Huh this is a different answer from the one above
#help-33
unique mural
shadow ibex
Yeah, I might be missing something that eliminates extraneous solutions
What answers were you getting
unique mural
This got 60 and 180
Which does seem to be the correct answer
I got w = 1/2 and -1
Which is indeed x = 60 and 180
Thanks for the help
shadow ibex
Yeah I messed something up but I don't know where
Oh
Wow, dumb
Messed up arithmetic in the discriminant
Otherwise, a perfect solution đ
unique mural
.close
dense pollen
On surface integral questions how do you know the direction of the normal vector you get after performing the cross product to double check the correct direction for the oriented surface?
marsh citrusBOT
On surface integral questions how do you know the direction of the normal vector...
@dense pollen Has your question been resolved?
dense pollen
Help pls
eternal tundra
can you give an example?
marsh citrusBOT
@dense pollen Has your question been resolved?
keen stump
I have the acceleration rate of 980cm/s². How would I change this to a graph with algebra?
marsh citrusBOT
I have the acceleration rate of 980cm/s². How would I change this to a graph wit...
keen stump
x-axis is seconds and y-axis is cm
leaden monolith
Just graph it
leaden monolith
Is y measuring displacement?
leaden monolith
You currently have the form $\frac{d^2y}{dx^2}=980$
sharp harness
(...is that x at the end supposed to be there?)
leaden monolith
Oh dear
elfin berryBOT
Frosst
leaden monolith
ie. your y (position) valueâs 2nd derivative wrt x (time) is 980, as in 980cm/s² acceleration
stark trail
Crepas, why do you keep asking calculus questions?
stark trail
yes
marsh citrusBOT
twilit arrow
eternal tundra
xD
sharp harness
...what
stark trail
he hasn't taken any calc/precalc before
supposedly these are "challenge" questions from diffferent math server he is trying to do
marsh citrusBOT
Available help channel!
still vortex
Pick any number $x+y+z=0$. Explain why $\frac{\mathbf{v}\cdot\mathbf{w}}{|\mathbf{v}||\mathbf{w}|}=-\frac{1}{2}$, where $\mathbf{v}=\langle x,y,z\rangle$ and $\mathbf{w}=\langle z,x,y\rangle$
marsh citrusBOT
Pick any number $x+y+z=0$. Explain why $\frac{\mathbf{v}\cdot\mathbf{w}}{\|\math...
elfin berryBOT
Math Is Fun
twilit arrow
!status
marsh citrusBOT
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
Have you tried subbing in the vector forms of v and w into the equation
still vortex
It makes a bigger mess
leaden monolith
If you have, show us
twilit arrow
It makes a bigger mess
well yeah
still vortex
Ok wait a second
leaden monolith
**Math Is Fun**
First convince yourself this is true
still vortex
I got $\frac{xz+yx+zy}{x^2+y^2+z^2}$
elfin berryBOT
Math Is Fun
marsh citrusBOT
Please read #âhow-to-get-help
twilit arrow
**Math Is Fun**
think about what the bottom looks like
for example
what does x^2 + y^2 resemble?
elfin berryBOT
Math Is Fun
leaden monolith
You just have to play around with it!
loud field
an airplane is flying at an airspeed of 345km/h on a heading of 040 degrees. The wind is blown at 18km at a bearing 087 degrees. Determine the ground velocity of the airplane and include a diagram in your solution.
marsh citrusBOT
an airplane is flying at an airspeed of 345km/h on a heading of 040 degrees. The...
@loud field Has your question been resolved?
sacred kestrel
!status
marsh citrusBOT
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
tender mantle
I am confused with properties of matrices
marsh citrusBOT
I am confused with properties of matrices
tender mantle
trace of AB= traceA*traceB
vagrant bolt
should be
tender mantle
so first need is to sequare?
tender mantle
suppose it is defined
tender mantle
trace of AB= traceA*traceB
this property will hold?
vagrant bolt
yep
it's pretty special since you know that matrix multiplication is not commutative
i.e. AB=/=BA
but tr(AB)=tr(BA)
assuming A and B are both nxn square matrices ofc
tender mantle
it's pretty special since you know that matrix multiplication is not commutative
yes
vagrant bolt
did that answer your question?
vagrant bolt
so here trace ab=trace ba?
you asked a different question though
that 4th property in the 1st screenshot is different from the 3rd
lean monolith
Afaik Trace is a linear functional that's only defined for elements in M_n(F), that is, nxn matrices with entries from F
$tr: M_n(F) \longrightarrow F
tr(A) = \sum_{i = 1}^{n} a_{ii}$
elfin berryBOT
Riku
Compile Error! Click the 
reaction for more information.
