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#help-17
river sierra
vocal sleetBOT
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digital veldt
if a tower was leaning at an angle and i want to consider the triangle formed by the point at the top of the tower, the base of the tower, and a point due west of the tower which has an angle of elevation to the top of the tower at 45. is this triangle a right angled triangle? i could draw it up if you are unable to visualise
vocal sleetBOT
if a tower was leaning at an angle and i want to consider the triangle formed by...
hushed tree
It's not right angled
Since the tower is leaning
For it to be right the tower must be straight
digital veldt
Even if the top view looks like this
I'm not sure how to explain it but it would be a face of a triangular pyramid I know that OC isn't vertically upward but does that mean COB isn't a right angle where B is On level ground
hushed tree
Yes
digital veldt
There's another point due south of the base of the building ( on level ground)
Alright so it's non right angle?
digital veldt
hushed tree
Is OC perpendicular to BO
digital veldt
yep on the groun bc B is due west to O and A is due south
hushed tree
But you just said CO isnt vertical
digital veldt
yes OC is a leaning tower
but im assuming it is due north in the top view
to O
as B is due west and A is due south
hushed tree
Ok and
How does this result in the fact that angle COB is right
Think about it
Since CO isnt vertical
Angle COB will always either be <90 or >90
It will never be 90
vocal sleetBOT
@digital veldt Has your question been resolved?
digital veldt
It will never be 90
ok thanks?
vocal sleetBOT
hushed tree
lol wdym youre the one who asked?
I meant your explanation made no sense
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glacial meadow
You and a friend take different flights in opposite direction but leave from the same airport.
Your flight starts out 210 miles due south and then turns 70 degrees west and goes another
80 miles. Your friend’s flight starts out traveling 80 miles due north and then turns 50
degrees to the east before traveling 210 mile. Explain how the Hinge Theorem would help
you find out whether you or your friend’s flight is farthest from the airport. Use the compass
for reference and provide a sketch.
vocal sleetBOT
You and a friend take different flights in opposite direction but leave from the...
glacial meadow
sorry for the block of text
ive done the sketch, and i think they are the same distance away??
tall atlas
Hmm
proven garden
so the Hinge theorem states that if two sides of two triangles are congruent, the third side of the triangle with larger included angle is longer than the triangle with smaller included angle
so compare the angle to find out who is farther
glacial meadow
so 70 degrees and 50 degrees
proven garden
yes
glacial meadow
wdym by compare them
vast shale
why is the answer not 3x-2
vocal sleetBOT
why is the answer not 3x-2
proven garden
which one?
upper iron
why is the answer not 3x-2
Show us how you found 3x-2
vast shale
i plotted the points down in desmos
then i counted how far apart it is on the y axis
the points i mean
and then how far apart they are on the x axis
upper iron
It's correct, but in exams you will not have desmos 😛
You should learn to do it on paper!
vast shale
You should learn to do it on paper!
i can do it on paper
upper iron
Awesome!
upper iron
How the hell is 3x-2 wrong, it's correct
vast shale
i want to cry 
vocal sleetBOT
@vast shale Has your question been resolved?
vast shale
given that sin(40) = a, express cos(50), tan(-50) and sin(220) in terms of a
vocal sleetBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@vast shale Has your question been resolved?
vast shale
idk how to start
how can you re-write sin(x) as cos(x)
sin x = cos (pi/2 - x)?
wait can it be cos(x + pi/6)?
vocal sleetBOT
@vast shale Has your question been resolved?
native dagger
Question in English : Which function has the following variation table?
paper depot
!status
vocal sleetBOT
What step are you on?
1. I don't know where to begin
2. I have begun but got stuck midway
3. I got an answer but I'm told it's wrong
4. I got an answer and would like my work checked
5. I have a question about someone else's worked solution
6. None of the above
@native dagger Has your question been resolved?
silk canopy
wait
1/sin^2* cos ^2 a
how do i make this into cos^2a - cos^4a
vocal sleetBOT
wait
1/sin^2* cos ^2 a
how do i make this into cos^2a - cos^4a
civic drift
Write $\sin^2(a) = 1 - cos^2(a)$
twin meteorBOT
coldtee
silk canopy
i did
that would just make it 1/1-cos^2a * cos2 a
and if i take common it would make
1/(1-1)cos^2a
nothing but but 1?
twin meteorBOT
coldtee
twin meteorBOT
coldtee
civic drift
Distributive property
civic drift
Yeah
vocal sleetBOT
modest grove
im i ryt
vocal sleetBOT
Available help channel!
