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#help-33
still temple
marsh citrusBOT
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dusk laurel
marsh citrusBOT
valid cape
tell me formula of acceleration
dusk laurel
faint karma
acceleration=1.6667
distance=1050 m
faint karma
yes
valid cape
whats the starting velocity?
dusk laurel
0
faint karma
whats the starting velocity?
it starts from the rest
marsh citrusBOT
As a helper, please do not give out answers that could be copied as a homework solution. Have the student work through the problem themselves and guide them along the way.
dusk laurel
i need solution
valid cape
it starts from the rest
i know that, i was asking him
dusk laurel
so please I want to answer it myself
elfin berryBOT
Lakshay
faint karma
here v1 is 0 because it starts from the rest
so you can put values in the formula to find it
valid cape
acceleration=1.6667
distance=1050 m
pretty sure the answer is incorrect as well
faint karma
distance is wrong
valid cape
accel is wrong too
faint karma
it is 1800
faint karma
accel is wrong too
how
valid cape
still wrong
faint karma
then tell me your answer
elfin berryBOT
FungusDesu
dusk laurel
v2 is 35m/s and then v1 is0
valid cape
t?
dusk laurel
t is 30s
valid cape
correct
plug that into formula and you get 7/6
which roughly equates to 1.166667
but i prefer using 7/6
dusk laurel
which roughly equates to 1.166667
is it 35 divided by 30?
valid cape
yes
dusk laurel
okay
valid cape
now, given acceleration and time, what is the formula for distance?
dusk laurel
vt
valid cape
go on
faint karma
now, given acceleration and time, what is the formula for distance?
s=ut+(at^2)/2
valid cape
sir, i was asking him
dusk laurel
its 1050?
faint karma
sir, i was asking him
sry
dusk laurel
where did the 2 come from?>
elfin berryBOT
FungusDesu
dusk laurel
ive never seen that formula before
maiden lotus
huh?
marsh citrusBOT
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wicked crystal
marsh citrusBOT
wicked crystal
it's the definite integral
stiff sundial
Anyway, did you try integration by parts?
wicked crystal
why ask?
hard gull
it integrated using integration by parts
wicked crystal
it integrated using integration by parts
why? is it the only way
hard gull
yeah
wicked crystal
what is integration by parts
hard gull
wicked crystal
hmh okay
wicked crystal
the heck
hard gull
u would be lny
v would be 1 (As a * 1 = a)
stiff sundial
Watch a video about it
smoky surge
Can someone help me with angles of depression and angles of elevation.
- A ship's captain wants to ensure that the angle of elevation of the top of a 25-m cliff from his ship is 7°. How far from the base of the cliff must his ship be?
late geode
have you drawn a diagram
smoky surge
Red what I have drawn
Here's*
I'm confused whether the 25m should be the opposite or adjacent
dry prawn
,rccw
elfin berryBOT
marsh citrusBOT
valid cape
maybe what you meant was extrema?
twin ether
I think that's different from what I meant
still temple
(x-a)^n (n>1)
if n is even its a turning point
if n is odd its not a turning point
willow owl
(x-a)^n (n>1)
if n is even its a turning point
if n is odd its not a turning poi...
is turning point the same as inflection point
willow owl
i checked it is probably the critical points
willow owl
the direction stays the same
wdym by direction
twin ether
(x-a)^n (n>1)
if n is even its a turning point
if n is odd its not a turning poi...
ah simple, thanks
still temple
wdym by direction
increasing/decreasing
willow owl
increasing/decreasing
oh ok
twin ether
.reopen
marsh citrusBOT
✅
twin ether
another question
can I find the exact number of turning points and zeroes from a polynomial in standard form
I know the max zeroes = degree, and turning points = degree - 1
but can I find the exact number?
marsh citrusBOT
@twin ether Has your question been resolved?
still temple
how do u verify that [
\4{\vj u \vd \vj v}{\norm{\vj u}\norm{\vj v}}
]
always lies on the interval [-1,1], knowing that $\vj u$ and $\vj v$ are some $n$-dimensional vectors
marsh citrusBOT
how do u verify that \[
\4{\vj u \vd \vj v}{\norm{\vj u}\norm{\vj v}}
\]
always ...
elfin berryBOT
still temple
So i know this needs cauchy-schwarz
hardy slate
are these vectors in R^n
still temple
yes thats what i said
still temple
So i know this needs cauchy-schwarz
But anyways how do i generalise cauchy-schwarz for any n-dimesnional real vector?
hardy slate
you can brute-force it
just write it in terms of components
you want like
(sum over u_i v_i)^2 =< (sum over u_i^2) (sum over v_i^2)
too fast or do you get that
marsh citrusBOT
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thorny jungle
what is the relationship between the parallel axiom/playfair axiom and the hyperbolic parallel axiom?
marsh citrusBOT
what is the relationship between the parallel axiom/playfair axiom and the hyper...
thorny jungle
Also, hyperbolic parallel axiom is very confusing for me. This is what the axiom says according to my notes.