(You may edit your message to recompile.)
lean monolith
Wait uh why does it say compile error
Try to see what are individual elements in the sum for trace(AB), that is, basically how the diagonal elements of AB look like
Then you can compare
marsh citrusBOT
@tender mantle Has your question been resolved?
tender mantle
you asked a different question though
So what do you think about it?
lean monolith
Hint: If $C = AB$, then
$c_{ii} = \sum_{j = 1}^{n} a_{ij}b_{ji}$
elfin berryBOT
Riku
lean monolith
C ii are the diagonal elements of the new matrix you get multiplying A and B
lean monolith
No it shouldn't
It will be equal 
How does trace A look like
$a_{11} + a_{22} + ...... + a_{nn}$
elfin berryBOT
Riku
tender mantle
All the diagonal elements sum
lean monolith
**Riku**
You get that these signify the diagonal elements?
Similarly calculate trace of B
$b_{11} + b_{22} + ...... + b_{nn}$
elfin berryBOT
Riku
tender mantle
lean monolith
Oh wait hm
Actually i might be wrong
Let's see if I am wrong
That's also going to get the answer
how will the diagonal elements of the matrix be which you get from multiplying A and B
Get those, and then sum and equate
If not equal then yes this is not true always
tender mantle
I tried this
lean monolith
Sorry had to go somewhere, I'm back
Lemme see
Yeah no
They won't be equal
@cold fox
tender mantle
Yes. Thanks riku
Have a good day
Good morning
Ahh wrong tagged
I am arjuuuunnn
lean monolith
<@765564341666840667>
I'm sorry if you see this that was a complete misping
lean monolith
Good morning
Good morning
tender mantle
You can edit it
lean monolith
I mean it still shows the ping to them so anyways
They will be nore confused if I edit it
But yeah, tr(AB) = tr(BA), this is 100% true
You apply the same method
In the end everything will equate
oh shit i gotta cancel my nutro trial or i'll be even more broke 
đ
long cape
marsh citrusBOT
long cape
something wrong with the calculation here?
maybe I should try radian? or it's just wrong altogether
radian doesn't work either
twilit arrow
,w 77.25 deg to radians
elfin berryBOT
deft apex
are you allowed to input trig expressions into your answer thing?
marsh citrusBOT
deft apex
online math moment
marsh citrusBOT
Available help channel!
frank orbit
marsh citrusBOT
marsh citrusBOT
@frank orbit Has your question been resolved?
grand isle
how do i solve physics problems like this in calc 3?
marsh citrusBOT
how do i solve physics problems like this in calc 3?
grand isle
i dont know what to google/lookup to find problems similar like this with solutions
stark trail
I'd start by drawing it*
grand isle
yeah but it's gonna end up coming down to a formula i dont know
and will have to memorize
stark trail
You will know which formula(s) to use, if needed, once you have first visualized the situation
grand isle
i dont know any of the formulas related to physics types of problems
and i know this isnt an initial value problem
because we dont start out with acceleration
and have to integrate back to position
we're given an angle which means theta/alpha/beta will be present in the formula i have to use
stark trail
we start with the velocity
we can integrate that to position
and there is an initial value
at time 0, it is in the javelin thrower's hand, at the point (0, 7)
grand isle
how do i parameterize velocity
into x,y
oh wait
80cos(45) 80sin(45)
i think i see now
crisp mantle
how do i parameterize velocity
a = dv/dt = (dv/dt)(dx/dx) = (dv/dx)(dx/dt) = (dv/dx)v
So a= v(dv/dx)
adx = vdv
And a = -g (y direction) and a=0 (x direction)
grand isle
đ
crisp mantle
For x tho since there is no acceleration, thereâll be a constant velocity
So you donât have to integrate
hasty elbow
I am in Geometry Honors and was wondering what the forumla for this is? I remember something about calculating chords using a tangent line but I can't find the formula on google. Thanks!
marsh citrusBOT
I am in Geometry Honors and was wondering what the forumla for this is? I rememb...
hasty elbow
Please ping me if you know the formula
desert socket
I am in Geometry Honors and was wondering what the forumla for this is? I rememb...
The formula is known as tangent secant theorem
@hasty elbow
fickle ermine
I donât really understand this and could use some help
marsh citrusBOT
I donât really understand this and could use some help
lean monolith
Hint: 70 + 52 + 58 = 180
rare talon
I donât really understand this and could use some help
Do you understand what "congruent triangles" means?
fickle ermine
Yes
rare talon
You know that the sum of the three angles in a triangle sum up to 180 degrees. Right?
fickle ermine
Yes
rare talon
Well, knowing that: what are the angles not shown in the ABC triangle and in the DEF triangle?
fickle ermine
E58 and C52
rare talon
Well. If we look at both sets of angles:
ABC angles = {70, 58, 52}
DEF angles = {70, 52, 58}
They're the same.
