You got it the wrong way around but yes its (9, 8)
#help-36
forest osprey
thanks man
wind glacier
If you think you're done with this please type .close
forest osprey
.close
keen warren
For the function f we have f(x) = x+1/x-3
final saddleBOT
For the function f we have f(x) = x+1/x-3
keen warren
And we need to find the asymptotes
$$f\left(x\right)=\lim _{x\to \infty }\left(\frac{x+1}{x-3}\right)$$
$$=\lim _{x\to \infty :}\left(\frac{x}{x-3}+\frac{1}{x-3}\right)$$
$$=\lim _{x\to \infty }\left(\frac{\frac{x}{x}}{\frac{x}{x}-\frac{3}{x}}\right)$$
$$=\lim _{x\to \infty }\left(\frac{1}{1-\frac{3}{x}}\right)$$
$$=\lim _{x\to \infty }\left(\frac{1}{1}\right)=1$$
soft zealotBOT
AuHasard
keen warren
This is the horizontal asymptote, do I need to do anything else?
Then the vertical asymptote is x = 3.
I don't think it has a oblique asymptote…?
If the numerator was x^2 + 1, we could've done polynomial division and found out the remainder mx + b is the oblique asymptote, right?
odd dove
I don't think it has a oblique asymptote…?
what is an oblique asymptote
Ah here we go, an asymptote of the form mx + b
set m to zero, and what do we get
royal gust
Can't really have two different asymptotes, unless you mean one to the left, and one to the right
keen warren
set m to zero, and what do we get
What's our m? We don't have it
odd dove
Well, exactly
keen warren
Can't really have two different asymptotes, unless you mean one to the left, and...
There are different asymptotes in this solution, one vertical and one horizontal
odd dove
A horizontal asymptote is just a special case of the oblique one
keen warren
So the horizontal asymptote replaces the oblique one?
royal gust
Okay I didn't think about the vertical one, but you know what I mean. Having two different asymptotes to infinity would mean you have two different limits
Or like, two different curves.
keen warren
Okay I didn't think about the vertical one, but you know what I mean. Having two...
Are you talking about the horizontal asymptote?
royal gust
Ye
odd dove
keen warren
,w graph (x+1)/(x-3)
soft zealotBOT
odd dove
Or well here
You see it gets closer to y = 1
as x grows to infinity
So the function can't then also get closer to anything else
at the same time
keen warren
Okay I didn't think about the vertical one, but you know what I mean. Having two...
So like we can't calculate the asymptotes for both x→∞⁺ and x→∞⁻?
odd dove
(in simple terms)
royal gust
Yes. Let's only consider asymptotes to infinity though
Can't just have two asymptotes to infinity
odd dove
I mean, you could try to compute the oblique asymptote in your task. (Using the standard formulas)
You'd get that m=0 and b=1
keen warren
If we consider this function f(x) = 1/x, x→0⁺ means x is closing on 0 from the right. So x→0⁻ means x is closing on 0 from the left.
So we can't have horizontal asymptotes for both x→∞⁺ and x→∞⁻?
Let me know if I am understanding correctly
odd dove
If we consider this function f(x) = 1/x, x→0⁺ means x is closing on 0 from the r...
The limit of this function as x approaches plus infinity = the limit as x approaches -infinity
royal gust
Yes. Let's only consider asymptotes to infinity though
I'm ignoring the left asymptote.
keen warren
You'd get that m=0 and b=1
So if we consider x→∞ then 1/∞ = 0.
This means that the horizontal asymptote is the x-axis.
Oops replied to wrong message
keen warren
You'd get that m=0 and b=1
Yeah so f(x) = 1 is the horizontal asymptote?
How did you get b =1 btw
odd dove
Well, the usual formulas I go with are $m = \lim_{x\to\infty} \frac{f(x)}{x}$ and $b = \lim_{x\to\infty} \left( f(x) - mx \right)$
soft zealotBOT
Remavas
odd dove
Those can be found from the definition of the oblique asymptote
odd dove
well it's pretty easy.
keen warren
This is all the information from my textbook about oblique asymptotes
So they write ”When x→±∞ then 1/x→0, therefore f(x) →x+1.”
odd dove
$\lim_{x\to\infty} \left[ f(x) - \left( mx + b \right) \right] = 0$ if mx+b is an oblique asymptote
soft zealotBOT
Remavas
final saddleBOT
@keen warren Has your question been resolved?
warm star
final saddleBOT
warm star
Can i get help
final saddleBOT
@warm star Has your question been resolved?
final tangle
you have a quadrilateral inscribed in a circle, i.e. a cyclic quadrilateral
look up the relevant theorems for those
warm star
final saddleBOT
mellow warren
you can use the the fact that a tangent to a circle is always orthogonal to the radius (angle QSL = 90) and the pythagorean theorem
wooden epoch
The probability of rolling doubles on two dice is 1/6. If you roll two dice 10 times, what is the expected number of doubles? Not sure on where to start with this one one.
final saddleBOT
The probability of rolling doubles on two dice is 1/6. If you roll two dice 10 ...
fallow zinc
I mean, let $X$ be the number of doubles you get in 10 rolls
soft zealotBOT
Mosh
fallow zinc
what distribution does X follow?
wooden epoch
are you referring to binomial ?
wooden epoch
thinking
I mean you could do P(x=0)+P(x=1)+.... P(x=10), but I'd imagine there's an easier way?
soft zealotBOT
Mosh
fallow zinc
what is n and what is p?
wooden epoch
10, 1/6
fallow zinc
yes, so now you want to find $E[X]$
soft zealotBOT
Mosh
wooden epoch
Not seeing the E[X] notation in my book... the mean of x?