ivory violet
vocal sleetBOT
civic otter
-1/m
ivory violet
its for this if need context
vast shale
[
m_{\text{tan.}} = -\f1{m_{\text{nor.}}}
]
twin meteorBOT
ivory violet
so its just a thing to remember in math
vast shale
you can prove it using some geometry
vast shale
\textbf{Question:} Show that if $G$ is a self-complementary simple graph with $v$ vertices, then $v\equiv 0$ or $1;(\bmod 4)$
\vs{3 mm}
\textbf{My solution:} If $G$ is self complementary, then $G$ and $\overline G$ are isomorphic, meaning they both have the same amount of edges
\vs{2 mm}
When we have $v$ vertices, there can be at most $\f{v(v-1)}2$ edges
\vs{2 mm}
Since that can be at most $\f{v(v-1)}2$ edges and $G$ and $\overline G$ have the same amount of edges, the number of edges in $G$ is half of the maximum number of edges :[
G \textss{has} \f{v(v-1)}4 \textsx{edges}
]
And since since the number of edges has to be an integer: [
v(v-1) \equiv 0 ; (\bmod 4)
]
We can note that $v$ is odd and $v-1$ is even, or vice versa. The product of the two integers will surely be a multiple of 4 in this case if either terms is a multiple of 4 [
v \equiv 0 ; (\bmod 4) \textss{or} v-1 \equiv 0 ; (\bmod 4)
]Adding one to both equations:
[
v \equiv 0 ; (\bmod 4) \textss{or} v\equiv 1 ; (\bmod 4)
]
vocal sleetBOT
\textbf{Question:} Show that if $G$ is a self-complementary simple graph with $v...
twin meteorBOT
vast shale
is my reasoning right here?
hard atlas
you are talking about "at most edges". why does this "at most" have to be attained
vast shale
you are talking about "at most edges". why does this "at most" have to be attain...
Because every vertex out of the $v$ vertices can connect to the other $v-1$ vertices, and when adding all connections to all the vertices, we count each edge twice and so the number of edges have to be $\ff{v(v-1)}2$
twin meteorBOT
hard atlas
well again, at most
vast shale
yes, at most
hard atlas
why is this "at most" number relevant
you arent using the definition of complementary graph anywhere
that should be a sign that you cant be completely right
vast shale
vocal sleetBOT
@vast shale Has your question been resolved?
glossy maple
try to think how many edges will the complementary graph have
vocal sleetBOT
glossy maple
oh rip
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Available help channel!
silk canopy
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worthy citrus
This is finding the common denominator of two fractions
That common denominator being sin(θ)cos(θ)(sin(θ)-cos(θ))
silk canopy
That common denominator being sin(θ)cos(θ)(sin(θ)-cos(θ))
doesnt the sintheta - cos theta in denominators get canceled?
paper depot
no, it does not.
silk canopy
can u explain what is happening here using the bot?
paper depot
abbreviating $\cos(\theta)$ and $\sin(\theta)$ with $c$ and $s$ respectively, you have:
$\frac{s^2}{c(s-c)} - \frac{c^2}{s(s-c)} = \frac{{\color{red}s} \cdot s^2}{{\color{red}s} \cdot c(s-c)} - \frac{{\color{red}c} \cdot c^2}{{\color{red}c} \cdot s(s-c)} \ = \frac{s^3}{sc(s-c)} - \frac{c^3}{sc(s-c)}$
twin meteorBOT
Ann
silk canopy
doesnt it become sin^3theta (sintheta - cos theta) - cos^3 theta (sin theta - cos theta)/ cos (sintheta - cos theta) (sin theta (sin theta -cos theta)
i dindt get it
silk canopy
doesnt it become sin^3theta (sintheta - cos theta) - cos^3 theta (sin theta - c...
all i did
was take lcm
well cross multip;y
and do it
worthy citrus
The product of the denominators isn't the lcm in this case, which is why what they did is better
worthy citrus
Cross multiplying is fine just less efficient
silk canopy
sin^3theta (sintheta - cos theta) - cos^3 theta (sin theta - cos theta)/ cos (sintheta - cos theta) (sin theta (sin theta -cos theta)
sin^3 theta - cos^3 theta (sin thetea - cos theta)/
(sin theta * cos theta ) (sin theta - cos theta)
i took sintheta - cos theta common in both
does this work? @worthy citrus
worthy citrus
You'll know if it works as you'll end up with the same as this
silk canopy
it ends up the same, but then i just want to know if im doingsome wrong shit to make it correct? @worthy citrus
worthy citrus
Cross multiplying will always work fine, can just be more difficult/inefficient
silk canopy
Cross multiplying will always work fine, can just be more difficult/inefficient
is it possible for u to justonce
cross mulitply
using the bot?