If two triangles have the same angles, so their sides are proportional. Right?
fickle ermine
Ya I think I get it
rare talon
Is there some non obvious part in my explanation until now?
rare talon
Ok.
Their sides are proportional, so what is that proportion?
What is the ratio between the sides of ABC to DEF?
fickle ermine
That i donât know
rare talon
Like: proportional means that one is a multiple of another.
You take one, multiply by a number and get the other.
fickle ermine
Multiply what
rare talon
I will give a example.
Let say candy bars cost 3 dollars per unit. 10 candy bars costs 30 dollars. 21 candy bars costs 63 dollars.
(Amount payed)/(number of candy bars) = constant.
The amount payed is proportional to the number of candy bars. You can multiply one quantity by a number (the constant) and get the other.
fickle ermine
So is 122 and 128 the constant
rare talon
How did you get 122 and 128?
fickle ermine
70 plus 58 and 70 plus 52
rare talon
That is just the sum of two angles.
In that case: the sides of one triangle are multiple of the other.
rare talon
In that case: the **sides** of one triangle are multiple of the other.
You can take the ABC triangle, multiply every side by a number and get the DEF triangle.
Are you following?
fickle ermine
Ye donât how do I find out the sides
rare talon
That is the neat part: you don't have to find the sides.
rare talon
I donât really understand this and could use some help
What the problem gives us about the sides?
What information it telled about the sides of the triangles?
fickle ermine
Are you asking me a question
rare talon
Yes.
fickle ermine
It only told me about the angles
rare talon
Look at the sides AB and DE.
fickle ermine
Oh there equal
rare talon
If the sides are equal, so what number should i multiply one side (AB) to get the other side (DE)?
lean monolith
Yes
fickle ermine
Multiply what
rare talon
Multiply what
The side AB.
The triangles are proportional.
I can multiply the sides of one and get the sides of the other.
fickle ermine
Multiply what numbers
rare talon
That is what i am asking you.
fickle ermine
The sides donât have numbers just the angles
rare talon
I know the sides don't have numbers in them, but they do have a length. The question just didn't give it.
fickle ermine
Nope
rare talon
You think the sides don't have length?
fickle ermine
No i donât but I donât know them
rare talon
Oh. Ok.
We don't have to know the exact length of sides.
The question is just asking for us to prove that the triangles ABC and DEF are congruent (both has the same sides and angles).
We already know that the angles are equal.
Half of the job js done.
How can we show that the sides are also equal?
fickle ermine
I donât know
rare talon
Am i even helping you?
rare talon
I don't know what to say.
rare talon
Am i even helping you?
I am asking to know if i have to change how i am explaning.
Maybe i am beeing too complicated and wanted to know.
fickle ermine
Probably
rare talon
Ok. Give me a minute.
fickle ermine
Ok
rare talon
Right.
We just have to prove that both the triangles ABC and DEF have the same sides (we already did it with angles).
rare talon
I donât really understand this and could use some help
The question telled us that AB and DE are equal.
If the triangles ABC and DEF have the same angles, so the sides of ABC are proportional to the sides of DEF. Right?
fickle ermine
Ya
rare talon
Well, what is the definition of "proportional"?
You, what you think when reads "proportional"?
fickle ermine
Crosponding sizes
rare talon
Almost.
Let say you running such that you traverse 10 meters each second.
If you ran for 6 seconds, how much meters you traversed?
fickle ermine
60
rare talon
What if you ran for 4.5 seconds?
fickle ermine
45
rare talon
You may note that the distance traversed is a multiple of the time running. Right?
fickle ermine
Yes
rare talon
That is what proportional means.
fickle ermine
Ok
rare talon
"A is proportional to B" means that you can multiply B by some number and get A.
fickle ermine
Ok
rare talon
Now. We know the sides of the triangle ABC are proportional to the sides of triangle DEF. Right?
fickle ermine
Yea
rare talon
What does it means their sides to be proportional?
fickle ermine
One side is equivalent to the other side
rare talon
Not quite.
rare talon
"A is proportional to B" means that you can multiply B by some number and get A.
Remember what i said.
fickle ermine
I do remember that but I donât get it in this context
rare talon
I see.
rare talon
What does it means their sides to be **proportional**?
You can multiply all the sides of the ABC triangle by some number and get all the sides of the DEF triangle.
fickle ermine
I donât quite get it
rare talon
I donât quite get it
I can give a example.
You can note that all the sides of the blue triangle are double the sides of the red triangle.
rare talon
What number should i multiply the sides of the red triangle to get the sides of the blue triangle?
fickle ermine
2
rare talon
What number should i multiply the sides of the blue triangle to get the sides of the red triangle?
fickle ermine
Wouldnât you divide
rare talon
Yes, exactly. By what number would i divide the sides of the blue triangle to get the sides of the red triangle?
fickle ermine
2
rare talon
Great.