How is parallel defined here?
Also, it would be great if someone could explain the relationship between the parallel axiom, hyperbolic parallel axiom, and incidence geometry
mental flicker
How is parallel defined here?
two lines that never touch
thorny jungle
well that cannot be possible
still temple
well that cannot be possible
it can
thorny jungle
thorny jungle
how do we construct l'' such that l', l'' is parallel to l?
whole sleet
You type the point into the computer
thorny jungle
You type the point into the computer
wdym
mental flicker
well that cannot be possible
The whole point of this axiom is it only works in hyperbolic space
still temple
it is constructed parallel
mental flicker
Throw away all notions of euclidian space you had before coming in
thorny jungle
Throw away all notions of euclidian space you had before coming in
oh. this makes sense.
is there a possible graphically representation of this?
mental flicker
for example here's a whole bunch of different lines that pass through a point yet never touch and as such are parallel to another
The curved lines reflect the hyperbolic geometry of the space
There's not a good representation of hyperbolic space but the most common one you'll see is this disc
thorny jungle
i see
mental flicker
You can search poincare disk model
This is a good representation of the 'scale' of things
thorny jungle
so Euclid's parallel axiom/playfairs axiom is in euclidean plane. And hyperbolic parallel axiom works in the hyperbolic plane.
mental flicker
Each triangle here is the same size in hyperbolic space
mental flicker
so Euclid's parallel axiom/playfairs axiom is in euclidean plane. And hyperbolic...
Yeah
thorny jungle
and lastly, how is incidence geometry related to these?
mental flicker
Sadly idk what incidence geometry is 😭
It seems like a form of geometry that is completely stripped down to its roots though
So it will apply no matter what space you're in? I have no clue
thorny jungle
😅
Here is the axioms in my notes
But then, it seems like the hyperbolic parallel axiom would contradict I2 and I3
Since I2 and I3 is basically saying there is exactly one line such that p,q is on l
mental flicker
Well I don't see how hyperbolic space is violating that
thorny jungle
ah
youre right
I think what you said "So it will apply no matter what space you're in" is true
thank you
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marsh citrusBOT
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still temple
<[e] esvect>
\let\vvv\vv \def\vv#1{\vvv{\vb*{#1}}}
so very simple question but im somehow messing this up. So the question is to find the measure of the angles of the triangle whose vertices are $A = (-1,0),\, B =(2,1),\, C = (1,-2)$ and I intend to solve this using vectors. Anyways I define the following vectors:
\begin{align*}
\vv{AB} &= 3\vc\I + \vc\J \\
\vv{BC} &= -\vc\I -3\vc\J\\
\vv{CA} &= -2\vc\I+2\vc\J
\end{align*}
and then using $\theta =\m\arccos{\ds\4{\vj v\vd\vj u}{\norm{\vj u}\norm{\vj v}}}$:
\vs{3 mm}
\begin{align*}
\theta_A &= \m\arccos{\4{\vv{AB} \vd \vv{BC}}{\norm{\vv{AB}}\norm{\vv{BC}}}} = \m\arccos{\4{-3 -3}{10}} \approx 2.214 \rad \\
\theta_B &= \m\arccos{\4{\vv{BC} \vd \vv{CA}}{\norm{\vv{BC}}\norm{\vv{CA}}}} = \m\arccos{\4{2-6}{4\3{5}}} \approx 2.034 \rad
\end{align*}
But obviously this result is impossible. So what went wrong?
hardy slate
it should be BA dot BC and CA dot CB
the vectors need to start from the same point and go in different directions
essentially
@still temple
still temple
ah
okay
yes thats fair
alright lets see
<[e] esvect>
\let\vvv\vv \def\vv#1{\vvv{\vb*{#1}}}
We have:
\begin{align*}
\vv{AB} &= 3\vc\I + \vc\J \\
\vv{BC} &= -\vc\I -3\vc\J\\
\vv{CA} &= -2\vc\I+2\vc\J
\end{align*}
so then:
\begin{align*}
\theta_A &= \m\arccos{\4{\vv{AB} \vd \vv{AC}}{\norm{\vv{AB}}\norm{\vv{AC}}}} = \m\arccos{\4{6-2}{4\35}} \approx 1.107 \rad \\
\theta_B &= \m\arccos{\4{\vv{BC} \vd \vv{BA}}{\norm{\vv{BC}}\norm{\vv{BA}}}} = \m\arccos{\4{3+3}{10}} \approx0.927\rad
\end{align*}
No wait
elfin berryBOT
elfin berryBOT
Result:
1.1119
valid kiln
could someone pls help me with 1.b?