twin meteorBOT
silk canopy
,w sin^2 theta
twin meteorBOT
silk canopy
,w sin^2theta
twin meteorBOT
silk canopy
,w (sin^2theta - cos^2theta / costheta (sin theta - cos theta) ) - cos^2theta/sin theta /sin theta (sin theta - cos theta)
twin meteorBOT
Requested by ars_95#0
silk canopy
...
sudden compass
(XY problem alert ⚠️)
Find c such that the probability that 1 >= c is 1/2
vocal sleetBOT
paper depot
.coose*
vocal sleetBOT
Available help channel!
vague root
how to find circumfrance and area?
vocal sleetBOT
how to find circumfrance and area?
vague root
of the circle segment
glad python
sector minus triangle
vague root
sector?
vague root
sector minus triangle
why do i do sector - triangle?
glad python
That’s the area of the circular segment
vague root
but is there a reason behind it?
glad python
Sector ACB-triangle ACB
glad python
but is there a reason behind it?
Yes, look at it visually
vague root
Yes, look at it visually
sorry, i am dumb, how do i do that?
glad python
I don’t know how to explain it
Look at the picture
If you take the triangle out of the circular sector
You get the segment
vague root
i think i skipped a chapter, what rule is that?
glad python
I don’t think you are understanding what I’m saying
vague root
I don’t think you are understanding what I’m saying
no i don't sorry
glad python
Do you see sector ACB?
vague root
Do you see sector ACB?
wait yes, the triangle?
vague root
what is a arc?
vague root
So A with arc BC
like the segment?
glad python
arc is curved line
vague root
arc is curved line
so the segment?
glad python
Segment is straight line
vague root
ok the arc
glad python
Ok do you see the sector?
vague root
what is definition of sector?
glad python
I’ll send a picture
vague root
thank you
glad python
here
vague root
so a pizza slize shape?
vague root
x/360*area?
vague root
1/6 * area of the big circle
but how do i know its 60 degrees?
glad python
how to find circumfrance and area?
It says it right here
glad python
No you are looking at the wrong sector
vague root
?
glad python
Look at the sector on the right
vague root
Look at the sector on the right
circle segment right?
vague root
The yellow part here
are we talking about your picture?
glad python
Sorry I’m bad at communicating
vague root
i never thought about this in that way
vague root
Sorry I’m bad at communicating
i am the problem, not you
glad python
If you have weird areas find a way to express them as two different areas
vocal sleetBOT
glad python
vocal sleetBOT
Available help channel!
ebon ocean
What do I do now?
vocal sleetBOT
What do I do now?
ionic hedge
vocal sleetBOT
@ebon ocean Has your question been resolved?
vocal sleetBOT
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Available help channel!
full flume
bit of a silly question but how would I write -6^7 on a ti-84
vocal sleetBOT
bit of a silly question but how would I write -6^7 on a ti-84
full flume
whenever I start with a - it defualts to my last answer-6^7
hidden kelp
you should have a button other than the subtract button to add negative signs
vocal sleetBOT
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viral galleon
Is this right?
vocal sleetBOT
Is this right?
steady helm
Is this right?
Didn't you forget a square while derivating t^3?
iron flame
^
viral galleon
Didn't you forget a square while derivating t^3?
oh yes my bad
but is the process right
steady helm
Yes absolutely
steady helm
do we right it as like ijk
I did not understand i'm sorry 😅
viral galleon
this form for example
cuz sometimes u write vectors
as ijk
oh sorry i wrote right and not write
steady helm
I would say that both forms are fine
iron flame
this is for breaking it down into a sum of its components
v=<... , ...> is expressing it explicitly as a vector quantity
both are correct
steady helm
this is for breaking it down into a sum of its components
It begins to really make sense when u start algebra
viral galleon
like when u do cross product and stuff?
iron flame
yeah there is a way/trick of remembering how to get the cross product using ijk unit vectors
viral galleon
yeah i know because its really weird
our professor
taught us all that before
and for some reaosn
the last module is this stuff
which is really weird
this module should have been before that imo
but whatever
steady helm
like when u do cross product and stuff?
Yaah and when u see what a basis is
short notch
vocal sleetBOT
short notch
can someone pls help me with this
I dunno what to do after this
" what percent is made on the cost?" this is confusing me
vocal sleetBOT
@short notch Has your question been resolved?
clear stirrup
You are not trying to find the cost %
You want to find the profit percentage on cost
short notch
You are not trying to find the cost %
should it be 10/60 * 100 ?
short notch
if selling price is 50, and profit is 10, then cost price 60..?
clear stirrup
...