Just a note: divide by 2 is the same as multiplying by 1/2 and that was what i was asking but you are right the same way.
Do you understand now "multiplying the sides of a triangle".
fickle ermine
Ya
rare talon
So, there's very little left to do.
rare talon
I donât really understand this and could use some help
Their sides are propotional.
fickle ermine
So they are all equal to ab side
rare talon
Oh, sorry.
rare talon
So they are all equal to ab side
You mean that every side in the ABC triangle is the same?
fickle ermine
I did but now I donât
rare talon
Ok.
rare talon
Their sides are propotional.
So i can multiply the sides of the ABC triangle and get the sides of the DEF triangle.
Right?
fickle ermine
Yes
rare talon
We have to multiply every side of the triangle by the same number, right?
fickle ermine
Yes
rare talon
Like: i cannot multioly one side by 3 and other by 2 and the other one by 6. I have to multiply all the sides by 2.
fickle ermine
Uh huh
fickle ermine
I did
rare talon
Ok. I asked because you normally say "right" but ok.
fickle ermine
My bad
rare talon
You can note that if i only gave you one side of each triangle: it would be suficient.
fickle ermine
Yes
rare talon
If i only gave you the 10 side of the blue triangle and the 5 side of the red triangle, so you could discover that you have to multiply by two.
fickle ermine
Yea
rare talon
I will try a example.
Consider a triangle with sides 13, 5, 17 which i will call A and other triangle i will call B.
Assume the sides of A and B are proportional. Assume one of the sides of B is three times one of the sides of A. What are the sides of B?
fickle ermine
39 15 51
fickle ermine
Ok
rare talon
I donât really understand this and could use some help
We know that one of the sides of ABC (AB) is equal to one of the sides of DEF (DE) and we know they are proportional.
fickle ermine
Ye
rare talon
Hou much do i have to multiply 4 to get 4?
fickle ermine
1
rare talon
How much do i have to multiply 13 to get 13?
fickle ermine
1
rare talon
Why 1?
fickle ermine
You said how much do i have to multiply 13 to get 13 and 13 x 1 is 13
fickle ermine
Can you elaborate on that one
rare talon
Sorry.
fickle ermine
1
rare talon
Do you notice something?
rare talon
If i have some number, what should i multiply it by to get itself?
fickle ermine
Of the ab side is equal and I only need one side to find out if itâs proportional and it equal that means there all equal right
rare talon
Not quite.
rare talon
If i have some number, what should i multiply it by to get itself?
Think about this.
fickle ermine
It would be 1
fickle ermine
1
rare talon
If i have to multiply AB by 1, so i have to multiply every other side of ABC by one.
fickle ermine
Yes
rare talon
If i have something and then multiply by one: i will get the same thing. Right?
fickle ermine
Yes
rare talon
If the sides of ABC are 12, 24, 17: what are the sides of DEF?
fickle ermine
12 24 17
rare talon
We have proven in the start that the angles of both triangles are equal.
fickle ermine
I think I get it
rare talon
Now we just proved that both triangles have the same sides.
fickle ermine
So I did it
rare talon
Yes.
fickle ermine
Thanks dawg
rare talon
Did you understand my explanation?
fickle ermine
Yes
rare talon
Thanks dawg
What do you mean by "dwag"?
fickle ermine
No
fickle ermine
What do you mean by "dwag"?
I like friend kinda like homie
rare talon
Thank you for beeing patient with me.
fickle ermine
Same to you
rare talon
Thank you (even if i didn't have to be patient).
fleet trench
marsh citrusBOT
tight furnace
,rotate
elfin berryBOT
tight furnace
what have you tried?
fleet trench
Let x=oldest
tight furnace
what are the 3 sister's ages then
fleet trench
I dont understand how to do this
tight furnace
In terms of x
tender mantle
marsh citrusBOT
tender mantle
I found a solution online but it was complicated. Is there any easy way to solve it?
What if I use modular arithmetic?
desert socket
(10^n)mod6 is always 4 where n is an integer and n>0
Well, old biscuit is right too
@tender mantle
tender mantle
What do you mean by old biscuit?
desert socket
He deleted his message
desert socket
The given number is product of three consecutive numbers
tender mantle
Yes
desert socket
Think about divisibility of product of three consecutive numbers by 6
marsh citrusBOT
@tender mantle Has your question been resolved?
tender mantle
.close
marsh citrusBOT
marsh citrusBOT
Available help channel!
still temple
What property is this?
marsh citrusBOT
What property is this?
