how do u get r^27 = 1.21674683?
#help-36
ornate knot
u showed that r = 3 here and 3^27 is 7625597484987
also r is the common ratio between 2 consecutive terms ie year 1 and 2 or year 5 and 6
cursive wave
How would I do this one?
final saddleBOT
How would I do this one?
cursive wave
This is what I did and it’s very wrong
ornate knot
This is what I did and it’s very wrong
u removed the 7 and simplifed sqrt50 to 5sqrt2
instead its $7(5\sqrt2)$
soft zealotBOT
JustToPro
cursive wave
OMG
YEAH
TYSM
Is everything else okay? Should I get the right answer if I continue like this?
ornate knot
yeah the rest of the steps are correct
ornate knot
np
cursive wave
.close
scarlet beacon
magic sparrow
.close
mental hill
$x^2 = -3i$
$|x| = \sqrt{-3i}$
$;-\sqrt{-3i} = \sqrt{-3i}$?
final saddleBOT
$x^2 = -3i$
$|x| = \sqrt{-3i}$
$;-\sqrt{-3i} = \sqrt{-3i}$?
mental hill
is it true for any z?
any complex number?
so i dont have to take the module here?
like x is always equal to $x = \sqrt{z}$ without the +-
viscid fossil
$$|x+iy| = \sqrt{x^2+y^2}$$
mental hill
and is it true for any even exponent?
soft zealotBOT
EndTimes
mental hill
yeah i was able to calculate this but i was wondering if this always holds true?
i used the exponential form of z
$\sqrt{3}e^{-pi/4 + pi/k}$
viscid fossil
Post the original question, you're being unclear
soft zealotBOT
Yanek
mental hill
Post the original question, you're being unclear
sorry
what i want to ask is whether
$x^2 = z; x = +-z$ can i omit the +- here?
soft zealotBOT
Yanek
mental hill
at least for x^2 = -3i it doesnt make difference
viscid fossil
There are always two square roots of a number
mental hill
ok i thought that maybe its different for complex solutions
viscid fossil
Except for 0 which has a double root
formal trail
ok i thought that maybe its different for complex solutions
the pattern keeps going if you include complex numbers, cube root has 3, 4th root has 4 etc
final saddleBOT
Available help channel!
cyan kelp
how do I solve this knowing that for t=0, x=1 and dx/dt = 1
final saddleBOT
how do I solve this knowing that for t=0, x=1 and dx/dt = 1
long copper
you can use laplace transform or take x = e^rt
tired plume
This integral is famously know as the simple harmonic oscillator, you can find the general solution on Google
If you want to know "how" you should first understand all the methods for solving second order ODEs
verbal steppe
Enter the equation of the line L that passes through the point (−3,−1, 4), is parallel to the plane : x+3y−z = 10 and intersects the line L1 : (x, y, z) = (−3, 3, 8) + t(1,−1, 2), t ∈ R. Make a principle sketch!
final saddleBOT
Enter the equation of the line L that passes through the point (−3,−1, 4), is pa...
verbal steppe
So my initial thought is that for a line to be parallel to a plane it has to be perpendicular ⊥ with the normal vector of a plane, right?
Considering it has 3 conditions:
- Has to pass (-3,-1, 4)
- Is paralelle to the plane x+3y−z = 10
- intersects the line L1 : (x, y, z) = (−3, 3, 8) + t(1,−1, 2), t ∈ R.
I'm not sure how to fulfill these conditions
tranquil pine
Here you try considering direction vectors as x,y,z then make equations by satisfying these conditions
verbal steppe
I know that the L i'm looking for should look something like:
L: (x,y,z) = (-3,-1,4) + t(x2, y2, z2)
However i have no idea what (x2, y2, z2) aka the directional vector should be
tranquil pine
Like to satisfy that line is parallel to plane you can make it's dot product with normal vector as 0
verbal steppe
Yes precisely
i was thinking that but
That doesn't take the other 2 conditions into account
(x,y,z) * (1,3,-1) = 0
only fulfills the conditions for perpendicular
tranquil pine
I know that the L i'm looking for should look something like:
L: (x,y,z) = (-3,-...
Like we have 3 variables now to solve them we need 3 eqns right
verbal steppe
well the value on t doesn't matter right? Since that only increases the length of the vector?
tranquil pine
Now other two equations we can make by considering a variable point on given line and putting that in our variable line
tranquil pine
well the value on t doesn't matter right? Since that only increases the length o...
Yeahh it doesn't matter we just need any parallel vector irrespective of it's length
verbal steppe
So (x2, y2,z2) has to fulfil all three conditions?
tranquil pine
Yeah exactly
verbal steppe
Well if we do
tranquil pine
Either there is also a slickier way to satisfy intersecting condition like you can make distance with lines 0
verbal steppe
$(x2, y2,z2) \cdot (1,3,-1) = 0$ then we get x y z for one vector that fulfills that is it perpendicular
soft zealotBOT
Merineth
verbal steppe
But with that equation we can't prove that it goes through the line , right?