Oh you added those
Ok so when we sell something
and have a selling price
Ideally we want the selling price to cover at least the whole cost of it
and then a bit of profit
Right?
short notch
is the selling price what the retailer bought it for?
clear stirrup
is the selling price what the retailer bought it for?
No
The selling price is the price they are selling the product for
short notch
ah okay
clear stirrup
that's why it's a selling price
short notch
so this means whatever the selling price is the store is making 20% more..?
short notch
okayy so 20% of the s.p was profit...?
clear stirrup
And profit is how much they are earning in profits based on a percentage of the revenue
Yes
So 20% of the selling price is profit right?
short notch
yepp
clear stirrup
That means the rest of it goes into the cost
So let's use $100 as an example
If they have a selling price of $100 (they earned revenue of $100)
They only made a profit of $20 (20% profit)
so cost = selling price - profit or cost = selling price - 0.2 * selling price
in other words, the remaining 80% is the cost
which is usually referred to as cost of goods sold
The question is asking what percentage of profit is made on the cost
short notch
ahhhh soo 20/80 * 100?
clear stirrup
ahhhh soo 20/80 * 100?
If you multiply by 100 that's the actual number of profit made on cost
20/80 by itself is the percentage value
short notch
0.25?
clear stirrup
Yes
and you don't really need an example number to figure it out
You can think of selling price as the max number
it's not that simple but for the sake of this we can just say selling price is the max
or 100%
if the percentage of profit (given in the question) is 20%
then we can just divide it by the cost percentage
100%-20%
short notch
so once you figure out cost, you want to find ``(profit / cost) ``
is the value we use for percentage and cost suppoussed to be in terms of % or in terms of $?
clear stirrup
so 20%/80%
clear stirrup
is the value we use for percentage and cost suppoussed to be in terms of % or in...
Wdym?
short notch
like is it different if i write 20%/80% vs 20/80?
clear stirrup
Yes
a percentage is expressed in decimals
100% = 1
so if you did 20% / 80% it would be 0.20 / 0.80
but if you use 20 / 80 you have to put that into the perspective of actual values (not percentage)
like your example of SP = $50 and profit = $10
cost = 50-10
So we can say 10 / 40
does that make sense
clear stirrup
np 👍
austere hearth
anyone mind helping me
vocal sleetBOT
anyone mind helping me
austere hearth
lyric fossil
are you able to find the area of the circle
austere hearth
yes
lyric fossil
how about the square surrounding it
austere hearth
dont know how for that
lyric fossil
what is the area of a square
austere hearth
how do i find out teh side length?
lyric fossil
look at what you were given in the picture
lyric fossil
show your work
midnight locust
If I have a function for all line segments in R^2 space, can I apply it to a closed curve? And how? What related mathematics knowledge I would need to use? Differential Geometry? Tysm
vocal sleetBOT
If I have a function for all line segments in R^2 space, can I apply it to a clo...
lyric fossil
what do you mean by "a function for all line segments in R^2"
and what do you mean by "apply it to a closed curve"
do you have a specific question in mind
midnight locust
A function that by giving coordinates of two points of a line segment, then it will return a value
And can a closed curve be divided into a collection of infinitesimally small line segments, so this function can be applied to this curve?
Thx you!
lyric fossil
A function that by giving coordinates of two points of a line segment, then it w...
what are these functions on the line segments like
what kind of functions are we working with
also you can always do the second thing you mentioned, but that limit might not converge
midnight locust
what are these functions on the line segments like
Just a combination of some inversed trigonometric functions and inversed hyperbolic functions
May be using arcoth and arctan
midnight locust
also you can always do the second thing you mentioned, but that limit might not ...
the function should be heavily depend on the length of the line segment
lyric fossil
can you give me an example of a function on a line segment
midnight locust
can you give me an example of a function on a line segment
Ok pls wait a moment, thx u so much btw
midnight locust
can you give me an example of a function on a line segment
ArcCoth[Length of the line segment/Height of its center from the x-axis]
lyric fossil
well this isn't defined for all line segments
if you did have a function that was defined for all line segments, or say some convex set containing the curve, then you could definitely do what you said in your second question
but it may not converge
and it may go as far as to depend on how you split up the line segments that approximate the curve
you may be able to characterize this as "functional analysis"
empty minnow
**If it take 1hours for two people to do some work in 240/11 days then how many hours they would have to work to get the work done in 5 days only? **
vocal sleetBOT
**If it take 1hours for two people to do some work in 240/11 days then how many ...
@empty minnow Has your question been resolved?
