking
nope I'm out
sorry I know trig , but i must not be getting the drawing either
Isn't the drawing supposed to be this??
hot garden
Maybe someone else should try solving it placing the tower tilted?
cedar kilnBOT
@hollow sapphire Has your question been resolved?
cedar kilnBOT
cedar kilnBOT
Available help channel!
median summit
cedar kilnBOT
cedar kilnBOT
@median summit Has your question been resolved?
median summit
.close
gusty lotus
Hi
drifting matrix
The first equaility is clear, I assume?
drifting matrix
$$\lim_{x -> 0} f(x)g(x) = \lim_{x -> 0} f(x) \lim_{x -> 0} g(x)$$
wraith daggerBOT
M8732
gusty lotus
yea
drifting matrix
(if the limes at the right hand side exist)
In this case just
f(x) = Pi/2
g(x) = sin(x)/x
drifting matrix
Sorry mistyped, I meant sin(x)/x
drifting matrix
two functions
drifting matrix
yes
gusty lotus
drifting matrix
yeah that is more intricate.
gusty lotus
cause we plug in a 0
drifting matrix
well
drifting matrix
,wolf graph sin(h)/h
wraith daggerBOT
drifting matrix
sin(h) is zero at h=0
so the zero cancels in a way
Do you know Hรดpital's rule?
gusty lotus
nope
drifting matrix
then this is difficult to proof
I assume they just used that as a fact
the second equality
gusty lotus
OH WAIT SO they put the pi/2 to the left
cause it wouldn't matter what limit it is it's a constant so itll always be the same
ok got it
it's just sin(h)/h
drifting matrix
yeah
drifting matrix
what do you mean by crossing them out?
drifting matrix
but there are no common factors in this case
drifting matrix
the only simple wqay to proof this is using Hรดptial's rule
everything else is a huge mess.
gusty lotus
dang we haven't learned that yet, i guess ill just ask my professor about this question
drifting matrix
Ok
drifting matrix
wow a lot of chapters also
gusty lotus
yea
drifting matrix
You are welcome ๐
zealous crystal
Yup
fluid elbow
Calculus BC help
cedar kilnBOT
Calculus BC help
violet rapids
Calculus BC help
Post ya question!!!
fluid elbow
I have my answer, if i get it wrong then i have to redo the entire assignment. I just wanted to check with someone
drifting matrix
So what is your answer for that?
fluid elbow
y+1 = -sqrt(3)(x+sqrt(3))
i figured it out, and got it right, thanks anyways
.cloe
.close
crisp escarp
Can someone help with question 7? I'm in desperation
cedar kilnBOT
Can someone help with question 7? I'm in desperation
crimson sedge
Me too ffs Iโm same school with this human
violet rapids
Is this 1 axis
crisp escarp
Is this 1 axis
I think it's like we need the rotational symmetry
violet rapids
Ok so just 1 axis
crisp escarp
Yes
violet rapids
So if rotational symmetry is if its the same shape after rotating
So how many times can you rotate the shape to get the shape to be the exact same
So Q6 is good
As is Q5
So lets do Q7
crisp escarp
Tyyy
violet rapids
Lets rotate this shape in our imagination
If we start rotating it, will there be a time where its the same shape?
crisp escarp
Not sure
crisp escarp
It's still the same shape, I think
violet rapids
Looks pretty much the same to me tbh
crisp escarp
Yep, probably
violet rapids
So how many times can it be rotateed to get the original shape?
crisp escarp
Once I think
violet rapids
Uh
I didn't mean to say times
How many ways can it be rotated to get the original shape?
crisp escarp
By turning it in different directions
Wait! I got the answer
Tysm for ur help
.close
noble igloo
Hey, I've been thinking and couldn't really find a way to solve this problem in this specific way (though I can think of others). How would I go about finding the average of a 4 variable function over a domain that is a subset of R4 Euclidean space?
noble igloo
I believe I would have to take the integral over that domain * 1/vol(domain), but I'm not sure about how to go about it
(The function in the screenshot isn't the actual function to integrate, since you can't just substract two complex numbers to get distance)
cedar kilnBOT
@noble igloo Has your question been resolved?
noble igloo
Basically, I want to integrate this over the following domain