We result in a directional vector for L that is parallel to the plane
Do we test it?
tranquil pine
Yeah we can do by 2 methods like by taking any variable point on given and satisfying in our variable line but this is quite clumsy either you can make distance between two lines as 0 cuz if they intersect then distance between them must be 0
verbal steppe
$(x2, y2,z2) \cdot (1,3,-1) = 0 \
(1,1,4)$
soft zealotBOT
Merineth
soft zealotBOT
Merineth
tranquil pine
From where you took 1,1,4
verbal steppe
well x * 1 + y * 3 + z*(-1) has to be = 0
tranquil pine
Yeah right
tranquil pine
Ooh you are putting values well if that works then it's good but many times that's doest satisfy other conditions so iť will be good if you cross check other conditions as well
Haha at times vectors are confusing especially with 3d geometry mix
verbal steppe
Yeahh my way of thinking might not be the best but if it works it works 
tranquil pine
Yeahh my way of thinking might not be the best but if it works it works <:happy:...
Yeah but sometimes it gives fast results so its good too
verbal steppe
L: (x,y,z) = (-3,-1,4) + t(1,1,4)
So this is my line now that fulfils that it is perpendicular to the plane and passes the point (-3,-1,4) and now lastly we have to check if it passes the line L1
tranquil pine
Yess exactly then job is done
verbal steppe
|(-3,-1,4) +t(1,1,4)| - |(-3,3,8) +t(1,-1,2)| = 0
is this what you meant?
i.e.
|L| - |L1| = 0
Then it passes
tranquil pine
Like i meant either you can see at what point these lines interect by making 3 equations from 3 direction vectors by using different 't's for each line but this method is really boring one
Now question doesnt want us to find point so there is no need to find it either make the distance between them 0 just like you find distance between two screw lines
verbal steppe
Oh wait sorry i just realized that the points (-3,-1,4) and (-3,3,8) doesn't matter, right? Since we are only interested if the directional vectors passes each other, right?
|t(1,1,4)| - |t(1,-1,2)| = 0
So this is what we are after ?
tranquil pine
Actually they do matter if want to find point of intersection of lines
Like first of all make different t s for each line
verbal steppe
oooh right
Yeah had to think there for a moment
but shouldn't it technically be
|(-3,-1,4) +t(1,1,4)| = |(-3,3,8) +t(1,-1,2)|
tranquil pine
Like you are try to find point of intersection between lines right
verbal steppe
well that's basically the same thing as = 0
tranquil pine
|(-3,-1,4) +t(1,1,4)| = |(-3,3,8) +t(1,-1,2)|
Like we can't be sure if they are same t s
So here we will have 3 equations to find point of intersection
-3+t=-3+r. ( I am considering other t as r )
-1+t=3-r
4+4t=8+2r
You can find r and t from first 2 eqns then make sure they satisfy 3rd if they domt then lines doesn't intersect
verbal steppe
that makes sense, one moment and i'll check
tranquil pine
Oh okay sure
verbal steppe
$(-3,3,8) + t(1,-1,2) = (-3,-1,4) +r(1,1,4) \
(-3,3,8) + (t,-t,2t) = (-3,-1,4) + (r,r,4r) \
(-3+t, 3 -t, 8 + 2t) = (-3 + r, -1 + r, 4+4r)$
soft zealotBOT
Merineth
verbal steppe
Isn't this how it works?
tranquil pine
Exactly yeah
verbal steppe
Now we can conclude that t ≠ r
tranquil pine
Like they can be equal but not always so in beginning we didn't take them equal here they are equal on solving equations like you will get t and r as 2
verbal steppe
But what does this tell us? If t is 1 and r is 1 then both x are the same however
3-1 = 2
-1 + 1 = 0
Their y will not be the same
However their z will
tranquil pine
Yes that's why we have to take any two equations by them we have to solve for t and r and then make sure that they satisfy 3rd equation
If they don't then we wilo conclude that lines doesn't intersect
verbal steppe
I'm not sure what you mean
tranquil pine
Oh like if you solve any equations for example take
-3+t=-3+r and 3-t=-1+r
Now from here we got t and r as 2 right
Then we will see if these values of t and r satisfy in 3rd equation if it does then we are done
tranquil pine
However their z will
Btw on putting 1 ,1 in t and r respectively doesnt make z equal
verbal steppe
Yeah mb
tranquil pine
Np
verbal steppe
This part is very tricky
tranquil pine
Yeah actually its bit confusing
verbal steppe
We just proved that my vector that we "guessed" fulfilled that is was perpendicular and passes the point but did not pass the vector
so we have to find a new vector that fulfills all three conditions at once
Does this result in a matrix of equations perhaps?
Using Gaus?
tranquil pine
Uhmm on putting t and r as 2 it does satisfy all three equations
tranquil pine
Yeah !!
Like if you solve 1st two equations you will get 2 and it satisfy 3rd equation too
verbal steppe
8+2t = 4+4r
verbal steppe
No it doesn't?
-3+t = -3+r
This one works for 2
ohgod you are right
How the hell did you solve that ? :O
$-3+t = -3+r \
3-t = -1+r \
8+2t = 4+4r$
soft zealotBOT
Merineth
verbal steppe
Did you do something like that?
tranquil pine
No it doesn't?
-3+t = -3+r
Yeahhh exactly now solve above 2 equation to find t and r and then put them in 3rd to see it satisfy 3rd or not
Mb I tagged wrong message
verbal steppe
Do you have a tips for solving such equations?