trim walrus
(2 ppl)×(1 hr)×(240/11 days) = (480/11 work)
(2 ppl) × (x hr) × (5 days) = (480/11 work)
Solve for x hr
I belive
(The units maybe vaguely described)
Sry for that
twin meteor
im taking the derivative of this
vocal sleetBOT
im taking the derivative of this
twin meteor
do
i combine the 2.0+3.0t before taking derivative?
and if not that means the 2.0 is gone right?
twin meteor
wait why not
vast shale
They are not like-terms
vast shale
Like for $x^2 + x + 6$ you can't just transform that to $x^2 + 7t$ or something using your logic
vast shale
becayse one has t
Yes
vocal sleetBOT
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Available help channel!
craggy hamlet
idk
craggy hamlet
do they mean vertical or horizontal
mild flower
there's no concept of vertical or horizontal in the question
vocal sleetBOT
@craggy hamlet Has your question been resolved?
vocal sleetBOT
twin meteor
would i choose (0,0) as my origin
or (0,100)?
because later in the question i used -100
dapper meteor
0,0 because 100 is the vertical distance of the rock from the ground
dapper meteor
because later in the question i used -100
And this is a nonsense is physics
Distances can't be negative
And here we are talking about distance
twin meteor
i see
dapper meteor
But you can't say "my rock is at -100m of altitude"
cobalt imp
Can someone check if this is correct?
vocal sleetBOT
Can someone check if this is correct?
spiral inlet
yep, x4 is free
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Available help channel!
bleak prawn
vocal sleetBOT
https://i.imgur.com/0t2zvIr.png
bleak prawn
I got pretty far but im stuck
full arch
Could you post your work?
bleak prawn
Yes sry im typing it 1 moment
A/(x+2) + B/(x-2)
A(x-2) + B(x+2)
Ax - 2A + Bx - 2B
(A+B)(x-2) = 7
Normally at this point in the question I get the form (A+B)(x) + n, but this time the 2 factors out, so I dont really know what to do next
Why are you 
ing me? 
half imp
(x+4)(x-4) isn't (x^2-4)
bleak prawn
(A+B)(x-2)
bleak prawn
7
full arch
Could you maybe try values of x to eliminate unknowns ?
full arch
Random with a purpose
If you eliminate A but B is still in the equality you can solve for it
Do you not see values of x that allow us to do that?
half imp
One note here is that the left side has to equal the right side for every value of x
peak matrix
A(x-2) +B(x+2) = 7 for all values of x, so you can choose some "random" value of x, and the equation will still remain true. So you probably want to choose some value of x, that would eliminate either A or B from the equation
bleak prawn
oh so +2 or -2 right?
Combo haha
So 4b = 7
And solve for A and B
Thats it right?
Okok I think I can manage that
Thank you everyone!
❤️
.close
vocal sleetBOT
bleak prawn
.reopen
vocal sleetBOT
✅
bleak prawn
Sry I got stuck on something again
A(x-2) +B(x+2) = 7
-4A = 7 so A= -7/4
4B = 7 so B = 7/4
(7/4)(x-2) + (-7/4)(x+2) = 7
0 = 7????
wraith venture
How did you get -4A = 4B = 7 ?
(A+B)x + 2(B-A) = 7
Is this an equation in x or is it supposed to hold for all x ?
bleak prawn
Im not really sure what either of those mean, A and B dont have a definite value yet, I just made them up
A/(x+2) + B/(x-2)
A(x-2) + B(x+2)
Ax - 2A + Bx - 2B
(A+B)(x-2) = 7
wraith venture
Oh you're doing PFD
bleak prawn
yeye
wraith venture
So it must hold for all x
wraith venture
(A+B)x + 2(B-A) = 7
Hence A+B = 0 and B-A = 7/2
bleak prawn
A+B=0?
wraith venture
A constant can't depend on x, can it?
bleak prawn
Ah oke
wraith venture
Hence 2B = 7/2 so B = 7/4 and A = -B = -7/4
bleak prawn
yeye
So did you also get 0 = 7? When you tried to work it out
Or did I make a mistake
wraith venture
Hence 2B = 7/2 so B = 7/4 and A = -B = -7/4
I didn't
In general if you find a contradiction, you made a mistake. Unless you made some assumptions, then they shall also be questioned
But here the assumptions are correct because it's known from the theory of PFD
bleak prawn
But here the assumptions are correct because it's known from the theory of PFD
So what did I do wrong sry?
wraith venture
A/(x+2) + B/(x-2)
A(x-2) + B(x+2)
Ax - 2A + Bx - 2B
(A+B)(x-2) = 7
What are these random expressions for ?