devout mauve
still temple
ĺăăăžăă
How would i simplify these so they don't have log
wolfgram doesn't help
paper folio
Would ask for someone to check over my work and tell me if itâs right or wrong and the answer yes this is just a check over for extra credit (letting you know bc somone who helped me noticed the blue background meaning extra credit)
marsh citrusBOT
Would ask for someone to check over my work and tell me if itâs right or wrong ...
paper folio
I wouldâve just turned it in for my credit but knowing my grade is low
I need it
winter dagger
hmm
paper folio
Hello!
winter dagger
can you remember soh cah toa?
winter dagger
right
paper folio
Which one are we working on
winter dagger
you can try memorizing soh cah toa since it'll make it a lot easier for you
number 1
do you remember what adjacent, opposite, and hypotenuse mean?
paper folio
A bit not to much Im a bit fuzzy i sit here and do math all day for credit
winter dagger
ok
so hypotenuse is the longest side in the right triangle
its the one that doesnt touch the 90 degree angle
fierce pulsar
yes
winter dagger
what do you mean ac?
winter dagger
in number 1?
winter dagger
it would be ba
paper folio
I mean line
winter dagger
remember, its the longest side
paper folio
Oh yes your right
paper folio
So that means
winter dagger
these are what you call the isdes of the triangle that arent the hypotenuse
paper folio
Sin(a)= 4/13
winter dagger
right!
paper folio
Okokok
winter dagger
do you remmeber what opposite and adjacent mean?
paper folio
And then
paper folio
do you remmeber what opposite and adjacent mean?
Not as much
winter dagger
ok
paper folio
Remind me please
winter dagger
so this is relative to the angle that you're using the trig function on
opposite would be the leg that isn't touching the angle youre using it on
adjacent would be the leg that is touching
winter dagger
hmm
remember which two sides are you gonna use?
like adjacent, opposite, hypotenuse...
winter dagger
it's actually adjacent/hypotenuse
this is where its really useful to memorize soh cah toa!
did you learn about how to use it yet?
winter dagger
ok ill give you an explanation since i found it reallt helpful when i was learning it
paper folio
it's actually adjacent/hypotenuse
But it is still 4/12
winter dagger
actually 4/13
winter dagger
yeah
but soh cah toa is this acronym
the beginning letters are the trig functions, like sine, cosine, tangent,
paper folio
Wait so son a and cos b is the same answer
paper folio
Sin(a)= 4/13
.
winter dagger
yep
winter dagger
do you want to learn about soh cah toa?
i found it really helpful but if you would prefer to work on the questions we can do that too
paper folio
do you want to learn about soh cah toa?
I would like to if I had a lot of time but I do need this credit to be in
paper folio
i found it really helpful but if you would prefer to work on the questions we ca...
Yea
It does seem helpful
winter dagger
sure, i'd highly recommend learning it later just since you'll struggle on tests if you don't have your trig functions down
paper folio
And I would like to learn it from you 100% but still my credit is low and it has to be in by Wednesday
paper folio
sure, i'd highly recommend learning it later just since you'll struggle on tests...
Yea on my test I got like a 2.3
Should we do this one now
winter dagger
actually tan(b) is wrong too...
paper folio
Oh
winter dagger
so remember which sides do you need to take for tan?
paper folio
adjacent,hypotenuse
winter dagger
no, that woukd be cosine
remember soh cah toa?
ah (adjacent hypotenuse) would be cosine
but tangent would be oa or opposite over adjacent
winter dagger
yep!
paper folio
Yess
winter dagger
see this is where the acronym is really useful
paper folio
This
winter dagger
the photo is a little blurry, is it asking to find angle H?
paper folio
Itâs asking to
Not that
hat is the correct trig ratio below in terms of Cosine of angle H? *
fierce pulsar
COSH=15/17
winter dagger
yep
winter dagger
remember, cah is adjacent over hypotenuse
paper folio
C
paper folio
remember, cah is adjacent over hypotenuse
Alrigjt ili note it down
Note
I resent a few
winter dagger
ok for the first one
look at the angle they give you can the sides they give you
relative to that angle, what are the sides?
like are they adjacent, oppposite, hypotenuse,
winter dagger
yep
its the hypotenuse
remember, the hypotenuse is the longest side
its also the one that's kinda slanty
ok so if you have opposite and hypotenuse, which trig function are you gonna use?
remember soh cah toa
paper folio
Uhh
winter dagger
remember how soh cah toa works?
winter dagger
can you try memorizing it? itll REALLY help you on tests
so what two letters do opposite and hypotenuse turn into?
paper folio
Wait a sec
winter dagger
i really think we should go over soh cah toa
i know you just want the answers to extra credit, but i really don't think you're learning anything currently
if you can't remember what the trig functions do, you're really gonna struggle as time goes on
i'm sorry, youve been away for some time now and i have other things to take care of
if you come back hopefully someone else can take over
marsh citrusBOT
@paper folio Has your question been resolved?