I see that the first equation gives us:
t = r
Do i just solve out r in the second equation and then substitute r with t in the 3rd equation?
tranquil pine
Yeah you can try eliminating one of variable
tranquil pine
Do i just solve out r in the second equation and then substitute r with t in the...
Yess that's what we need to do like from 1st you will know t = r then put t in place in 2nd then then you will know t and r
tranquil pine
so that means we have done all three conditions?
Yess
verbal steppe
L: (x,y,z) = (-3,-1,4) + r(1,1,4)
tranquil pine
Yeah now we have the line
tranquil pine
You are welcome!
buoyant plinth
Can someone help me ik I did something wrong but idk what, I need to solve for x intercepts by completing the square
final saddleBOT
Can someone help me ik I did something wrong but idk what, I need to solve for x...
drowsy sigil
u can complete the square after the first line
drowsy sigil
yh
buoyant plinth
oh wait
no its not
i have to multiply the 9/16 by 4
nvm nvm
i see where my problem is
thx
.close
final saddleBOT
final saddleBOT
Available help channel!
vagrant tundra
why did the t from the right side disappear here?
final saddleBOT
why did the t from the right side disappear here?
final tangle
is there more context?
is this cropped from a larger section of work
vagrant tundra
yes
this is a exercise from khan academy
this one has been buzzing me out for a while
final tangle
show full context
vagrant tundra
final tangle
they distributed the $\frac{1km}{6min}$ to the stuff in parentheses
soft zealotBOT
ℝαμΩℕωⅤ
final tangle
a(b+c) = ab + ac
vagrant tundra
i get how they did this but im asking where did the t go and why
like by what rule did they cancel it out or whatever was done
final tangle
subtracted 5km/(30min) * t from both sides,
combined like terms
similar to how you'd solve something like
9x = 5x + 2
tardy lark
I solved the limit on the left hand side of the equation but I'm unable to solve the limit on the right hand side
final saddleBOT
I solved the limit on the left hand side of the equation but I'm unable to solve...
soft zealotBOT
xd_senBugha
final saddleBOT
@tardy lark Has your question been resolved?
final saddleBOT
@tardy lark Has your question been resolved?
dawn thorn
Describe 4/x-3 as x approaches each value:
a) +∞ b)-∞ c)3+ d) 3-
final saddleBOT
Describe 4/x-3 as x approaches each value:
a) +∞ b)-∞ c)3+ d) 3-
dawn thorn
I don't know what this means or how to start
gentle barn
Are you familiar with limits?
dawn thorn
Are you familiar with limits?
Yes they're the asymps
dawn thorn
The denom increases
half geyser
The denom increases
and the fraction value decreases
same things will happen to the negative infinity . . but the difference will be that its negative
but something different happens when x tends towards 3
what happens here is that the difference between 3 and x will be so small
like just an explanation ( 4/2.99999999999 - 3 ) so this will lead to the fraction getting bigger
( the smaller the number on the denominator the bigger the fraction gets )
but this will be negative because the difference between x and 3 will always be negative
final saddleBOT
@dawn thorn Has your question been resolved?
dawn thorn
but something different happens when x tends towards 3
what happens here is tha...
As x reaches +∞, -∞ the fraction decreases, ok but what about 3+ 3-?
half geyser
As x reaches +∞, -∞ the fraction decreases, ok but what about 3+ 3-?
as i said for x approaches 3
the fraction value will increase, toward infinity
but its different with -3
i hope you read this
rotund radish
How do I do this
final saddleBOT
How do I do this
rotund radish
cold gorge
Do you mean "moment" of the force?
cold gorge
$\vec{\tau} = \vec{r} \cross \vec{F}$
soft zealotBOT
! What the hell am I doing here?
rotund radish
Alright so
rotund radish
Explain it to me as if I have brain damage
Please
cold gorge
**! What the hell am I doing here?**
Moment of force, or torque is represented by tau here.
All you need is that cross product in rhs
cold gorge
I'm glad you asked,
r would be the position vector of the point of action of force wrt the point about which you're considering the moment.
rotund radish
So the difference between the initial vector and the new vector?
cold gorge
I'm not sure what you're considering new and initial, but it is going to be a difference, yes.
Why not write it down and I tell you if you're doing it right?
rotund radish
Okay wait
Initial vector was the vector before F was applied
And the new vector is after F was applied right
Lemme write this down
Another question
What does it mean if a force is applied to a vector
The answer is root57 units btw
?
@cold gorge
rotund radish
Something
cold gorge
rotund radish
I applying force to a vector means adding them right?
cold gorge
You're treating F as some sort of displacement? But that's not true at all.
No.
NO
NO
rotund radish
What does force applying to a point imply
cold gorge
Pushing or pulling that point.
Force is a physical quantity.
Your weight would be a force applied by Earth on you.
(You're overthinking this shit) you said you knew what cross product meant, but you ended up adding some random vectors when asked for a cross product.
You should revisit some key fundamentals. Maybe what a vector is in the first place? Then position vector and stuff.
And finally, cross product.
rotund radish
You should revisit some key fundamentals. Maybe what a vector is in the first pl...