µx = np
I think that's it!
@fallow zinc I got it, thanks for pointing me in the right direction.
fallow zinc
µx = np
yes
the mean of Bin(n,p) is np
$E[X]=:\mu \
\operatorname{Var}[X]=:\sigma^2$
soft zealotBOT
Mosh
final saddleBOT
final saddleBOT
Available help channel!
kindred wing
Anyone know how to work this
final saddleBOT
Anyone know how to work this
kindred wing
ocean lintel
,rotate
soft zealotBOT
kindred wing
It's ab equations
ocean lintel
have you done 1) ?
kindred wing
I tried 600+5(50) which is 99% wrong
ocean lintel
profit = benefit - costs, so there has to be a - somewhere
kindred wing
Ah
ocean lintel
and an x, since profit is definitely not constant
ocean lintel
that would be equating 2 things. This is not a function as such. You're looking for f such that profit = f(x)
kindred wing
I'm really bad at making expressions so not sure what to write
I can work out quadratic or them easily but can't make the equations
600+5x-50x=
I don't really know the answer
ocean lintel
profit = benefit - costs, so there has to be a - somewhere
You're given the formulas for benefits and costs and are asked for profit
kindred wing
Alright
So originally you got 50x
Then she sold them for 600+5x
So she got (600+5x)-(50x)= profit
Because its total made - original cost
That's what I'm understanding
ocean lintel
So she got (600+5x)-(50x)= profit
yes
ocean lintel
what's your starting equation?
kindred wing
(600+5x)-(50x)=x/100
ocean lintel
that's not what I said
ocean lintel
profit of x% means profit = x% of costs
no subtraction here
x% of costs means x/100 * costs
kindred wing
So instead = I write +?
ocean lintel
ocean lintel
I got 600+5x-x²/2
- that is not an equation 2)I can't know what you did wrong if I don't see the computations
final saddleBOT
@kindred wing Has your question been resolved?
tranquil pine
Someone buss help
hallow quartz
Someone buss help
With?
tranquil pine
Thank you
Will send now
Don’t need it to be literally solved obviously
Just need pointing in right direction
Mark scheme is useless
hallow quartz
Which question?
tranquil pine
Both
hallow quartz
Oh
tranquil pine
I can do the second one on my own actually after I figure out the first one
So just a please
hallow quartz
I will attempt the first and see what I can do...
hallow quartz
Not so much, but I would recommend writing everything in sin and cos first
tranquil pine
I feel like you might have to use double angle formula as well
tranquil pine
How old are you if you don’t mind me asking?
hallow quartz
Nobody nose
inland stream
Hello, i need a lot of help.
i want to set the ratio of a pulse, for example 1:3 so the pulse is >0 1x while <0 3x
i wish there is a propper way to do it but basically this is it. thank you for any help
final saddleBOT
Hello, i need a lot of help.
i want to set the ratio of a pulse, for example 1:...
inland stream
so k:l = 1:3 for example.
but it needs to be modifiable
if i said for example 60:1 and something like this
this is btw just
cos(x)+(2/3)
solemn sage
so for the ratio 1:3 you want 33.3% of the graph to be above the x-axis and 66.6% of the graph to be below the x-axis? @inland stream
inland stream
excactly
i mean, isn't this actually already 2/3 ratio? :D when im looking at it now
inland stream
well it is actually that ratio but unfortunately that's only this case..
inland stream
so k:l = 1:3 for example.
no, basically this k:l in ratio a:b where a and b will be variables
solemn sage
???
inland stream
1:3 => 1 - 1/3 = 2/3 above 0, and 1/3 below zero?
oh, yeah
exactly that
but 60:1 the same way
solemn sage
Okay so let's just consider the interval [0, pi] for cos(x)
say we want 0 <= p <= 1 (in %) to be above zero
inland stream
exactly
solemn sage
To do this we need to shift cos(x) by a yet unknown amount a along the y-axis
inland stream
well if cos(x) then just pi/2 + pi/2
solemn sage
what
inland stream
yeah i think you're right, sorry my english really limits how i meant that..
solemn sage
Ok so say p = 2/3 = 66.6% should be > 0
inland stream
exactly
inland stream
yes
solemn sage
so we want a to be such that the root is exactly at (2/3) * pi
inland stream
i think so
solemn sage
$\cos((2/3)\pi) + a = 0$
soft zealotBOT
Navix
solemn sage
so here a = 1/2
in general for any p between 0 and 1, we have
$$\cos(p \cdot \pi) + a = 0$$
soft zealotBOT
Navix
solemn sage
so now relating that back to the ratios
1:3 ratio meant that 1 - 1/3 = 2/3 is > 0
so we for any ratio m:n, we can find p by writing p = 1 - m/n = (n - m)/m
inland stream
it looks that should be correct
solemn sage
if thats what you meant to do
inland stream
so if i wanted to do this 60:1 i will just say p = 1 - 60/1=(1-60)/60?