marsh citrusBOT
could someone pls help me with 1.b?
hardy slate
could someone pls help me with 1.b?
do you know how to differentiate
native anchor
2x + 4 = 0
x=?
valid kiln
do you know how to differentiate
Here’s my answer
hardy slate
yeah looks about right
valid kiln
To find the maximum and minimum values, I have to let y’ = 0 then x will be found
hardy slate
yes
so you have ab(a^2 - x^2)/(x^2 + a^2)^2 = 0 at the maximum and minimum
so a^2 - x^2 = 0 at the maximum and minimum
valid kiln
So I don’t have to give any values for a and b right?
hardy slate
So I don’t have to give any values for a and b right?
?
valid kiln
Here
hardy slate
no, you shouldn't take a specific value of a and b
your answer should have a and b in
valid kiln
so a^2 - x^2 = 0 at the maximum and minimum
Does that mean I only have to write this ?
hardy slate
no
at the minimum and maximum, a^2 - x^2 = 0
but this only tells you about the x values
you need to find what the function actually is at those x values
to find the minimum and maximum values of the function
valid kiln
at the minimum and maximum, a^2 - x^2 = 0
So x = +- a right?
hardy slate
yes
valid kiln
you need to find what the function actually is at those x values
Does that mean I have to find x? If so, how do I find it when x= +- a?
hardy slate
Does that mean I have to find x? If so, how do I find it when x= +- a?
no
you know that the function is min/max when x = +-a
you want the min/max values of the function
so find f(a) and f(-a)
valid kiln
so find f(a) and f(-a)
Is that how i should write it?
hardy slate
Is that how i should write it?
yes
valid kiln
Therefore the maximum value is (a,b/2) and the minimum value is (-a,-b/2) ?
hardy slate
if b > 0, the maximum value is b/2 when x = a
if b < 0, the maximum value is -b/2 when x = -a
and so on
valid kiln
Alright tysm
valid kiln
if b > 0, the maximum value is b/2 when x = a
Is there a website where I can learn about the serpentine function in more detail?
hardy slate
Is there a website where I can learn about the serpentine function in more detai...
i've never heard of it before so it probably isn't very important
valid kiln
I see
Idk where did the a and b come from, they said it’s from the cubic curve formula
And idk what does a and b represent on graph
marsh citrusBOT
@valid kiln Has your question been resolved?
uncut mauve
Just wanna know if this uis the correct method or nah. if wrong please enlighten me on where I went wrong
marsh citrusBOT
Just wanna know if this uis the correct method or nah. if wrong please enlighten...
uncut mauve
still temple
the second equation is incorrect
uncut mauve
how so (forgive me if I take long to reply my internet is very slow)
still temple
because you have added an additional negative sign in the denominator of the second term in the sum
$\frac{2}{x+3} = \frac{2}{3+x}$
elfin berryBOT
ampl
uncut mauve
thanks
still temple
otherwise what youve done is correct
uncut mauve
.close
marsh citrusBOT
marsh citrusBOT
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marsh citrusBOT
dang i thought i got it but i dont
still temple
$\frac{2}{x+3} = \frac{2}{3+x}$ because $3+x = x+3$
elfin berryBOT
ampl
still temple
its the same numbers in both denominators and both numerators
uncut mauve
the numerators are not the same
still temple
the numerators are both 2
uncut mauve
so ill do:
x/x+3 - 2/3+x
=x/(x+3) - 2/(x+3)
leaden monolith
Use brackets!!