Yeah I should
But I need to finish this assessment in 2 hours
So can you like tell me to how to solve this
cold gorge
Two hours are more than enough to know what a vector is.
And r × F is what you have to do, that's about as much as I can tell you.
After this, you'd do the product and end up getting the answer? So it's just that really after that.
rotund radish
.close
final saddleBOT
final saddleBOT
Available help channel!
topaz yacht
final saddleBOT
topaz yacht
can I just let K be >= the expression?
why is the hint even there
(the work is for part a)
final saddleBOT
@topaz yacht Has your question been resolved?
eager leaf
can we define a new vector in R^infinty
s.t for every K in R there is m in N s.t X_m > k
and say that it is in R^infinity \ W?
tranquil pine
help
vivid walrus
!1c
final saddleBOT
Please stick to your channel.
stoic temple
can somebody help me
?
tranquil pine
I need help on how to solve this problem
because Im confused on what C is
because if c is nothing the right side is always bigger
i usually would do 100 - 35 then divide 12
I understand how to do it
although Im having a problem with the equality sign
stoic temple
because Im confused on what C is
c determines how much additional fee is paid
the question says at least which means
topaz yacht
because Im confused on what C is
you’re right
stoic temple
its minimum value should be = 100
and it can also be higher than(>) 100
so the sign is > or =
≥
tranquil pine
can you explain how you would solve the problem
step by step
and with the inequality signs
and I think that would be enough for me
stoic temple
can you explain how you would solve the problem
the fixed fee is 35
additional fee per class = $12
total additional fee = $12 X no of classes(C)
total fee = fixed fee + total additional
35 + 12C
she wants the to tal fee to be at least( have a value equal to or more than) $100
there fore the values that satisfy it are 35 + 12C ≥ 100
tranquil pine
she wants the to tal fee to be at least( have a value equal to or more than) $10...
may you show the statement from the problem with having a value equal to or more than 100
that shows what it says about having a value equal or more than 100 because that would help me understand
@stoic temple
stoic temple
may you show the statement from the problem with having a value equal to or more...
the third line said at least
at least means not less than
not less than is greater than or equal to
tranquil pine
so do you just flip the greater than or less than symbol
when it says atleast
@stoic temple
May you go over it all
and say how you switched the greater than sign or less than symbol and why you switched it in the equation
what caused you to switch it
final saddleBOT
@tranquil pine Has your question been resolved?
fossil shuttle
what did I do wrong
final saddleBOT
what did I do wrong
fossil shuttle
because isn't the x^2 supposed to be alone
marsh temple
What's the question?
fossil shuttle
solve each of the following quadratics by factoring
marsh temple
You can factor with a coefficient in front of the x^2
It'll just be in the form (x+a)(3x+b)
marsh temple
Indeed
fossil shuttle
of 5 and -2?
marsh temple
Your product needs to be scaled by the leading coefficient
So you need a product of 3*(-2)
marsh temple
I'm not sure what that means
marsh temple
You want two numbers that add to 5 and multiply to -6
fossil shuttle
-6 doesn't get divided by 2?
marsh temple
Why would it?
marsh temple
10 got divided by 2 because you're factoring out a 2
fossil shuttle
ohh
marsh temple
Your product needs to be scaled by the leading coefficient
After factoring, your constant term is -2, which must be adjusted thusly
marsh temple
You can divide both sides of your equation by 2 to remove it if you want
fossil shuttle
2 (3x^2+6)(x-1)
marsh temple
That gives you a leading term of 3x^3
fossil shuttle
😭
marsh temple
I think you need to stop skipping steps
fossil shuttle
what did i skip
marsh temple
You're starting with the equation 3x^2 + 5x - 2 = 0
Now you should decompose the 5x term using the two numbers you previously found
fossil shuttle
3(x^2+6-1) = 0
marsh temple
No
fossil shuttle
..
marsh temple
To decompose 5x means to rewrite it as 6x - 1x
jolly viper
final saddleBOT
jolly viper
im so confused
final saddleBOT
im so confused
jolly viper
my answer is - (e^x)/
ok idk how to explain it in writing
thats my answer
2 problems
not only is that none of the answer choices i see
but when i search up the derivative to the problem the answer it gives isnt any of the answers either
glad glacier
one of their answers is correct
jolly viper
hoq
how
oh and number 3
the answer choices have 1-u^2
instead of u^2-1
which is what the trig derivative of cscx is
<@&286206848099549185>
so I tried using right triangle method to further look into this problem
and i got
which still isnt equal to any of the answers
final saddleBOT
@jolly viper Has your question been resolved?
final saddleBOT
@jolly viper Has your question been resolved?
pseudo grove
Where did i go wrong at the end? There shouldnt be a e^-0 but i dont know how to get rid of it
final saddleBOT
Where did i go wrong at the end? There shouldnt be a e^-0 but i dont know how to...
rapid sky
e^-0 = e^0.
vital crag
Where did i go wrong at the end? There shouldnt be a e^-0 but i dont know how to...
1-0=?
pseudo grove
e^-0 = e^0.
Isnt e^0 = 1?
pseudo grove
No i mean like the answer sheet says i should get 2-1/e
vital crag
Yea so
pseudo grove
but rn im getting a -1 at the end too
vital crag
You messed up the sign on e^0
pseudo grove
You messed up the sign on e^0
Not sure what u mean by this
vital crag
Where did i go wrong at the end? There shouldnt be a e^-0 but i dont know how to...