solemn sage
yeah that would give a = 0.998 approximately
if you want 60 times more to be above 0 than below 0
inland stream
ok so.. if i was about to make a function out of it i will write it as..
i can do the ratios but i need to do the function..
solemn sage
function?
inland stream
probably not the word for it but how to write it in geogebra that i am using so it will give me a function where its 60:1 in ratio
solemn sage
no idea about geogebra >.>
inland stream
like if i wanted to do a function just like cos(x) will show me it, what to write in it?
like so i will write
cos(x)+a
where a = (n - m)/m?
although m=>n
right?
actually wow! that's it! thank you so much <33
.close
glad basalt
I have a sort of weird question
final saddleBOT
I have a sort of weird question
soft zealotBOT
geoxcaliber
glad basalt
(I know this is not true)
Let's say it was. You would be able to remove the two 5x's
of course you could do it via subtracting -5x from one to the other, but is it because
The equation is equal? because x = y? Is it the same equation as
$$\frac{x}{y}=1$$
soft zealotBOT
geoxcaliber
glad basalt
So you can look it as
hallow quartz
Chill out.
glad basalt
$$\frac{5x+5}{5x+4}$$
soft zealotBOT
geoxcaliber
final saddleBOT
@glad basalt Has your question been resolved?
fleet rain
If you roll two dice what is the probability that one is a power of the other?
fleet rain
@fallow zinc
fallow zinc
why did you feel the need to ping me?
fallow zinc
same thing as last time.
write out the sample space and find the outcomes you want to happen.
fleet rain
oh
fallow zinc
what oh?
fleet rain
what do they mean by power?
fallow zinc
a^n
fallow zinc
n is the power.
fallow zinc
so for example (2,4) is desired
fleet rain
since 2^2 is 4?
fallow zinc
yes.
fallow zinc
write out the sample space and go through the options
fleet rain
is my example right at least?
fleet rain
yeah its only 2
spaces
the others wont work
(6, 1) is wrong
6^n = 1
n=0
theres no 0 in a die
fallow zinc
yeah its only 2
No?
(6,6) works, since 6=6^1
Again, go through the entire sample space
fleet rain
(6,6) works, since 6=6^1
where did you get 1 from?
fallow zinc
...
fleet rain
"one is the power of the other"?
fallow zinc
yes
fleet rain
it gotta be whole numbers right?
fallow zinc
yes.
fleet rain
i got 1/3
is that right?
If you get a dollar for every head you roll in a coin flip, what is the expected amount you'll make with 4 flips?
i got 2 for this^
fallow zinc
i got 2 for this^
yes
fleet rain
I think you overcounted the number of desired outcomes.
i did
(1,1), (2, 1), (2, 2), (2, 4), (3, 1), (3, 3), (4, 1), (4, 4), (5, 1), (5, 5), (6,1), (6, 6)
these are all my desired counts^
fleet rain
ye
fleet rain
how 18?
fleet rain
3 = 1^n?
fallow zinc
....
fleet rain
thats for (1, 3)
fallow zinc
where does it say order matters?
fleet rain
order doesnt matter?
fallow zinc
clearly not
fleet rain
ok i guess than
fallow zinc
if I roll 3 and 1, regardless of which die is which, I still have that 3^0=1
fleet rain
true true
im thinking in a weird way
alright i just messed up on order
ill review this prob tmrw
and do it again
final saddleBOT
Available help channel!
spark citrus
How can I show that every finite Integral Domain that accept an identity element is a field
final saddleBOT
How can I show that every finite Integral Domain that accept an identity element...
hearty zephyr
Show that every non-zero element has an inverse
royal gust
"that accept an identity element"?
hearty zephyr
"that accept an identity element"?
some texts don't include identities in the definition of a ring. They make a distinction between 'rings' and 'rings with unity'
spark citrus
I didn't understand why we need a finite Integral domain
hearty zephyr
because it isn't true for an infinite integral domain. Take Z, for example.
royal gust
Oh, all finite IDs with an identity are fields. Cool!
spark citrus
But for z it s a problem of inverse
hearty zephyr
right, it's not a field
you're trying to show
Finite integral domain with identity -> field
if you don't have finite, it isn't true. The integers are a counter example because Z is an integral domain with identity that isn't a field
spark citrus
Iike if we took a finite part of Z it will not be a field either
hearty zephyr
it also wouldn't be a ring
final saddleBOT
final saddleBOT
Available help channel!
willow sierra
final saddleBOT
silk cobalt
By multiplying and rearranging
willow sierra
How exactly?
willow sierra
I got that far but don't know what to do next to get the solution
silk cobalt
U then shift -n to rhs by adding n to both sides
After this compare this with the equation on the top right
U will get a,b value
willow sierra
Do you divide by n next?