What are they equal ?
What do they represent?
Can't proofread work I can't begin to try to understand
bleak prawn
7/(x^2 - 4)
It needs to be split into 2 fractions A and B to make integration possible
A/(x+2) + B/(x-2)
To work out A and B I set them equal to the numerator
A(x-2) + B(x+2) = 7
Ax - 2A + Bx + 2B = 7
(A+B)(x-2) = 7
bleak prawn
What are these random expressions for ?
What are they equal ?
What do they repre...
Then I tried to work out A and B using substitution but it didnt work...
like substitution -2 and 2 for x into A(x-2) + B(x+2) = 7
wraith venture
7/(x^2 - 4)
It needs to be split into 2 fractions A and B to make integration po...
You expand wrong on the second-to-last line
It's +2B
wraith venture
Then you get where I was
bleak prawn
Then you get where I was
Does thit just mean that its (-7/4)/(x+2) + (7/4)/(x-2)?
Or its not allowed because of the 7 = 0?
wraith venture
There's no 7=0
bleak prawn
Oh
wraith venture
That's the bullshit you made by mistake
Forget it
If it comes from an error, it doesn't hold. Then it can't object to anything
bleak prawn
ok sorry
wraith venture
If it comes from an error, it doesn't hold. Then it can't object to anything
Unless ofc it happens to hold for some other reason. But not in this case, since it's clearly wrong
bleak prawn
I thought I had it but its wrong
(-7/4)/(x+2) = -ln(x+2), no?
And (7/4)/(x-2) = ln(x-2)?
wraith venture
Clearly off by a constant at least
wraith venture
(-7/4)/(x+2) = -ln(x+2), no?
And (7/4)/(x-2) = ln(x-2)?
Awful use of the = sign
Can't approve of that
-7/4 /(x+2) -> -7/4 ln(x+2)
Simple linearity
quartz mauve
what do the different shadings mean? i think one's greater than and one's greater than/equal to but i don't know which is which
vocal sleetBOT
what do the different shadings mean? i think one's greater than and one's greate...
shut briar
i don't think they're different
greater than is represented with dotted line
while greater than equal to is represented by a solid line
the way the area is shaded doesn't matter
quartz mauve
i see
makes sense i dont think theyd throw in a new thing on a test when we didnt learn it
.close
vast shale
im just unsure of how to solve this one. i know its an easy proportion but ive never had to solve one with a variable
18 is to 12x as 5 is to __
vocal sleetBOT
im just unsure of how to solve this one. i know its an easy proportion but ive n...
twin meteorBOT
Result:
3.3333333333333
np
vocal sleetBOT
Available help channel!
bleak prawn
vocal sleetBOT
https://i.imgur.com/rELa0rJ.png
bleak prawn
First thing for any of these questions is to get the roots right? How do I get the roots of sin(x/2)?
viral copper
Equate it to 0
bleak prawn
Equate it to 0
So like sin^-1(0) = x/2
pi(k) = x/2
2pi(k) = x?
What do I do next?
Ah wait I think I see it
Yeye I can do this
Thank you!
❤️
.close
verbal merlin
vocal sleetBOT
vast shale
Hello again
verbal merlin
doing it now one second
i might have troubles with yp more lemme write down yc and add here
i think yc will have the complex root thing right?
@vast shale is this correct?
The particular integral yp = Asint + Bcost
vast shale
Sorry lemme see
verbal merlin
hehe sure np
vast shale
Yeah that should be fine
verbal merlin
The particular integral yp = Asint + Bcost
is this correct?
vast shale
Yes
verbal merlin
im blind haha
verbal merlin
The particular integral yp = Asint + Bcost
this correct?
i think a & b would be 0 eventually but is yp correct??
@vast shale is yp correct
also the username with flowers is nice hehe!
vast shale
The particular integral yp = Asint + Bcost
Yeah that should be right
vast shale
also the username with flowers is nice hehe!
Haha ty
Differentiate twice and plug into the equation and solve for the coefficients
See what you get out of that I guess
vast shale
Lemme see
verbal merlin
oki
verbal merlin
hehe okie
lemme cont
i got A = 2/5 e^t
i thought a and b wld become 0 oml
i feel smth is sus o.0
verbal merlin
mhmm haha
vast shale
Sorry I can't see it rn lmao I believe there should be a repeated root for ur particular solution tho
verbal merlin
oh lemme try looking through again
verbal merlin
Sorry I can't see it rn lmao I believe there should be a repeated root for ur pa...
im not so sure also lmaoo
shld i ask the helpers??
vast shale
Yeah I believe there should have been a t in there
verbal merlin
Yeah I believe there should have been a t in there
wait where o.0
im lost
i think yc is right o.0 yp seems screwed?
vast shale
shld i ask the helpers??