keen wigeon
Hi, i need help with part b) I have forgotten how to do when X is not equal to x (2 in this case)
marsh citrusBOT
Hi, i need help with part b) I have forgotten how to do when X is not equal to x...
still temple
you could calculate the complement instead
still temple
N is normal distribution right?
keen wigeon
Yeah
still temple
do you know about pdfs?
keen wigeon
hmm which is short for?
still temple
probability density function
keen wigeon
No I haven'f done that yet
still temple
P(Xâ 2) = P(X<2) + P(X>2)
keen wigeon
Oh ok
still temple
(in general, the probability at a single point is 0 for continuous distributions)
keen wigeon
so do i make P(X>2) 1-P(X<2)? or do i just make 2 the lower bound?
still temple
so do i make P(X>2) 1-P(X<2)? or do i just make 2 the lower bound?
if you know that result, you can
keen wigeon
alright
still temple
P(X>2) + P(X<2) = 1 - P(X<2) + P(X<2) = 1
still temple
(in general, the probability at a single point is 0 for continuous distributions...
(and using this fact, P(Xâ 2) = 1 - P(X=2) = 1 - 0 =1)
still temple
if you use exact results, you would get exactly 1
still temple
P(X>2) + P(X<2) = 1 - P(X<2) + P(X<2) = 1
but you dont need to calculate anything ^
keen wigeon
Ok so i just know it i 1
still temple
yes
keen wigeon
Thanks mate!
still temple
yw :)
marsh citrusBOT
@keen wigeon Has your question been resolved?
soft wigeon
What is theta intercept?
marsh citrusBOT
What is theta intercept?
soft wigeon
I don't understand 2 c
marsh citrusBOT
@soft wigeon Has your question been resolved?
mystic heath
What is theta intercept?
you need to find the points that cos(theta) = 0
marsh citrusBOT
marsh citrusBOT
Available help channel!
void tangle
marsh citrusBOT
dim mantle
Whatâs the difference between doing sin(x), referring to opposite/hypotenuse, and sin(x) with Taylorâs series
marsh citrusBOT
Whatâs the difference between doing sin(x), referring to opposite/hypotenuse, an...
dim mantle
The kinda x - (x^3/3!) + (x^5/5!)
knotty trellis
It's the same function. In right triangle with one angle being x, opposite/hypotenuse = sin(x) = x - (x^3/3!) + (x^5/5!)...
dim mantle
Iâm not sure I understandâŚ
quaint elm
sin(x) is exactly equal to the Taylor series; that's actually how it's calculated on your computer probably
it's also exactly equal to opp/hyp, but if you don't have those values then you won't be able to calculate it that way
ofc the Taylor series is infinite so if you don't have infinite time you won't get an exact answer that way
knotty trellis
3/10 = x - x^3/3! + x^5/5! etc
knotty trellis
sin(x) is exactly equal to the Taylor series; that's actually how it's calculate...
I think there's more sophisticated algorithm on computers, taylor series is rather useful to make computation in head
late geode
,w solve 3/10 = x - x^3/3! + x^5/5!
elfin berryBOT
late geode
,w sin(0.304693)
elfin berryBOT
late geode
close enough
knotty trellis
Here, the angle x was computed and in the second calculation, ramonov tried to make sin(x) and as you can see, it's aproximately 3/10. Which is your opp/hypo ratio
so if you wanted to compute e.g. sin(0.5), you could instead compute 0.5 - 0.5^3/3! + 0.5^5/5! ...
which is easier to do by hand
dim mantle
So the taylor series is to like calculate the o/h of a triangle of which we donât know o or h?
knotty trellis
yes, if you know the angle x, the normal way you would calculate o/h is by doing sin(x) on your calculator. But instead, you can do it by hand by evaluating the taylor series
burnt dust
I've tried to think of a way to solve this but have yet to find how to solve this
marsh citrusBOT
I've tried to think of a way to solve this but have yet to find how to solve thi...
quaint elm
so you have two lines that each go through the point P and are tangent to f(x)
so the first line goes through some (a, f(a)) and is tangent to f(x) at that point
quaint elm
no! it takes some thought dw
quaint elm
ok so you know what the slope of a tangent line is right?
burnt dust
Yea f'(a) of the function f(x)= x^2 -x +2 is equal to f'(x) = 2x-1, and the point where tangent t_1 and f(x)=x^2 -x+2 intersect will have the same slope which is equal to the slope of the tangent line with a function rule in the form of y =mx+c, so the m in that function rule will be the derrivative of the function F(x)= x^2 -x +2 where the x values are the same
(sorry if it's unclear English isn't my first language and the maths terms have to be translated)
quaint elm
right okay so we have that it goes through (a, a^2 - a + 2) and (3, -1) and that it has slope (a, 2a - 1)
quaint elm
if I gave you two points how would you compute the slope of the line?