silk cobalt
After multiplication
N(t+1)-n(t)=rs-rn(t)
Rearranging
N(t+1)=rs-rn(t)+n(t)
N(t+1)=rs+n(t)*(1-r)
willow sierra
Yes
silk cobalt
After this compare this with the equation on the top right
U will get a,b value
Next u do this
naive rock
final saddleBOT
naive rock
crisp plover
Why are you even trying that value for theta when it asks for it to be in [0, 2pi)
naive rock
so do I add 2pi to theta?
vital crag
do you know why +2pi ?
naive rock
because 2pi is like 360 deg. You add it to try to get it into [0, 2pi)
solemn sage
also the angle theta, as you have sketched it, doesnt make sense in the context of polar coordinates
naive rock
so the answer is the sum of -1.2490 + 2pi?
solemn sage
maybe try understanding what you are doing instead of trying random stuff
final saddleBOT
@naive rock Has your question been resolved?
vital crag
maybe try understanding what you are doing instead of trying random stuff
good ol' spaghetti math
icy pivot
Hi
Could anyone help with a binary relation?
R1 = {(a, b) ∈ Z^2 | a = bn, n ∈ Z}
I can see that the set Z^2 = {0, 1, 4, 16, 25, 36..}
aRb if a = bn , do I need to enumerate through n = 1,2,3,4.. ?
final saddleBOT
Hi
Could anyone help with a binary relation?
R1 = {(a, b) ∈ Z^2 | a = bn, n ∈ Z...
mint orbit
Hi
Could anyone help with a binary relation?
R1 = {(a, b) ∈ Z^2 | a = bn, n ∈ Z...
not sure thats what they mean by Z^2
icy pivot
mint orbit
my guess is they mean all coordinate pairs where both elements are integers
(1,4), or (-1,0)
or (0,15)
like R^2 is the cartesian plane
here you just have a grid of points instead of a plane
icy pivot
we haven't looked at coordinates/planes yet so i'm not sure
just trying to define which properties that relation is
mint orbit
well lets think
is it reflexive?
say b=a
so we have the point (a, a)
is a an integer multiple of itself?
icy pivot
when n = 1 yes
mint orbit
cool
how about symmetry?
all we need to think here
can we prove this:
$a=nb \to b=na$
soft zealotBOT
jan Niku (Shuri for Honorable)
mint orbit
where everything is an integer
is this always true?
can you think of a counter example?
mint orbit
why?
whats your counterexample
which combinations of b and a have you tried?
and whats your justification for an n not existing that makes the implication true?
icy pivot
Can you explain what the n is an integer here means
mint orbit
sure
so our option for things that are in this set
like candidates
does that make sense? the grid?
every point where both coordinates are integers
we can start thinking of examples of points that are in R_1
if the candidates make sense
icy pivot
sort of
like.. for the reflexive property to hold, n has to be 1, but when I used n = 2, it's not reflexive
icy pivot
at least when looking at Z^2 = {0,1,4,16,25..}
mint orbit
at least when looking at Z^2 = {0,1,4,16,25..}
this is irrelevant to this problem
this is not the set they are describing
mint orbit
like.. for the reflexive property to hold, n has to be 1, but when I used n = 2,...
maybe more just think about points that are in this set
how about uhh
b to be 1
so all the points (a,1)
i want to convince you that all of these points are in the relation
so ill say we have some integer, a
and the number 1
is it true that there exists an n which makes a=1*n true for any choice of a?
sure, let n=a
this is what it means for n to be an integer
we can think of a point which is not in this relation
(2,3) is not
because there is no integer n such that 2=3*n
@icy pivot does that example make sense?
the existence of n is what makes a and b related
icy pivot
sort of, I'm struggling to see why Z^2 is irrelevant
mint orbit
sort of, I'm struggling to see why Z^2 is irrelevant
im saying Z^2 is not the set of integers squared
its the cartesian product of the set Z with itself
$Z^2 = Z \otimes Z = {(z_1, z_2) \mid z_1, z_2 \in \bZ}$
soft zealotBOT
jan Niku (Shuri for Honorable)
icy pivot
the existence of n is what makes a and b related
right..
mint orbit
right..
so we want points where the first coordinate is an integer multiple of the second
on the grid of integers
icy pivot
by coordinates you mean a and b, not literal graph coordinates
mint orbit
by coordinates you mean a and b, not literal graph coordinates
no, literal graph coordinates
well i guess you dont have to think about them that way
but this is how i would think of them
since its visual
just like most functions in uhh
ever since youve been plotting functions in pre algebra and stuff
icy pivot
-3,-2,-1,0,1,2,3
mint orbit
youve been using R^2
icy pivot
like this
mint orbit
-3,-2,-1,0,1,2,3
what does this mean
icy pivot
coordinates?
mint orbit
coordinates here will have 2 entries
think about functions
a normal line
just like every line you ever plotted
on the same plane youve always plotted lines on
this is a relation
$L_{ {m,b} } = { x,y \in \bR ^2 : y = mx+b$ for some fixed $m,b \in \bR }$
soft zealotBOT
jan Niku (Shuri for Honorable)
mint orbit
the line defined by slope m, and y intercept b
satisfies this relation
if x and y are related, then the point (x,y) is on the line
does this help at all?