still temple
so ill do:
x/x+3 - 2/3+x
=x/(x+3) - 2/(x+3)
youre right i thought you meant the other numerators
$\frac{x}{x+3} + \frac{2}{3+x} = \frac{x}{x+3} + \frac{2}{x+3}$
elfin berryBOT
ampl
marsh citrusBOT
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turbid prism
I don't know how to solve the following problem
marsh citrusBOT
I don't know how to solve the following problem
turbid prism
Given a dynamic discrete system $f: D \subset \mathbb{R} \rightarrow \mathbb{R}$ continuous with $f(D) \subset D$ and $x_0$ an n-periodic atractor point of $f$, I have to show that every other point in the cycle ${x_0, f(x_0),\dots,f^{n-1}(x_0)}$ is an atractor
elfin berryBOT
contradamus
turbid prism
My definition of $n$-periodic atractor is an $n$-periodic point that is a fixed point of $f^n$
elfin berryBOT
contradamus
turbid prism
In my notes, I see I have to show that for every $i=0,1,\dots,n-1$, exists an $\varepsilon_i > 0$ so that if $|x-x_i| < \varepsilon_i$ then $\lim_{k \to \infty} (f^n)^k (x) = x_i$ assuming that is true for $i=0$. I tried using the definition of a continuous function but I couldn't get anywhere.
elfin berryBOT
contradamus
turbid prism
Can someone help me?
marsh citrusBOT
@turbid prism Has your question been resolved?
turbid prism
<@&286206848099549185>
marsh citrusBOT
@turbid prism Has your question been resolved?
stark trail
marsh citrusBOT
stark trail
How should I know which prime to pick other than just randomly trying a few?
hardy slate
idk if there's an easy general way to do this
one shortcut might be to try just mod a prime factor of the leading coefficient
and that would just explode the first term
but in general it might be annoying
ask in #groups-rings-fields though i'm not actually good at rings
like if you mod 7 then you just have a quadratic and you could complete the square and consider quadratic residues
stark trail
like if you mod 7 then you just have a quadratic and you could complete the squa...
we can't mod 7 because the theorem requires p does not divide 7
but mod 5 works for (a) and mod 2 works for (b)
I did figure that one out though
so I'm going to post a new question
For problem (2)
The contrapositive would be
f(x) is reducible , show this implies that f(x+c) is reducible
and I'd like to say well
if f(x)=g(x)h(x)
then f(x+c)=g(x+c)h(x+c)
But is that enough?
Because WLG we need say g(x) is not a unit/associate/constant
so then we'd need that one of g(x+c) or h(x+c) is still not a unit/associate/constant
and I'm not sure if that follows immediately or not?
spark otter
degree
hardy slate
if g(x+c) were constant on F that would be a strong criterion because of the number of roots
stark trail
What do you mean by that?
spark otter
What do you mean by that?
degree(g(x)) = degree(g(x+c))
or arguably if g(x+c) is constant then g(x) is constant too
spark otter
still talk about the degree
if it's associate, then the degree of the other polynomial...
stark trail
is 0
if g(x+c) is an associate of f(x)
then h(x+c) is a constant
but
h(x) was not a constant
so h(x+c) can't be either?
spark otter
yes
stark trail
So earlier though
f(x)=g(x)h(x)
doesn't only one of these polynomials need to be non-constant / non-associate
for f(x) to be reducible
spark otter
doesn't only one of these polynomials need to be non-constant / non-associate
if one of them is non-constant/non-associate, then the other is non-constant/non-associate too
marsh citrusBOT
@stark trail Has your question been resolved?
stark trail
thank you guys
marsh citrusBOT
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austere scroll
marsh citrusBOT
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@austere scroll Has your question been resolved?
marsh citrusBOT
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marsh citrusBOT
still temple
k = 16 is the answer to the question
desert dirge
you determined the k such that g would be continuous
marsh citrusBOT
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vestal mist
i kinda need some help doing this
marsh citrusBOT
i kinda need some help doing this
vestal mist
what i put is wrong
but using the proportion
10/3=(10-y)/r, using the similar triangles, i found r=(30-3y)/10
is that right so far?
and then i used the fact that the cross section of a cone is a circle. so i use the area of that using the value of r in terms of y
light bane
what is the formula for a cone?
vestal mist
light bane
wait sorry i misread that, cone not necessary rn
vestal mist
why is my answer wrong?
light bane
think of the value of the radius as an equation. in this case r = 3 when y = 0 and r = 0 when y = 10, so r = (3 - 3y/10)
vestal mist
oh
light bane
this will work for any linear relationships
vestal mist
but
light bane
think of r in terms of slope intercept form
y=mx+b
if we think of y and r in terms of x and y we have these coordinates:
0, 3
10, 0
so the slope intercept is 3, and the slope is -3/10
thus r = 3 - (3y/10)
i understand my notation earlier confused you sorry
does that make sense
light bane
think of r in terms of slope intercept form
this is because we know we have a linear relationship between the height of the cone and it's radius. any linear relationships can be represented in slope intercept form
vestal mist
y=mx+b
if we think of y and r in terms of x and y we have these coordinates:
0,...