burnt dust
Do I use the formula Y - F(a) = F'(a) x (x-a)
quaint elm
please don't use x as a multiplication symbol, use * instead
sure that'll work
burnt dust
I'm still lost
quaint elm
have you seen the formula $m = \frac{y_1 - y_0}{x_1 - x_0}$?
elfin berryBOT
Hayley
burnt dust
Yeah differntial quotient
But I'm a bit lost I know one point would be (3,-1) but the other
the interception point with the tangent line and the function F(x)=x^2 -a +2
How do i find that x coordinate
quaint elm
the other point would be (a, f(a))
which i know sounds like a non-answer
but we also have that the slope matches the derivative at that point, so $m = f'(a)$
elfin berryBOT
Hayley
burnt dust
I get that m = f'(a) but how would the point be equal to (a, f(a))
flat raft
the tangent line to f at a point a is defined to be the line with the slope m = f'(a) and that goes through the point (a, f(a))
burnt dust
is that like a general law? I have never heard of that before let's say the second point is (a,f(a)) and I fill it into my differential Quotient formula of (Y1- Y2) / (x1-x2) then I get ( F(a) +1) / (a-3)
burnt dust
Alright
flat raft
a law sorta implies that there's some mathematical argument behind why it's true
but this is one of those things that just describes
what it means to be "tangent" in this particular case
burnt dust
Alright
but I filled my differential equation in correctly right? How do I get the formula of the slope from that? I'm sorry I'm very lost right now
flat raft
honestly maybe Hayley has a better way of doing it, because I'm way too lazy to scroll up and read. I'm just thinking of the brute-force way of giving variables to everything
and then stacking up the equations and solving
quaint elm
you've got $m = \frac{f(a) + 1}{a - 3} = \frac{a^2 - a + 3}{a - 3}$
elfin berryBOT
Hayley
quaint elm
you also have $m = f'(a) = 2a - 1$
elfin berryBOT
Hayley
quaint elm
so $2a - 1 = \frac{a^2 - a + 3}{a - 3}$
elfin berryBOT
Hayley
quaint elm
go forth and algebra
quaint elm
yeah ;) it suddenly becomes clear once you solve it
marsh citrusBOT
Available help channel!
still temple
\frac{p-1}{1+\frac{2}{p}+\frac{3}{p^3}}
marsh citrusBOT
\frac{p-1}{1+\frac{2}{p}+\frac{3}{p^3}}
still temple
\frac{p-1}{1+\frac{2}{p}+\frac{3}{p^3}}
calm anvil
$\frac{p-1}{1+\frac{2}{p}+\frac{3}{p^3}}$
elfin berryBOT
Arctic
calm anvil
!status
marsh citrusBOT
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
stoic saddle
explain what is troubling you
calm anvil
^
still temple
bro i dont know where the begin
calm anvil
so its 1 not 6
stoic saddle
- don't call me bro
- why say 6 and not 1?
still temple
**Arctic**
the question is simplified this form
still temple
1. don't call me bro
2. why say 6 and not 1?
Because im blank
calm anvil
id start by getting rid of fractions
stoic saddle
Because im blank
i mean you could at least read what we're saying & what we're asking you
anyway like
ok
so you have the expression $\frac{p-1}{1 + \frac{2}{p} + \frac{3}{p^3}}$, and you need to simplify it, and you don't know where to start.
elfin berryBOT
Ann
still temple
yes
stoic saddle
multiply top and bottom by p^3 to get rid of the nested fractions.
still temple
okey
calm anvil
$\frac{p^3(p-1)}{p^3+2p^2+3}$
stoic saddle
$\frac{p^3(p-1)}{p^3+2p^2+3}$
!nosols and also dont say blatantly wrong shit
marsh citrusBOT
$\frac{p^3(p-1)}{p^3+2p^2+3}$
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.
elfin berryBOT
Arctic
calm anvil
!nosols and also dont say blatantly wrong shit
youre the one who told them exactly how to simplify it
stoic saddle
youre the one who told them exactly how to simplify it
i gave the instruction
it was up to him to execute it
and either achieve his goal or screw up and complain
still temple
miss, what's the next stepp?
stoic saddle
is there anything you see in the fraction right now that needs extra simplification?
stoic saddle
if you don't see anything in the fraction that screams "this needs to be simplified", there is probably nothing.
and in this case there really is nothing
placid mountain
Just need a math check for all of these to ensure no mistakes.
marsh citrusBOT
Just need a math check for all of these to ensure no mistakes.