i'm assuming you have intuition about lines from like
maybe algebra or something
icy pivot
I have only done basic straight line graphs before, and when learning about relations now we haven't used coordinates as an example
icy pivot
Yes but only a small amount
mint orbit
okay
well how do you know, in the y=2x+1 case
say i tell you that the point (0,1) is on that line
but im not sure
how could you convince me
what would you check?
can you convince me that the point (0,10) is not on the line?
icy pivot
i guess I would draw it out :\
thanks for the help jan but I think i will go rewatch lecture videos, i am struggling to follow 💀 🥲
mint orbit
thanks for the help jan but I think i will go rewatch lecture videos, i am strug...
you can get there
functions are already strange enough (like lines)
relations are a weird concept, but once you break off the rust youll see!
icy pivot
.close
final saddleBOT
timber tulip
rotate by 50 has complex eigen values, so thats not it
not sure about the other 2
for Q2, think it does contain 0? 0A=0
lol sounds fun
(B+C)A = BA + CA so it seems like a subspace too?
hmmm the dimension
so $$A = \begin{pmatrix}1 & 0 \ 1 & 0 \end{pmatrix}$$ ?
soft zealotBOT
Pishleback
timber tulip
yeahh it seems 2d to me
$$U = \left{\begin{pmatrix}a & a \ b & b \end{pmatrix} : a, b \in \mathbb{R}\right}$$ i think
yeahh
I think in the the case of your Q2 you can do a similar thing but its a bit easier because you can treat B as a pair of vectors
or like row vectors
nah idk im confusd now
i did it on the wrong side lol
new answer: $$U = \left{\begin{pmatrix}a & 0 \ b & 0 \end{pmatrix} : a, b \in \mathbb{R}\right}$$
soft zealotBOT
Pishleback
timber tulip
becausseeee take an arbitrary B with entries x, y, z, w
then for B to be in U you must have $$\begin{pmatrix}x & y \ z & w \end{pmatrix}\begin{pmatrix}1 & 0 \ 1 & 0 \end{pmatrix} = \begin{pmatrix}x & y \ z & w \end{pmatrix}$$
soft zealotBOT
Pishleback
timber tulip
which implies $$x+y=x$$ and $$y=0$$ so basically you just know y is zero
soft zealotBOT
Pishleback
timber tulip
same thing to get $$w=0$$
soft zealotBOT
Pishleback
timber tulip
so $$B = \begin{pmatrix}x & 0 \ z & 0\end{pmatrix}$$
soft zealotBOT
Pishleback
timber tulip
and stuff of that form is in U
2
yeee
basis $$\begin{pmatrix}1 & 0 \ 0 & 0\end{pmatrix}$$ and $$\begin{pmatrix}0 & 0 \ 1 & 0\end{pmatrix}$$
soft zealotBOT
Pishleback
timber tulip
np
idk tbh, maybe just post that first part again here saying that you still need help with it?
scenic scarab
Simplify it. W = {(x,y,z) : y - z =0, x,y,z in R}.
So x is free, and y = z.
so W={(x,y,y) : x,y in R} = {x(1,0,0) + y(0,1,1)}
Hence {(1,0,0), (0,1,1)} is a basis
a plane through the origin spanned by (1,0,0) and (0,1,1)
Hint: symmetric real matrices are diagonalisable
nvm, sorry it's the reflection one which is symmetric
the rotation one is also diagonalisable, but not over R
here's the reflection one
and rotation
final saddleBOT
final saddleBOT
Available help channel!
fresh musk
final saddleBOT
final saddleBOT
@fresh musk Has your question been resolved?
rain crane
wdym
weary wharf
final saddleBOT
@fresh musk Has your question been resolved?
fresh musk
.close
fossil swallow
<@&286206848099549185> Help me simplify this :
sinx*tan^2x / 1+tan^2x
grim badger
<@&286206848099549185> Help me simplify this :
sinx*tan^2x / 1+tan^2x
You have to wait at least 15 minutes before pinging helpers
final saddleBOT
@fossil swallow Has your question been resolved?
fossil swallow
Idc, they'll never help me anyway ;'P
haughty bay
write tan=sin/cos, that should help simplify 1+tan^2
boreal bluff
<@&286206848099549185> Help me simplify this :
sinx*tan^2x / 1+tan^2x
tan^2x + 1 = sec^2x which might help, but I didn't attempt to simplify yet
final saddleBOT
@fossil swallow Has your question been resolved?
hazy fog
hi everyone, this questiojnj seems simple but i am struggling with it, how would i show that the integral from 1 to x 1/t dt is equal to the integral a to ax 1/t dt for any a>0
final saddleBOT
hi everyone, this questiojnj seems simple but i am struggling with it, how would...
hazy fog
using change of variables
i dont know how to apply change of variable, i feel like there needs to be more in the integral
royal gust
First one is ln(x)
Second one is ln(ax) - ln(a)
solemn ferry
royal gust
or do the u-sub. Since you need to divide the bounds by a, you'd want:
u = t/a
Or, multiply the bounds by a using u = at
hazy fog
ok, all of those suggestions help, thank you!
cold epoch
final saddleBOT
@hazy fog Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
thorny nebula
Hi, can someone tell me if I did this correctly (Trigonometry)
final saddleBOT
Hi, can someone tell me if I did this correctly (Trigonometry)
wanton python
I dont know what sides you are talking and with A,B,C. Should be in the form AB, BC, etc
thorny nebula
this?