oh i think this makes sense
but it says this is wrong
light bane
it looks correct to me, maybe it's needing Δy
i think in the case of that problem Δy is represented by "Dy"
you found the area of a slice of it, but need to multiply it by the thickness of the section to get volume
light bane
i’m stumped
marsh citrusBOT
@vestal mist Has your question been resolved?
vestal mist
Same
marsh citrusBOT
@vestal mist Has your question been resolved?
vestal mist
.close
ivory marlin
marsh citrusBOT
ivory marlin
i've literally tried everything idk what goes here
stray hound
circles are of the form $x^2+y^2 = r^2$, where r is the radius. all it's asking for is what r is
elfin berryBOT
doaby
stray hound
you have an expression that helps you right above it
stray hound
8 isn't an answer
where do you see 8? I see $x^2+y^2 = 64 - k^2$
elfin berryBOT
doaby
stray hound
yep
stray hound
it happens, you're good
ivory marlin
.close
marsh citrusBOT
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Available help channel!
real night
hey
real night
I need help with explanations in conics
im trying to convert to standard form
this is what I did
and i know its wrong
so im trying to fix it
sweet quiver
Sure.
So first step is we get the -x^2 to the right side of the equation, along with the 12x. For now, keep the -39 on the right. So it would be y-39=x^2-12x
We then have this y-39=(x^2-12x) then complete the square by dividing 12 by 2 and squaring it so y-39=(x^2-12x+36). Then we need to add the 36 to the left side because you can just add a number in randomly to one side, so -39+36 = -3 so y-3= (x^2-12x+36)
To finish this off, we can do this
y-3=(x-6)^2 since when you do (x-6)^2 it is (x^2-12x+36). So yeah the final answer SHOULD be:
y-3=(x-6)^2
@real night lmk if that helps 🙂
real night
<@531173230753349632> lmk if that helps 🙂
that was very helpful thanks
sweet quiver
Ofc
real night
I guess I seperated the wrong side first?
sweet quiver
Not that, you just didnt complete the square or go about it the correct way.
real night
Im going to be posting for a bit cause I have a test tomorrow So if i need help I will let you know
real night
Not that, you just didnt complete the square or go about it the correct way.
I guess that makes sense
sweet quiver
I guess that makes sense
Do you understand completing the square?
real night
Its because I added 39 to the other side
real night
Do you understand completing the square?
yea
sweet quiver
And you know standard form, right?
real night
(x-6)^2 = (x-6)(x-6) = x^2-12x+36
Yea
one thing that I do not understand though
is
where 4p ties in
sweet quiver
If you know the standard form equation and also know how to complete the square well, you should be solid for your test
real night
thats the one thing i dont get about parabolas
real night
If you know the standard form equation and also know how to complete the square ...
Well im going through everything in conics
Test is on like
sweet quiver
Well im going through everything in conics
Yeah I get that
sweet quiver
Test is on like
Ik about conics
real night
but where does p tie into these equations
Majority of all of it
just parabolas I struggle on
real night
Is p the focus for you guys?
sweet quiver
p is distance from vertex
To quote the great google cause it can describe better than me, "The specific distance from the vertex (the turning point of the parabola) to the focus is traditionally labeled "p". Thus, the distance from the vertex to the directrix is also "p". The focus is a point which lies "inside" the parabola on the axis of symmetry."
https://mathbitsnotebook.com/Geometry/Equations/EQParabola.html#:~:text=The specific distance from the,on the axis of symmetry. this diagram shows it quite well
real night
im also a little bit confused on ones such as these
this is the answer
im just not quiet sure how to start
sweet quiver
this is the answer
Im not sure why they would write it like this lmao
sweet quiver
Im assuming because of the negative but still doenst make any sense to me.
sweet quiver
idk but i know my answer is correct based off of that equation they gave
real night
they got me confused 😭
sweet quiver
lol
real night
If i need help
I will lyk
cause im ab to move onto looking at hyperbolas after this
sweet quiver
I might be offline by then cause my computers getting really low lol
real night
I might be offline by then cause my computers getting really low lol
ok
have a good 1 then
.close
marsh citrusBOT
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real night
yo
valid cape
identify the coordinate of the center and radius
real night
identify the coordinate of the center and radius
I think i found everything 1 sec
lofty gyro
does this seem correct?
yea, although the 4's and 9's are so similar i can't distinguish between them
real night
yea, although the 4's and 9's are so similar i can't distinguish between them
sorry my handwriting is trash 😭
real night
ah
one more question
let me get the piuc
hold up
this is what i got for
this
which is correct
BUT
originally, I got 18 and 8 instead of 36 and 16
I am a little confused because arent I supposed to subtract one of the 36's?