@placid mountain Has your question been resolved?
placid mountain
<@&286206848099549185>
inner grove
4 to 8 are ok
1 c) is wrong
slope is already expressed in the function
it's -3/2
placid mountain
Ah ok
inner grove
everything else is right
12 is also wrong
remember that perpendicular graphs have a slope that is not only opposite but also inverse
inner grove
remember that perpendicular graphs have a slope that is not only opposite but al...
.
you forgot to invert the slope
elfin berryBOT
purrthagorascat
inner grove
I see that one but whatâs wrong with 1c?
that the slope is -3/2
you really don't have to calculate anything, it's already expressed in the equation of the function
inner grove
Where are you getting the b in 12
in 12, it says it's the same as the b of the other function
which is 4
placid mountain
But thereâs no b in 11 or 12
placid mountain
Ah ok for 11?
inner grove
both
inner grove
**purrthagorascat**
yup
placid mountain
So whatâs wrong with it?
inner grove
on ex 12, you wrote b right, but the slope is wrong
placid mountain
Right?
inner grove
sorry, wym by right?
placid mountain
There two different questions Iâm confused by what you mean?
inner grove
i know they are two different question
and on exercise 12, the function has to be perpendicular, which means that the slope is inverted and opposite, you only did opposite
you also have to invert the slope in order for the other function to be perpendicular
inner grove
bruh
placid mountain
Iâm sorry Iâm very confused. How is the question b=4 ??
placid mountain
11
placid mountain
Not question answer
placid mountain
Excuse me? No Iâm not Spanish not that that was any of your business in the first place. Secondly your not making any sense your saying question 11 is b=4 I am asking you how itâs that answer and not what I put down. If your not able to explain that to me Iâll leave and find help elsewhere.
inner grove
okey, i am going to rephrase. I only asked if you speaked spanish because i do, and since you were writing confusing sentences, maybe that way we could understand each other
i will try my best to make my point clear
placid mountain
Iâm not trying to be rude but I made two typos and you kind of lost it for no reason. Alright then letâs start over.
Hm okay. I see what your saying, can I ask where you got the +4 from?
inner grove
the -2/3 is just the same as writing -4/6 (i just simplified the fraction)
and the y=-2 and x=6 are just info given by the instructions (that's the point the function goes through)
placid mountain
Right okay, wouldnât -2/3 be simplified?
inner grove
placid mountain
Ah okay.
inner grove
was that more helpful?
placid mountain
Kind of. However I still donât see where you got +4 from. I see the simplifying however wouldnât-2/3 be the simplified equation?
inner grove
you mean the simplified fraction?
placid mountain
Yes.
inner grove
yes it is, but it is the same thing
elfin berryBOT
purrthagorascat
inner grove
i just rewrited the fraction -4/6 as -2/3, but it is the same really, nvm that
marsh citrusBOT
marsh citrusBOT
Available help channel!
stoic tapir
hi
stoic tapir
can someone explain how a limit approaching from the left and a limit approaching from the right are different in the context of this problem
the first one says 0 remains positive while the second one says 0 remains negative
winged field
Approaching from the left would be like if we considered the numbers 4.9, then 4.99, then 4.999, etc as we approached 5. If we do this, then 5-x is positive, since x is always a tiny bit less than 5, but we still approach 5, so 5-x still approaches 0, it just stays positive
From the right is similar: we can consider x being, like, 5.1, then 5.01, then 5.001, etc, and then 5-x is still approaching 0, but since x is always slightly larger than 5, 5-x is negative
winged field
ofc!
stoic tapir
.close
mystic terrace
I dont understnad how they went got the laststep
marsh citrusBOT
I dont understnad how they went got the laststep
stoic saddle
$\log_2(x) = y \iff 2^y = x$
elfin berryBOT
Ann
stoic saddle
do you understand this Y/N
marsh citrusBOT
@mystic terrace Has your question been resolved?
mystic terrace
how do i solve the last step
i made a writing error
it should be
5/2=log2(x)
i did it wrong
how do i solve
marsh citrusBOT
@mystic terrace Has your question been resolved?
last brook
Which one do you want to solve you posted 3 different
marsh citrusBOT
marsh citrusBOT
Available help channel!
north prism
how do i get this started
marsh citrusBOT
how do i get this started
cunning jackal
Are you aware of any property of pure polynomial functions with regards to their continuity?
north prism
i dont think so
cunning jackal
Alright, do you know the definition of continuity in limit form?
And what about the definition in graphical form
north prism
doesnt that mean that you can write it down without like putting ur pencil up
cunning jackal
Yes graphically it means that
Now the question says the function shouldn't be continuous in the CLOSED interval [-1,3]
Now option C is a quadratic polynomial
And if you're aware of this, their graph is a parabola
Which can be drawn without lifting the pen at all everywhere
In fact if you had known the definition in limit form I'd have proven it to you for any polynomial
Polynomial functions are always continuous