You have a - on -e^0. It should be +e^0
pseudo grove
You have a - on -e^0. It should be +e^0
Isnt it supposed to be f(1) - f(0)?
vital crag
Yes. What's f(x)?
pseudo grove
Yes. What's f(x)?
e^-x
vital crag
Isnt it supposed to be f(1) - f(0)?
You need to evaluate this using the antiderivative
pseudo grove
Oh -e^-x?
vital crag
Yes
vital crag
,w diff -e^(-x)
soft zealotBOT
vital crag
final saddleBOT
final saddleBOT
Available help channel!
timber grail
final saddleBOT
timber grail
how do i do this?
final saddleBOT
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 was told that it's wrong.
4. I got an answer and would like my work checked.
5. I have a question about someone else's work/solution.
6. I have completed the problem and don't need help anymore. Thank you.
7. None of the above
3
final saddleBOT
Show your work, and if possible, explain where you are stuck.
loud sundial
.close
sweet summit
how insightful
trail mango
worldly vale
.close
final saddleBOT
sweet summit
whoah
final saddleBOT
Available help channel!
loud jasper
can someone help me with this i came up with the equation 2000-2x=sqrt2x^2 and solved for 2000-1000sqrt2 but that isnt an option
final saddleBOT
can someone help me with this i came up with the equation 2000-2x=sqrt2x^2 and s...
final tangle
careful with how you defined x
note that you defined x to be the leg of the isosceles triangle
and not the side length of the octogon
loud jasper
what do you mean?
final tangle
did you draw a diagram with this?
loud jasper
yeah
final tangle
show what you drew
loud jasper
final tangle
solved for 2000-1000sqrt2
is this the value of x?
final tangle
well you said that's the value you obtained
solving your equation lead you to
something = 2000-1000sqrt2
was that "something" x
loud jasper
yeah
final tangle
now look at your diagram
loud jasper
oo
final tangle
your x represents
the leg of the isosceles triangle
loud jasper
yeah
final tangle
so that's what you've calculated from that
loud jasper
so what equation would make sense to get the length of the octagon?
final tangle
well what's the equation initally you set up and why
why did you set
2000-2x equal to sqrt(2x^2)
where did those expressions come from?
loud jasper
i thought that 2x would be the kinda "excess" of one of the side lengths of the square and sqrt(2x^2) would be the hypotenuse of the triangle which is also the side length of the octagon
final tangle
yes
exactly
those are the lengths of the octogon
(in terms of x)
having found x
plug that in and you'll have the numerical value for the side length
loud jasper
o ok but is there like a seperate equation where i can find the side length directly?
final tangle
you could set it up differently
i.e. use your variable of choice to represent the side length of the octogon, instead of leg of the triangle
express the other lengths in terms of that
and solve like before, applying the same principles/idea
loud jasper
so what would the equation look like if i use x as the side length?
final tangle
determine the side legs of the triangles in terms of x
loud jasper
(2000-x)/2?
final tangle
yes
applying the same principles/idea
i.e. pythag for the hyp (a side of the oct)
and set the expressions for sides equal to each other
and solve for x
loud jasper
so what would the other side be?
final tangle
read above
applying the same principles/idea
i.e. pythag for the hyp (a side of the oct)
the same way you applied pythagoras before
loud jasper
o ok i think i get it thanks
final saddleBOT
@loud jasper Has your question been resolved?
wicked musk
Is it true that when there is a dot between a scalar and a vector, it is just scalar multiplication and not dot product? I'm confused because they're contradicticng each other.
final saddleBOT
Is it true that when there is a dot between a scalar and a vector, it is just sc...
royal gust
It could be. However, since the question is about "whether or not the operations make sense", I think they're trying to be very clear about the operations they're using
So every • is a dot product
wicked musk
In this question (letter c), is it dot product or scalar multiplication?
@royal gust
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@wicked musk Has your question been resolved?
whole halo
In this question (letter c), is it dot product or scalar multiplication?
the x means cross product
the . means dot product
wicked musk
how can I solve them?
whole halo
you should google what cross product is
wicked musk
you should google what `cross product` is
cross product is between vectors, right? but in letter d, I am getting a scalar quantity from (3u.v). How can I solve the cross product between a scalar and a vector?
whole halo
then presumably for (c) and (d), . and x can also stand in for scalar multiplication
sick roost
Is it true that when there is a dot between a scalar and a vector, it is just sc...
the coordinate definition of a dot product is undefined, as they must be the same length
likewise, the transpose definition
$$a\cdot b = a^{T}b=ab^{T}$$
is also undefined for the same reason
soft zealotBOT
Cycadellic
sick roost
a dot product is generally an inner product, which must always be a scalar
so the interpretation that a scalar dot a vector is a scalar product does not make much sense, and i feel it is ill defined to say they are the same
wicked musk
then should I just say that the letter c is impossible to compute?
sick roost
yeah
if we know that * is a dot, and a,b,c are vectors
a*b*c isnt computable
unless, i suppose, they are all singletons
sick roost
the coordinate definition of a dot product is undefined, as they must be the sam...
then this definition can work, but in general, no
also, most lin al people dont traditionally see singletons as vectors, so, its a pedantic point you shouldnt worry about
final saddleBOT
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unborn fern
Can someone help me get the answer for those two angles, I keep getting undefined for both of them
,rcw
final saddleBOT
Can someone help me get the answer for those two angles, I keep getting undefine...
soft zealotBOT
vital crag
Can someone help me get the answer for those two angles, I keep getting undefine...