lofty gyro
reading
real night
lofty gyro
oh, i get what you don't understand
here's a hint:
(a+b)²=a²+2ab+b²
and
(a-b)²=a²-2ab+b²
↑
this is still a plus sign
real night
we add both sides by 36, no matter it's + or - in the 6x or 9y
and is this under every circumstance?
lofty gyro
here's a hint:
(a+b)²=a²+2ab+b²
and
(a-b)²=a²-2ab+b²
↑...
yep, and it's because of this
lofty gyro
yea?
lofty gyro
oh lol
lofty gyro
cheers!
lofty gyro
horizontal or verticle right?
not sure about your question
real night
well like
as in
u would always add
not subtract
to the other side
(a-b)²=a²-2ab+b²
with this
lofty gyro
perfect square is easier
marsh citrusBOT
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raven sierra
marsh citrusBOT
runic temple
can yall chill
ive been watching from a distance
ill help out, in #help-1
.close
hoary pine
lol
marsh citrusBOT
hoary pine
thanks
raven sierra
lol
marsh citrusBOT
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steel sluice
dont ask to ask
grand lily
how does that work
grand lily
how can i find k if the area is unbounded
it would be infinite area always it seems
grand lily
oh snap
i thought it was the second quadrant
wait how do i even solve this
i got to (k^4)/3 - (k^4)/4
is it just the fourth root of 24
nvm i got it
fringe kite
what math rule is being used to get sin(A)/a = sin(C)/c to c x sin(A) = a x sin(C). how did the denominators become multiplied and then how did they isolate for a please show steps
marsh citrusBOT
what math rule is being used to get sin(A)/a = sin(C)/c to c x sin(A) = a x sin(...
valid cape
$\frac{a}b = \frac{c}d \Leftrightarrow ad=bc$
elfin berryBOT
FungusDesu
still temple
sine rule states that $\frac{sina}{a}=\frac{sinb}{b}$
elfin berryBOT
EinPest
vast shoal
$\frac{\sin(A)}{a}=\frac{\sin(B)}{b} = \frac{\sin(C)}{(c)}$
fringe kite
?
valid cape
i dont think he was asking for a definition on sine rule
elfin berryBOT
ColdTee
valid cape
he was asking on how a/b = c/d went to ad = bc
vast shoal
i dont think he was asking for a definition on sine rule
Yeah but pest wrote it wrong
marsh citrusBOT
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light flicker
marsh citrusBOT
light flicker
how do we do this man 😟
i tried rationalising but didnt get anywehre
<@&286206848099549185>
atomic ruin
how do we do this man 😟
i think i can
light flicker
how
atomic ruin
lemme write it out for u
light flicker
do we take it as 1/root a2-x2 and solve
light flicker
😟 what substituiton
light flicker
yes
atomic ruin
@light flicker
light flicker
bro it worked holy shit
light flicker
how did u think of it
light flicker
t should be 4-lnx
there's square in lnx tho
atomic ruin
loge base e is what
1
light flicker
there's whole squareed
atomic ruin
there's whole squareed
oops
atomic ruin
this im getting stuck
for this i think u need a substitution
atomic ruin
lemme try
light flicker
im not getting both of them
atomic ruin
this im getting stuck
im doing this one wait
light flicker
tried partial fractions for second one but im getting to the power 4 and all
yes after that
light flicker
yes
atomic ruin
nah
light flicker
im not getting both of them
these
atomic ruin
im not getting both of them
u need to do both or what
atomic ruin
hmm
boreal wing
heya
boreal wing
im not getting both of them
I believe in (a) you need to use the sum identities
atomic ruin
I believe in (a) you need to use the sum identities
ye
hold on
my ans is so similar to the actual ans
boreal wing
im not getting both of them
and in the second one, try making $u = log(x^2+1)$
elfin berryBOT
proofAd
atomic ruin
this is what i got for the first one
but wolfram alpha gives a different answer in the second ln
atomic ruin
its a website that helps u do math
boreal wing
who is wolfram alpha
software for computing mathematical expressions
it's pretty useful to check answers
light flicker
damn
boreal wing
atomic ruin
wolfram gives this
i havent learnt logarithms yet so that might be the same? probably not though
boreal wing
how did you split $\frac{1}{(u(3-4u^2))}$ into $\frac{1}{3u} - 4/3\frac{u}{4u^2-3}$ ?
elfin berryBOT
proofAd
atomic ruin
how did you split $\frac{1}{(u(3-4u^2))}$ into $\frac{1}{3u} - 4/3\frac{u}{4u^2-...