final saddleBOT
@thorny nebula Has your question been resolved?
fresh musk
if in a hypothesis test, i write rho = population product moment correlation coefficient instead of population correlation coefficient, is that wrong?
final saddleBOT
if in a hypothesis test, i write rho = population product moment correlation coe...
fresh musk
or is it the same thing?
final saddleBOT
@fresh musk Has your question been resolved?
ebon dew
That’s a real population product moment
final saddleBOT
final saddleBOT
Available help channel!
harsh ruin
harsh ruin
<@&286206848099549185>
harsh ruin
<@574676935582548019> ?
honestly
dont know where to start
hearty zephyr
You have a constraint on the perimeter (framing), and you want to maximize area.
so finding functions for those two things would be a good place to start
harsh ruin
i think i have area with
24=1-2(2πr)+2L+w
wait thats not area
but im trying to fine the sides
.close
plush geyser
Sooo uhh was just wondering for number 4 I came out with 22.12 but answer key says 23 is the right answer
final saddleBOT
Sooo uhh was just wondering for number 4 I came out with 22.12 but answer key sa...
shell mountain
Did you use the rounded value for c, or the exact value?
plush geyser
wdym by that
grim badger
Even with a rounded answer for c, you should still get 23, rounded up
Did you use 31 or 30.52306...?
plush geyser
30.52
grim badger
Then you typed something wrong
shell mountain
Idk, when I use c = 31 I get 22.12
plush geyser
wait am I supposed to round off 30.52 to 31?
grim badger
You can, because the value you'll get, it'll round up to 23
shell mountain
13² = 23² + 31² - 2(23)(31)cos(A)
-1321 = -1426cos(A)
cos(A) = 0.92636746
A = 22.124532 degrees
plush geyser
13² = 23² + 31² - 2(23)(31)cos(A)
-1321 = -1426cos(A)
cos(A) = 0.92636746
A =...
and it came out this
grim badger
Or use law of sines
Because that's how my answers round up to 23
Because law of cosines, you used 31 twice, where both times it was rounded
shell mountain
Gonna be honest, I forgot the law of sines existed
grim badger
Law of sines used 31 once
plush geyser
hmm
grim badger
The rounded answer of 31
shell mountain
Anyway, in general, it's better to use more exact values as opposed to rounded ones
shell mountain
I normally round to 3 decimal places, though I remember one specific problem I did involving compound interest where 3 decimals weren't enough, and that was annoying
grim badger
If you're using a calculator that can scroll up, like a ti or scientific calculator, just scroll up to that answer and hit enter and it'll paste the entire number, decimals and all
plush geyser
hmm
i dont got that kinda calc tho
I just did inverse cos ((23^2 + 30.52^2 - 13^2) / (2(30.52)(23))
grim badger
That works too
knotty raft
can someone explain this
final saddleBOT
can someone explain this
daring nexus
can someone explain this
divide the second equation by the first
knotty raft
but why?
daring nexus
eliminates a, so you can solve for r
grim badger
And eliminates 1 - r
daring nexus
yes
daring nexus
1-r^2 is not 10
grim badger
Something to do with the ratios of those
daring nexus
nor is 1-r^4=30
grim badger
Hard to tell without the full context
grim badger
As I said, ratio
daring nexus
you can't just cancel a and 1-r
daring nexus
ab/c = 10 ... 1
ad/c = 30 ... 2
when you divide 2 by 1, a and c cancel and you get
d/b = 3
daring nexus
what do i do
you're just supposed to show r^2 = 2
you can substitute that and verify
knotty raft
yea but i wanna understand the process if i were to find r
daring nexus
multiply by 1-r^2 on both sides
1-r^4 = 3-3r^2
then let x = r^2
1-x^2= 3-3x
x^2 - 3x + 2 = 0
then solve the quadratic
knotty raft
ab/c = 10 ... 1
ad/c = 30 ... 2
when you divide 2 by 1, a and c cancel and you...
i dont understand this
the part where its stacked on top of each other
daring nexus
$\frac{\frac{ad}{c}}{\frac{ab}{c}} = \frac{ad}{c} \times \frac{c}{ab}$
daring nexus
now can you see why a and c cancel?
knotty raft
i dont getthat process
i just wanna understand why is 1-r^4=30 stacked above
to divide
grim badger
You want to find the ratio of the equations
knotty raft
yea
daring nexus
knotty raft
https://youtu.be/nssAxTLINpU
i get this
daring nexus
**Swas.py**
its the same thing here
knotty raft
So you take one of the equations, divide it by the other
k
grim badger
As an example, because that's what your problem did
knotty raft
.close
final saddleBOT
knotty raft
So you take one of the equations, divide it by the other
would it work as a simulteanous equation?
final saddleBOT
Available help channel!
tender mirage
anyone can help with b?
final saddleBOT
anyone can help with b?
tender mirage
just the general direction what to do would be great
jaunty sorrel
bruh this channel is occupied
alpine jacinth
ok sorry @jaunty sorrel
jaunty sorrel
anyone can help with b?