Use law of cosines
pale oracle
but I get undefined at the end
undefined what
vital crag
but I get undefined at the end
!show
final saddleBOT
but I get undefined at the end
Show your work, and if possible, explain where you are stuck.
unborn fern
pale oracle
well, make sure you are operating in degrees for one thing
unborn fern
I have no idea what I did wrong
pale oracle
that's not the right formula
pale oracle
c^2 = a^2 + b^2 - 2ab*cos(C)
...or at least
not the right context
how is BAC = a^2???
vital crag
You solved for cosine incorrectly
pale oracle
find AC first.
vital crag
Don't skip algebraic steps
unborn fern
pale oracle
,rotate
soft zealotBOT
pale oracle
from A to C?
...yes.
unborn fern
I found it to be 9.9
pale oracle
I found it to be 9.9
this is correct
pale oracle
I recommend you use Law of Sines to find either one of the missing angles.
unborn fern
so cos law doesn't work for these?
pale oracle
but if I plugged in everything y is it still wrong
AC?
well, you rounded to one decimal place
do you need higher precision?
9.868576408
unborn fern
I don't think my school is that precise
pale oracle
that answer is correct.
unborn fern
hmmm
pale oracle
$\frac{\sin{(75)}}{9.868576408} = \frac{\sin{(A)}}{9} \rightarrow A = \arcsin{\left(\frac{9\sin{(75)}}{9.868576408}\right)}$
soft zealotBOT
Melvin Eugene Punymier
pale oracle
shouldn't be, if you did it right
unborn fern
pale oracle
I got 61.75239055 degrees
unborn fern
tru
pale oracle
but there's only 3 points on this one triangle
so it's unambiguous what we mean if we just say, "angle A"
pale oracle
wat
unborn fern
my other angle was right!
pale oracle
~neat~
unborn fern
I added them up to be 179.9
unborn fern
I'll try use law of cos again to redo it with all the decimal places
pale oracle
mmm...
you'll be faster if you only use that when you need it
law of sines is faster than law of cosines
unborn fern
do u know of any videos that are helpful for rational functions
pale oracle
no, I would just look for the topic if it were me
unborn fern
law of sines is faster than law of cosines
I never used law of sine before so I didn't try it for this guy
pale oracle
I never used law of sine before so I didn't try it for this guy
Law of Sines is introduced before Law of Cosines in school.
unborn fern
I haven't learned it in school
I only learned it yesterday
because I was sick half the year at school
pale oracle
ok, well pick that up too then
unborn fern
yup
pale oracle
it's useful and pretty easy
unborn fern
no, I would just look for the topic if it were me
what's that mean
unborn fern
I think law of cos is easier to rmbr
pale oracle
what's that mean
I would just google the topic and read the best page that came up
what do you need to know about rational functions
pale oracle
the asymptote rules are well-documented
unborn fern
I would just google the topic and read the best page that came up
but I'm in year 12 wouldn't the google show more advanced stuff
pale oracle
this is a VERY well-traveled subject
pale oracle
but I'm in year 12 wouldn't the google show more advanced stuff
no, you are at the bottom of the bottom
unborn fern
well travelled wuts that mean
pale oracle
you don't know what math is yet
unborn fern
pale oracle
YOU DON'T KNOW THE CRAZY MATH THAT'S OUT THERE!
unborn fern
pale oracle
🤓
unborn fern
is this stuff easy for u
pale oracle
yeah, so Calculus is "the top of the bottom" of Math imo
unborn fern
my maths
pale oracle
it's the least you need to know before you can explore the frontiers of Math
"frontiers" meaning areas of math that are still being established
unborn fern
I'm not gonna try any harder stuff I'm only doing this to get good in tests
maths is too hard
pale oracle
I'm not gonna try any harder stuff I'm only doing this to get good in tests
that's alright
unborn fern
this is the hardest level of maths in my school
pale oracle
is this stuff easy for u
the stuff we are talking about is
pale oracle
this is the hardest level of maths in my school
I don't think that it is
they probably at least offer a Modeling class
unborn fern
in my country there's either methods maths
or specialist maths
and this is specialist
like the hard math
pale oracle
Paul's Online Notes is the best resource I know for studying Calculus. He also has very good review sections
like this one
pale oracle
do u think graphing is hard
no
pale oracle
have you ever been tested for some kind of something
unborn fern
Paul's Online Notes is the best resource I know for studying Calculus. He also h...
okok I'll look at it when I'm done
unborn fern
have you ever been tested for some kind of something
huhh
pale oracle
Mathlexia or visual processing something or other
unborn fern
pale oracle
I'll take that as a "no"
unborn fern
what grade r u in
pale oracle
I'm almost 36.
unborn fern
r u a professor
unborn fern
I have a bachelors degree
in maths?
pale oracle
in whatever, but preferably Math
unborn fern
I came across a YouTuber
pale oracle
I came across a YouTuber
in the wild?
unborn fern
he teaches
every single maths
and each topic is only a few minutes
is this actually everything there is to learn
pale oracle
oh I remember him
unborn fern
is he good?
pale oracle
I used a video he made on geometry once
in a summer school class
I only saw a couple of videos but I thought so
I am not easy to please
or maybe I just screenshoted his diagrams?