Yeah go for it. I gtg
verbal merlin
mhm
verbal merlin
np
it looks wrong lol so complicated?
<@&286206848099549185> anyone can help me with yp
twin meteorBOT
verbal merlin
oh hey again!
main spade
Looks like we have "Case 2".
verbal merlin
Looks like we have "Case 2".
time to pull out the magic math book
oh wow
which page is case 2 on
theres alot
main spade
It's in Chapter 21.
verbal merlin
oh ye that book is huge i was reading it
yp = Asint + B cost
this is what i had at first
but now i think its not so right?
main spade
Q(t) = 2e^t sin(t) contains a term u(t) of y_c(t) which, when ignoring constant coefficients, is t^0 times a term of Q(t).
verbal merlin
so one time of Q(t)
main spade
verbal merlin
hm so yp shld have the 2e^t sin t in it?
im still not so familiar with the cases still tryna digest it
main spade
I said earlier than you could choose which is u(x) but I think you actually have to consider both. You would arrive at a contradictory result if you use e^t cos(t) instead of e^t sin(t) as one would use Case 1 and one would use Case 2.
verbal merlin
oh wow sounds complicated o.0
main spade
Set Q(t) = 2e^t sin(t).
y_c(t) = c_1 e^t sin(t) + c_2 cos(t).
We can now see that y_c(t) contains a term t^0 times a term of Q(t), namely, Q(t) = t^0 u(t), where u(t) = e^t sin(t).
Hence by Case 2,
y_p(t) is equal to the linear combination of
t e^t sin(t) and it's finite number of linearly independent derivatives.
It is a bit tricky for this one, for sure.
It looks like y_p(t) is going to get pretty big.
main spade
No.
y_p(t) is equal to the linear combination of
t e^t sin(t) and it's finite number of linearly independent derivatives.
verbal merlin
o.0 i think im quite lost on this question
verbal merlin
y_p(t) is equal to the linear combination of
t e^t sin(t) and it's finite numbe...
okayy
main spade
Essentially, you need to find all of the different terms when you differentiate t e^t sin(t).
verbal merlin
i am really sorry to dissappoint but i dont understand
main spade
Just add a t to your original guess and call it a day.
verbal merlin
okay ill try
verbal merlin
Just add a t to your original guess and call it a day.
Atsint + Btcost
@main spade am i right o.0
i think i lost the final brain cell oml im sorry if i sound a 100% dumb
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
boreal path
what is the answer to C and is B AAn
vocal sleetBOT
what is the answer to C and is B AAn
mild flower
B is indeed A1An (which is what i think you meant to write...)
mild flower
that one i don't know
paper depot
"polygonal chain rule"??? idk lmfao
thats the only thing i can think of
in any event this is not math but just vocabulary
boreal path
<:thonk:406575732563902485>
is vectors part of linear algebra
vocal sleetBOT
paper depot
don't reply-ping me on a message irrelevant to what you are saying
if you just wanted to get my attention you could plain ping me lol
mild flower
reply-ping suggests that what you're saying has to do with that message and confuses us because we try to find a connection
boreal path
well
its an emoji
i dont think there exists a connection between linear algebra & emojis, but i digress
vocal sleetBOT
Available help channel!
boreal path
vocal sleetBOT
boreal path
unrelated note: why does this work
mild flower
same slope -> parallel
boreal path
.close
vocal sleetBOT
vocal sleetBOT
Available help channel!
lone bridge
vocal sleetBOT
flat whale
what about taylor expansion?
glacial meadow
vocal sleetBOT
west raptor
Do you mean the ratio |AB| to |BY|?
west raptor
Ohhhh
Ok
Do you know the 45-45-90 triangle?
If no, you can use the pythagorean theorem
west raptor
Does ^2 mean the square root of 2?
glacial meadow
yeah sorry too lazy to grab symbols
west raptor
I usually do sqrt(2)
west raptor
that was my thinking for 1:1:^2
Yeah that's right
west raptor
What's the larger triangle for though?
glacial meadow
wdym
west raptor
I mean the triangle XYZ
glacial meadow
i got a handful of these practice problems theres probably another question abt the other bits
west raptor
Oh ok
glacial meadow
whats the area of triangle xwz?
vocal sleetBOT
whats the area of triangle xwz?
glacial meadow
where do i start here, is there a formula or something i can use 
mild flower
,tex .plane geom
twin meteorBOT
Hayley
mild flower
yeah
mild flower
couple options
first and my favorite is that the big triangle is an equilateral one (do you see why?) so you can figure out the length of the slanted side
flat whale
how does figuring out a slanyed side help though?