wolframalpha
atomic ruin
wolfram gives this for sin(3x)
search it up though
still temple
its the same thing wolfram just removed the absolute value for some reason
boreal wing
since the answer has an absolute sign around it, you can rearrange the 4sin^2(x)-3 to be 3-4sin^2(x)
boreal wing
not aware why wolfram gets rid of the absolute signs though, very interesting
atomic ruin
when integrating ur always supposed to do ||
afaik
im almost done with the 2nd integral @light flicker
light flicker
oh\
atomic ruin
thanks man
welcome
atomic ruin
.close
regal umbra
marsh citrusBOT
regal umbra
I need help with question 1
night turtle
The ratio of corresponding sides is equal
sinful thistle
that is, AB:DE::BC:EF and so on
if one side is scaled by a factor of 2, all the others must be as well since they're similar
night turtle
they're similar
*similar
regal umbra
Can you break down the question I don’t really understand
regal umbra
Ok
sinful thistle
that means that they're resized versions of each other
regal umbra
So they displayed
sinful thistle
so that means that the side ratios will be the same, right?
regal umbra
Dilated
sinful thistle
So they displayed
?
regal umbra
They resized so they dialated
sinful thistle
what do you mean "dilated" here
regal umbra
Becuase they changed sizes
sinful thistle
i don't understand your use of the word "dilated" in this context
oh i see
by dilated you mean scaled
i get it
regal umbra
Yes
regal umbra
Yes
sinful thistle
okay
use that
you already have one side ratio
14 turned into 35
so a scaling factor of what
regal umbra
2
regal umbra
Ik but 14 times 3 is 42
marsh citrusBOT
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marsh citrusBOT
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slim sphinx
trying to understand the example and how it went from line 5 -> 6. is where 0=cos2x to 2x= { }
marsh citrusBOT
trying to understand the example and how it went from line 5 -> 6. is where 0=co...
slim sphinx
can someone help explain that to me?
late geode
consider that
from -pi <= x <= pi
-2pi <= 2x <= 2pi
so they essentially listed all the solutions to cos(2x) = 0 in that interval
slim sphinx
consider that
from -pi <= x <= pi
-2pi <= 2x <= 2pi
so they essentially listed a...
is that the procedure, to 2x both sides of the inequality when you have a (2x) angle?
not inequality but domain restriction
and what about when there is no restriction, how would i go from 0 = cos2x ---> to an answer (2x) =
late geode
general solutions
slim sphinx
one point where my confusion happens is how did they just get rid of the cos part algebraically
or am i just thinking about it wrongly?
marsh citrusBOT
@slim sphinx Has your question been resolved?
worn plank
I had the same question yesterday
what I did is use cos(x) = cos(x+2πk), k integer, and cos(x+π) = -cos(x)
but being honest is more easy just doing it geometrically
slim sphinx
but being honest is more easy just doing it geometrically
so from the first line to the second i should just skip something that shows how cos disappears from the equation and solve for 2x by taking the values from the unit circle?
worn plank
you get '
"the same angle"
by going 360 degrees or substracting 360 degrees
that's why you use k,n integers
additionally to x = pi/2 and x = 3pi/2, you can go further by adding 360 degrees (2pi)
indefinitely, or even substracting
you just have to check x = π/2 + 2πk and x = 3π/2 + 2πn are always within -π <= x <= π
in your case is 2x, not x
slim sphinx
in your case is 2x, not x
but then i have to apply the restrictions back again i think because in the original problem? or....
i know im missing like a lesson or something for when i have to deal with (2x) type angles and multiplying those intervals for x
things are confusing me on that level
slim sphinx
so i have to solve for 2x angles first even though my restrictions are between 0 to pi, and 0 to - pi
worn plank
the domain is not -π <= 2x <= π but -π <=x <= π
first you know that 2x is the angle, so one set of solutions is 2x = π/2 + 2kπ
slim sphinx
the domain is not -π <= 2x <= π but -π <=x <= π
then how come 3pi/2 is a solution? we shouldnt even include that (?)
slim sphinx
so then whenever im faced with a cos (kx) problem i should find all values on the unit circle first then divide by k?
worn plank
you dont divide by k
x + 360 ends in the same position
same x - 360
same x - 360 - 360 - 360
in general, x + 360n, n times
slim sphinx
i get that 3pi/4 and -3pi/4 satisfies cos(2x)=0. because the x value is zero on the unit circle for these radian rotation amounts
worn plank
here you have what is x1 and x2. Now you need to check for what k's they lie between -pi <= x <= pi
slim sphinx
i get that 3pi/4 and -3pi/4 satisfies cos(2x)=0. because the x value is zero on ...