I think I showed the video
unborn fern
but there only 150 ish videos
is maths really that short
around 1000minutes in total
,rcw
soft zealotBOT
soft zealotBOT
sour trail
- I've learned how to integrate equations and find it's antiderivatives in order to verify my solutions.
not realy a math question but sorry is this worded right or do i find the antiderivatives of diffrential equations to verify answers
final saddleBOT
1. I've learned how to integrate equations and find it's antiderivatives in orde...
vital crag
If you're working on a problem just show it
sour trail
i am not it is a discussion board post based on 3 videos
vital crag
Well just do some problems to test your knowledge then
sour trail
alright but is my wording right
vital crag
No
sour trail
can u tell me whats incorrect about iti
vital crag
Pick an actual problem to talk about
final saddleBOT
final saddleBOT
Available help channel!
unborn fern
guys I need help I dunno how to do that
final saddleBOT
guys I need help I dunno how to do that
hollow geyser
guys I need help I dunno how to do that
its 4
vital crag
easy stuff
Can you not spam other people's help channels
fleet maple
?
fleet maple
to use trig identities is a big hint
final saddleBOT
@unborn fern Has your question been resolved?
ornate knot
guys I need help I dunno how to do that
i sent this formula list yesterday , use them
final saddleBOT
@unborn fern Has your question been resolved?
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Available help channel!
proven chasm
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proven chasm
How do I go about the first part??
golden basin
convert the equation into the general equation of the function
golden basin
i dont remember coordinate that much, sorry man
proven chasm
np
final saddleBOT
@proven chasm Has your question been resolved?
final saddleBOT
@proven chasm Has your question been resolved?
final saddleBOT
@proven chasm Has your question been resolved?
modest birch
you could always just plug in y = 2 and then show that there are x_1, x_2 such that (x_1, 2) and (x_2, 2) are on the curve
but arguably changing it into the equation of a circle isn't a bad idea
final saddleBOT
@proven chasm Has your question been resolved?
green plank
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rancid prairie
LCM
hybrid heath
I believe they used a first order approximation of square roots (this could be incorrect)
green plank
I believe they used a first order approximation of square roots (this could be i...
what is that
is that binomial expansion
livid ice
I would guess you must have some kind of formula for that approximation
Notice it's all squiggly signs not equal signs
Each step is an approximation
livid ice
"Small angle approximation for cos x"
They are basically saying when x is sufficiently small you can say cos x is decently approximated by that formula
green plank
They are basically saying when x is sufficiently small you can say cos x is dece...
i get the cos x part
i mean the part after that
how did they do that
livid ice
It looks like another approximation formula
It's not equality so there's no algebra to make those equal
You must have been given a formula for approximating that, maybe related to binomial expansion form mentioned in that other step
green plank
You must have been given a formula for approximating that, maybe related to bino...
i think this
livid ice
The class youre in must have specifically gone over this method for approximating square root of a sum
green plank
they subbed in the 2 - x^2 /2 , got rid of the power and put a half at the front
how
livid ice
Because it's not equality
They are showing you a trick for approximating square roots
The expressions aren't equal to each other
floral nova
This is just the result of a taylor expansion of sqrt(1-x^2). If you've seen how to find the small angle approximation for cosine you should have seen this at some point
Write $\sqrt{1-x^2} = 1 - \frac{x^2}{2} + \mathcal{O}(x^4)$, then $\int_{0}^{0.4} \sqrt{1 - \left(\frac{x}{\sqrt{2}}\right)^{2}} dx \approx \int_0^{0.4} 1-\frac{1}{2} \frac{x^{2}}{2} dx$ which is what you have.
green plank
This is just the result of a taylor expansion of sqrt(1-x^2). If you've seen how...
i have never seen this , what part of maths is this?
soft zealotBOT
JessicaK
floral nova
Calculus
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Available help channel!
tranquil pine
,, \lim_{n\to\infty}\f{\s[n]{\f{n^n}{n!}}n^n +(n+\s[n]n)^n}{n^{n+\ff{\s[n]n}n}+n^n}
final saddleBOT
,, \lim_{n\to\infty}\f{\s[n]{\f{n^n}{n!}}n^n +(n+\s[n]n)^n}{n^{n+\ff{\s[n]n}n}+n...
soft zealotBOT
tranquil pine
how do you go about evaluating this?
the answer ends up being e, but this is really monstrous
gritty solar
someone gave a toddler a crayon
plush merlin
how do you go about evaluating this?
you probably dont go about solving it
gritty solar
first thought is to divide throughout by n^n
because that seems to be a common thing going on in all the terms
final saddleBOT
@tranquil pine Has your question been resolved?
faint locust
first thought is to divide throughout by n^n
Yep, then I guess you can split it up, the denominator will approach 1
The numerator will approach something + 1
,w n to infinity ((n^n)/(n!))^(1/n)
faint locust
the answer ends up being e, but this is really monstrous
Not e + 1?
plush merlin
no e
faint locust
Dividing everything through n^n, that square root in the numerator approaches e, the bracket approaches 1, the denominator 1
plush merlin
i used wolfram to evaluate it
faint locust
ok
If we exapnd (n + n^(1/n))^n, won't it be n^n + o(n^n)
And when we divide by n^n, everything o(n^n) -> 0
And n^n/n^n = 1
faint locust
,, \lim_{n\to\infty}\f{\s[n]{\f{n^n}{n!}}n^n +(n+\s[n]n)^n}{n^{n+\ff{\s[n]n}n}+n...