Do you know any trig
mild flower
you don't really need trig here
once you have the slanted side you can use Pythagorean theorem to get the height
glacial meadow
Do you know any trig
i js started trig
glacial meadow
once you have the slanted side you can use Pythagorean theorem to get the height
ohhhhh
vocal sleetBOT
@glacial meadow Has your question been resolved?
glacial meadow
once you have the slanted side you can use Pythagorean theorem to get the height
i take it back lol, i dont understand how to get the slanted side ._.
mild flower
the big triangle is equilateral
do you know the length of any of its sides?
or what lengths do you know?
mild flower
base is 24 good
so one side of length 24
and it's an equilateral triangle
meaning all of its lengths are the same
glacial meadow
oh
glacial meadow
base is 24 good
so itd be 24*24
mild flower
,calc 12*sqrt(3)
twin meteorBOT
Result:
20.784609690827
yeah
glacial meadow
ZY- 24 since equilateral
using pythag theorem h-= 20.78
then solving for area using the formula,
area= 249.36
hows this?
mild flower
,calc 12*20.78
twin meteorBOT
Result:
249.36
looks good!
pearl coyote
How do I go from the bottom step to the top step? Why is this not (aa+ba)(ba+bb)?
vocal sleetBOT
How do I go from the bottom step to the top step? Why is this not (aa+ba)(ba+bb)...
gray yarrow
treat a+b as one thing
let's introdue c=a+b
so we get
ac+bc=(a+b)c
otherwise we could get:
(aa+ab)+(ba+bb)
but we can't just switch the + to a * here
pearl coyote
a(a+b)+b(a+b)
c = a+b
a(c)+b(c)
ac+bc
c(a+b)
(a+b)(a+b)
that is
weird
so we're basically turning the things in parenthises into a variable temporarily?
mild flower
yeah we're treating them as one unit
gray yarrow
yes, exactly
nothing wrong with that
pearl coyote
And the same thing is being done here?
*something similar
c = 5a+2
5a(c)+2(c)
5ac+2c
c(5a+2)
(5a+2)(5a+2)
ok that is pretty cool and weird, thank you!
.close
pearl coyote
another question:
why is 2a^3-250 factored not 2(a^3-125). Why is it 2(a-5)(a^2+5a+25)?
pearl coyote
another question:
why is 2a^3-250 factored __not__ 2(a^3-125). Why is it 2(a-5)...
In the picture like why even do this? Why not just leave it?
cyan talon
I mean 2(a^3-125) works, it's just that you can factor a bit further if you wish
a^3-125 = a^3 - 5^3 and there's a nice identity for that
if you're looking for roots and stuff, you might want to factor your polynomial as much as you can
pearl coyote
So we're doing this to break it down further into the absolute simpliest terms because 2(a-5)(a^2+5a+25) is actually in simplier terms than 2(a^3-125)?
mild flower
"simplest terms" is relative
factored form is useful for some things
like solving equations like polynomial = 0
pearl coyote
So we're doing this to break it down further into the absolute simpliest terms factored form because 2(a-5)(a^2+5a+25) is actually in simplier terms more factored than 2(a^3-125)?
And this can be used in certain things like, your example, polynomial = 0?
mild flower
ye3ah
i will note that you asked for "2a^3 - 250 factored"
not "2a^3 - 250 in simplest terms"
pearl coyote
not "2a^3 - 250 in simplest terms"
Sorry if this is a stupid question what would the difference be?
pearl coyote
Got it that makes sense
To fully factor a polynomial like this one I could use "grouping" right?
I'm not super great at this but I think you have to split the middle term in two and the third term must be divided by one of it and have no remainder?
(I.e. a+b = -31x. 9/b = integer)?
pearl coyote
"fully factored" is objective
Sorry, I keep forgetting to ping
mild flower
To fully factor a polynomial like this one I could use "grouping" right?
I'm no...
you want uh
two numbers a and b that multiply to 9*12 and add to -31
and then yes split the middle term in two and group them
serene hazel
vocal sleetBOT
serene hazel
Does B and D sound right?
dull maple
Yes
serene hazel
grave falcon
What is the frequency of the screen lol
hasty pulsar
the screen has a rainbow gaussian curve
serene hazel
Still?
grave falcon
ahah
grave falcon
no its better
serene hazel
Ok cool
near island
where are you stuck