i just dont really get why...when the restriction is -pi <= x <= pi
we would look out beyond pi to find that 3pi/2 value
worn plank
because they are between -pi <= x <= pi
slim sphinx
3pi/2* is greater than pi?
worn plank
trying to understand the example and how it went from line 5 -> 6. is where 0=co...
honestly, i think step 2x = {...} just makes everything more complicated
slim sphinx
it does, it needs something inbetween 😬
worn plank
the other way would start from -π <= x <= π. Multiplying everything by 2 says -2π <= 2x <= 2π
and if 2x = 3π/2 = 1.5π, it would be between -2π <= 1.5π <= 2π
slim sphinx
the other way would start from -π <= x <= π. Multiplying everything by 2 says -2...
yeah i think im just coming around back to this method now
then divid my answers by 2 after
thnx for taking the time to explain things a bit @worn plank gonna try to just work on it a bit more, hope there are more examples ect
.close
marsh citrusBOT
proven vault
i don't remember but it might be related to rolle's theorem
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
@still temple Has your question been resolved?
marsh citrusBOT
marsh citrusBOT
Available help channel!
tender sparrow
could we somehow use the characteristic equation of a matrix to solve this
main idol
Yes look for the characteristic poly in terms of beta
tender sparrow
See if you can spot a pattern
im not getting a pattern
tender sparrow
Yes look for the characteristic poly in terms of beta
the trace of the matrix is beta -1
does that
kinda
hint towards something
main idol
if you can use it sure
main idol
<@&268886789983436800> proselytizing
tender sparrow
anyways
tender sparrow
if you can use it sure
like
im not really
familiar w the characteristic eqn
all i know is that
for 3x3 matrices
we have a general equation
that
main idol
could we somehow use the characteristic equation of a matrix to solve this
characteristic equation of a matrix
what do you think this means?
tender sparrow
A^3-tr(A)A^2...so on
tender sparrow
> characteristic equation of a matrix
what do you think this means?
the equation which the matrix satisfies....?
i genuinely dont know
i literallyjust memorised the result and im tryna use it
but i have no idea
main idol
A^3-tr(A)A^2...so on
yea find this for your A
marsh citrusBOT
@tender sparrow Has your question been resolved?
dusty flare
could someone help me here
marsh citrusBOT
could someone help me here
dusty flare
i thought to determine if a matrix is invertible, you need to find the determinant
hardy slate
i thought to determine if a matrix is invertible, you need to find the determina...
sure
gloomy ridge
i got -150
should be 150
and if it is invertible its RREF form is the identity matrix
gloomy ridge
do you know what a pivot point is?
dusty flare
i've read the definition for it but I didn't understand it
gloomy ridge
try google, unless that was what you read
dusty flare
oh yeah the definiton that came up now seems easier to understand
so you put a matrix in RREF, and the first non zero in a row is the rows pivot point?
gloomy ridge
yeah or "position"
pale tiger
Hello there, tmr I have a FAMAT math comp test for precalculus, I will send the standards below, but was wondering if anyone has any advice/resources for these
marsh citrusBOT
Hello there, tmr I have a FAMAT math comp test for precalculus, I will send the ...
main idol
holy shit
help channels are for specific math problems
google books/resources for your subjects and do the problems in them
hardy slate
Hello there, tmr I have a FAMAT math comp test for precalculus, I will send the ...
khan academy
marsh citrusBOT
@pale tiger Has your question been resolved?
pale tiger
google books/resources for your subjects and do the problems in them
any specific resources other than khan academy?
marsh citrusBOT
@pale tiger Has your question been resolved?
graceful herald
marsh citrusBOT
graceful herald
If thats not clear I can rewrite
but I used the correct table of integral equation (#42) and set U to the right thing
and also found y^2
wary kite
hmm did u make sure to do the change of variables
graceful herald
Change of variables?
wary kite
du=5 dy
wary kite
yea
marsh citrusBOT
spring stirrup
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Available help channel!
twin nebula
marsh citrusBOT
twin nebula
Is this valid
main idol
what even is the question
twin nebula
wary river
probably no
twin nebula
I found a formula for n
main idol
,rotate
twin nebula
And now it wants me to find that formula with math I think
elfin berryBOT
twin nebula
The formula for A(n) should be x-1 over x+q1
And my two formulas for the area between the curves is x^1/n and x^n
marsh citrusBOT
@twin nebula Has your question been resolved?