Is that /n only meant for the root
Or the entire exponent
plush merlin
idk what o(n^n) is but using binomial theorem will leave 1 so ig yes
tranquil pine
Is that /n only meant for the root
for the root
faint locust
idk what o(n^n) is but using binomial theorem will leave 1 so ig yes
I use o(n^n) to say n^(...) with ... lower than n
tranquil pine
i would have specified with parentheses otherwise
faint locust
idk what o(n^n) is but using binomial theorem will leave 1 so ig yes
Exactly
,w n^(n^(1/n)/n) for n to infinity
ocean lintel
primal sierra
For a list of 5 numbers, you can either add or subtract 1 from the first, 2 from the second, 3 from the third ... 5 from the last, or you can do the same, 1 from the second, 2 from the third, 3 from the fourth, 4 from the fifth, so on and so forth up to adding/subtracting 1 from the fifth. What is the minimum number of moves it takes for this list to become a list of 0's? (-2, 1, -7, -3, 8)
final saddleBOT
For a list of 5 numbers, you can either add or subtract 1 from the first, 2 from...
primal sierra
Right now, I have the answer of 25
I don't think that it is correct, and would like help in either verifying or disproving my answer.
primal sierra
there are 5 types of moves, and each can be an add or subtract, so there are a total of 10 moves
sturdy cypress
got it
primal sierra
the 5 types are 1 2 3 4 5, 0 1 2 3 4, 0 0 1 2 3, 0 0 0 1 2, and 0 0 0 0 1
each can be either added or subtracted
<@&286206848099549185>
Anyone?
sturdy cypress
if you focus on one number left to right i get 37 moves
so i don;t understand what you did
primal sierra
first we add the 1 2 3 4 5 spray twice, to get 0 5 -1 5 18
sturdy cypress
same
sturdy cypress
right i think that's the way, that's 37
primal sierra
I got 35?
sturdy cypress
hm
primal sierra
sturdy cypress
no i think this is the only way
primal sierra
how so?
sturdy cypress
there's no point using both + and − 1 2 3 4 5
we would only use one type
and nothing else affects the first number, so we know we would use 2 and 0 of those
now exclude those operations and the logic repeats for the second number
primal sierra
How about the list 1 3 -2 -7 6?
sturdy cypress
oh you mean calculate this faster
yeah there's maybe a shortcut i just meant you can;t use less ops
primal sierra
but is there faster?
no I mean less steps
ur explanation makes sense
so for this list, we would get 0 1 -5 1-11 0
0 0 -7 -14 -4
0 0 0 0 17
0 0 0 0 0
right?
for a total of 26 moves
@sturdy cypress
sturdy cypress
yeah but it's 1 after step 1
sturdy cypress
i get 27
sturdy cypress
well F
sturdy cypress
they wrong
primal sierra
they explained one question, although it was pretty trivial
it was 0 0 0 -1 3
they made it
0 0 0 -1 -2
and then
0 0 0 0 0
for 6 moves
but the order we do it in shouldn't matter
even if we did our method, working from the back, we still get 6
0 0 0 0 5
0 0 0 0 0
which is 6
argh
OH
IM STUPID
@sturdy cypress the list is 1 3 -2 -7 5
so we get
0 1 -5 -11 0
0 0 -7 -14 -4
0 0 0 0 17
0 0 0 0 0
for 26!
primal sierra
.close
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vivid spear
Probably an ignorant question but how do functions like $sin^2(x)$ work? what does it even mean to 'square' a trigonometric function?
final saddleBOT
Probably an ignorant question but how do functions like $sin^2(x)$ work? what do...
soft zealotBOT
Wapple
terse folio
sin(x) multiplied by sin(x) ?
vivid spear
sin(x) multiplied by sin(x) ?
stuff like this
terse folio
Oh
vivid spear
thats just a random screenshot from google images but thats what it is
terse folio
that comes from the identity sin^2x+cos^2x=1
vivid spear
but what does it even mean to square sin(x)?
how is it calculable? is it even a true function?
terse folio
but what does it even mean to square sin(x)?
multiply sin(x) by itself?
terse folio
how is it calculable? is it even a true function?
yes
rocky tusk
but what does it even mean to square sin(x)?
the same way you square any number
sinx gives you a number value between -1 and 1
vivid spear
multiply sin(x) by itself?
oh, so $f^2(x) \implies f(x)^2$?
soft zealotBOT
Wapple
vivid spear
yea it’s just the notation
lmao i thought it would be way more complex