multiply and divide by 5^n
tender mirage
multiply and divide by 5^n
i don't really get it xd
jaunty sorrel
$\lim_{n\to\infty} 4^n-5^n=\lim_{n\to\infty}5^n\left(\left(\frac{4}{5}\right)^n-1\right)$
soft zealotBOT
R31_
jaunty sorrel
i don't really get it xd
you agree with this?
jaunty sorrel
no
(5/4)^n as n goes to infty is 0
so inside the parentheses its -1
and 5^n goes to infty
so the answer would be -infty
elfin latch
A jet airplane travelling at the speed of
500 km / hr
ejects its products
of combustion at the speed of
1500 km / hr
relative to the jet plane. What
is the speed of the latter with respect to an observer on the ground?
final saddleBOT
@elfin latch Has your question been resolved?
rain crane
pretty sure v_rel will be v_product - v_nuke
final saddleBOT
@elfin latch Has your question been resolved?
left solstice
Confused on how to do this, my work so far was finding the base that will equal to 343
final saddleBOT
Confused on how to do this, my work so far was finding the base that will equal ...
hearty zephyr
whats M?
left solstice
21
boreal bluff
Confused on how to do this, my work so far was finding the base that will equal ...
$$log_a(bc) = log_a(b) + log_a(c)$$
$$log_a(b^n) = nlog_a(b)$$
I think you only need these?
soft zealotBOT
Doggo
hearty zephyr
left solstice
I know it's a product but
the process of solving it
is where im stuck at
what happens to the 2?
boreal bluff
what happens to the 2?
for $M^2$ you use the $log(b^n) = nlog(b)$ rule
assuming that's the 2 you meant
soft zealotBOT
Doggo
left solstice
Im still confused
hearty zephyr
use the product rule to break up 343 and M^2
Then use the power rule to deal with M^2
hearty zephyr
is M^2=21 or is M=21?
left solstice
M is 21
hearty zephyr
log(343) + log(21)
log(343)+log(21^2)
left solstice
hearty zephyr
that doesn't say M is 21
hearty zephyr
again.... that doesn't say M = 21
left solstice
ok so how do I find that 21..??
I assumed because the question is with it
and for question a I was right
it was 21
hearty zephyr
$\log_7\left(\frac{M}{49}\right) = 21$
soft zealotBOT
Zybikron
left solstice
Yes
hearty zephyr
$M\neq 21$
soft zealotBOT
Zybikron
hearty zephyr
you're given $\log_7(M) = 23$, so in part b) use the log rules to get $\log_7(M)$ by itself, and you can sub in 23 for it.
soft zealotBOT
Zybikron
trim zodiac
how the hell do i solve this
final saddleBOT
how the hell do i solve this
trim zodiac
go somewhere else
carmine fox
Why?
trim zodiac
because this is my channel bud
wanton python
This channel is occupied
trim zodiac
yeah
carmine fox
Ok
trim zodiac
anyways i need help with this problem
whats the first thing to do
i have absolutely no clue
final saddleBOT
@trim zodiac Has your question been resolved?
hoary bone
final saddleBOT
hoary bone
how would i be able to tell if the pair of congruences has solutions or not? and how would i find them?
like it does there ^
how did he go from p = 8k +1 and p =12t + 1 to p = 24m+1
i don't think i can use chinese remainder th. since 8 and 12 are not coprime
ok i guess i get the first point since is p = 1mod 24 then it is bothe 1 mod 8 and 1 mod12
what about the other cases like point 4?
hearty zephyr
8k+a = 12t+b -> 8k-12t = b-a
Factor the left side
4(2k-3t) = b-a
So you know b-a must be a multiple of 4
in the cases where there is no integer solution, b-a is not a multiple of 4
final saddleBOT
@hoary bone Has your question been resolved?
hoary bone
8k+a = 12t+b -> 8k-12t = b-a
Factor the left side
4(2k-3t) = b-a
So you know b-a...
so that allows me to say whether it has solutions or not, but how would i find a solution, for example point 4, which has p = 8k + 7 and p = 12t + 11
hearty zephyr
24 is the lcm of 8 and 12. From there it's a matter of checking what to add so those two things agree...
so, 8k+7 takes values 7, 15, 23, 31 (we can stop here because we're already larger than 24)
12t+11 takes values 11, 23, ...
so 23 is on both lists, so add that.
I'm sure there's a more algorithmic way to do it, but for these values that'd be overkill
I think it might have to do with 7 and 11 are both -1 in their respective mods. So for 24 we get 23 which is also -1 mod 24
final saddleBOT
final saddleBOT
Available help channel!
compact monolith
Hi, may I know if there is any alternative solution to this question?
compact monolith
The solution given is a bit time consuming for me
Is there any way to apply permutation and combination here?
compact monolith
Is there any way to apply permutation and combination here?
It is okay if there isn't
final saddleBOT
@compact monolith Has your question been resolved?
compact monolith
<@&286206848099549185> please help, thanks
clever dagger
It is okay if there isn't
i guess no, that's the easiest way to do ig
final saddleBOT
@compact monolith Has your question been resolved?
compact monolith
i guess no, that's the easiest way to do ig
What if there are even more lines in between A and B? Branching method is definitely ineffective in that case though
compact monolith
<@658187568399253536> Has your question been resolved?
No
final saddleBOT
@compact monolith Has your question been resolved?
final saddleBOT
tranquil pine
I think it has to do with the ratios
boreal bluff
they are similar, so ratio of one side in triangle 2 to the same side on triangle 1 is the same for each side
I feel the question would be much clearer if it gave angles or tell you which sides are similar
tranquil pine
I feel the question would be much clearer if it gave angles or tell you which si...
I guess since the first triangle we can see isosceles, they gave us the 2nd triangle in the exact same orientation so we could pick up what the similiar sides were?
boreal bluff
I guess since the first triangle we can see isosceles, they gave us the 2nd tria...
probably, yeah
shy steeple
a/d=b/e=c/f ( this is the meaning of corresponding sides are proportional)
boreal bluff
but at least in turkey we are taught to not trust the shapes and to rather trust in the calculations
because people mess up a lot over here
yupp
$\frac{63}{8x-2} = \frac{49}{42}$
49/42 simplify the 7's, then divide by 7 on both sides cause 49 has a 7 left after simplifying and 63 = 9 * 7
boreal bluff
it should be easier to work with once you do that
x is actually a whole number
once you solve it
8x - 2 right?
anyways now you can divide left and right side by 7
to simplify it even more
you can do both
white tendon
$$\ce{Zn^2+ <=>[+ 2OH-][+ 2H+] $\underset{\text{amphoteres Hydroxid}}{\ce{Zn(OH)2 v}}$ <=>[+ 2OH-][+ 2H+] $\underset{\text{Hydroxozikat}}{\ce{[Zn(OH)4]^2-}}$}$$
boreal bluff
$$\frac{63}{8x - 2} = 63 \cdot \frac{1}{8x - 2}$$ do you agree on this?
soft zealotBOT
Chunkin
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
boreal bluff
the fuck is that chunkin
soft zealotBOT
Doggo
boreal bluff
see that's what happens if you don't divide, you get messy numbers
boreal bluff
**Doggo**
the numerator can be written like this
dividing the denominator is just multiplying both sides
boreal bluff
dividing the denominator is just multiplying both sides
that's because anything in the denominator is division
if we want to undo that, we multiply
anyways did you solve the problem?
$$\frac{63}{8x-2} = \frac{7}{6}$$
soft zealotBOT
Doggo
boreal bluff
I'm just gonna go back to this
what happens if we multiply both sides by $\frac{1}{7}$?
soft zealotBOT
Doggo
boreal bluff
let me explain it this way I guess
much simpler
which is..?
don't distribute the 7 yet
keep it there in denominator
boreal bluff
keep it there in denominator
this helps you cancel it with the 7 in 63
final saddleBOT
@tranquil pine Has your question been resolved?
tranquil pine
final saddleBOT
vital crag
looks right
tranquil pine
can I simplify it even more further??
my answer
I FUCKING HATE ALEKS
I STG I MIGHT END MY LIFE RN
vital crag
user error
tranquil pine
💀💀💀
vital crag
your handwriting isn't even that bad
vital crag
do you see your mistake?
tranquil pine
do you see your mistake?
final saddleBOT
@tranquil pine Has your question been resolved?
final saddleBOT
final saddleBOT
Available help channel!
waxen prawn
I don't know how to continue from here
final saddleBOT
I don't know how to continue from here
tired walrus
a and 9 are dangerously similar in your handwriting
waxen prawn
I can't reduce the gcd expression anymore using Euclides algorithm
waxen prawn
_a_ and _9_ are dangerously similar in your handwriting
But they are coloured and in purple there's just one 9
tired walrus
still, it caught me off guard.
also have you considered rewriting $32a \equiv 17 \pmod{9}$ as $5a \equiv 8 \pmod{9}$?
soft zealotBOT
Ann
soft zealotBOT
Ann
waxen prawn
Oh I didn't think about reducing the 32a too
tired walrus
i do believe that this problem might be nontrivial or impossible though
waxen prawn
**Ann**
and then since 5 and 9 are coprimes I can just say a is congruent to 5
This is where I'm at now
final saddleBOT
@waxen prawn Has your question been resolved?
waxen prawn
**Ann**
wait this isn't correct. It should be 26 not 25 rip
I think it's done now
tough stuff
Is that right now?
final saddleBOT
@waxen prawn Has your question been resolved?
upper sphinx
in linear algebra, when im finding determinant, what is the formula to find the exponent again
final saddleBOT
in linear algebra, when im finding determinant, what is the formula to find the ...
upper sphinx
like lets say i got [ (x x x) (A 0 0) (x x x)] determinant is A^something * det[...]
final saddleBOT
@upper sphinx Has your question been resolved?
upper sphinx
.close
ruby musk
hello
ruby musk
can someone please help me with this one
desert mantle
write $v=\sum_i a_i v_i$ and then calculate the inner products $\langle v, v_j\rangle$ for all j in two different ways
soft zealotBOT
Denascite
final saddleBOT
@ruby musk Has your question been resolved?
ruby musk
write $v=\sum_i a_i v_i$ and then calculate the inner products $\langle v, v_j\r...
ah got it, thank you so much