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1. matrix, is that the definition of
R
?
2. So again,
r
here basically is just the borrowing rate.
3. in polar coordinates
r
, theta.
4. move the
r
over there than to first solve for
r
and theta as
5. derivatives either in terms of x, y or in terms of
r
and theta
6. velocity vector. So, this is v cross v plus
r
7. natural log of g of
r
.
8. minus
r
squared sine squared theta, I want to simplify that.
9. the length of the cross products
r
cross v measures the rate at
10. SENATOR JOHN KENNEDY (
R
-LA): State or federal court? MATTHEW PETERSEN: I have not.
11. positive. So, it's
r
dr d theta.
12. evaluate it at
r
equals 0, you get the expected value of Z.
13. The "d", "
r
", and the "w", they're consonants, and the "e" is a vowel.
14. But I know that North American accents usually pronounce the
R
anyway at the end of words.
15. in fact, that the length of this cross product
r
cross v
16.
R
is pronounced as err.
17. y sub theta is
r
cosine. And now, if we compute this
18. delta
r
, is approximately equal to v
19. Sometimes at a certain value of
r
, it stops existing.
20. And I haven't quite figured I how to put an
r
in the front
21. theta). And, that simplifies to
r
.
22. If I take a line of slope gamma prime of
r
, that's a
23. revenues are going into
R
&D compared to
24. calculation about a derivative of the cross-product
R
cross v.
25. But one of them,
r
is bigger than 0.
26. so if you multiply
R
with itself: I'll let you do it as an
27. This is mu sub X of
r
.
28. So, let me do it underneath. So, we said x sub
r
is cosine
29. SENATOR JOHN KENNEDY (
R
-LA): Can you tell me what the Daubert standard is?
30. e squared over 4 pi, epsilon nought
r
squared.
31. How did I come up with this
R
? Well, secretly,
32. If you take that product of terms g to the
r
to the n-th
33. function negative. Well, sine is y/
r
right. So when you start with the initial rotation
34. linear. Don't look for just a high '
r
', either a high
r
value or an
r
squared value to validate
35.
R
is err.
36. picture where
r
and theta are the Cartesian coordinates,
37. And this guy is in all of
R
.
38. And, when we multiply
R
by j, we get this guy here.
39. gX of
r
exists for
r
less than alpha in this case.
40.
r
equals
r
of t, that stays inside,
41. switched to polar coordinates, you know, setting u equals
r
42. If you take the second derivative evaluated at
r
43. Namely, it's e to the
r
.
44. and
r
^n sin(n*theta).
45. theta; x sub theta is negative
r
sine
46. If I'm going from here to here, then delta
r
is going to be
47. Minus g of
r
and g prime of
r
.
48. need to think for a second about what happens when
r
goes
49. determinant, we'll get (
r
cosine squared theta) (
r
sine squared
50. divided by g of
r
squared.
51. So, this is the same
r
cross a equals zero,
52. And y is
r
*sin(theta).
53. I have
r
squared cos squared theta,
54. I have two, I've got an
r
squared, again,
55. to n to the
r
minus 1 times alpha to the n
56. And, that's also the position vector
r
of t.
57. So, we have
r
at time t. We have
r
at time t plus delta
58. The number "three", t-h-
r
-e-e is often pronounced
59. theta. But, remember that
r
is always
60. the subspaces of
R
^3.
61. that is x equals
r
cosine theta and y equals
r
sine theta.
62. Partial x over partial
r
is just cosine theta.
63. can describe the force as a function of
r
.
64. thing. You get two
R
dot dR/dt,
65. So we like to find the
r
for which this bound is tightest.
66. is first derivative of
r
divided by g of
r
.
67. dx dy we could switch it to
r
dr d theta.
68. delta s. And now, delta
r
should be
69. So it's gX or
r
to the n-th power.
70. length then
R
dot
R
is also constant.
71. this permittivity constant times the distance,
r
, squared.
72. your
r
value is to 1 or -1, the stronger your linear relationship. But that is not a test
73. delta
r
. The length of this vector is
74. So what's the smallest subspace of
R
^3?
75. thank you. Ik ben ook goed, dank u. Pardon. is pronounced as Pardon.
R
is pronounced
76. So, dx dy is, well, absolute value of
r
dr d
77. at
r
equals 0.
78. So it's got an
r
squared, and it's got
79. cross product
r
cross v? Well, it's the direction that's
80. we just have g prime of
r
squared
81. to reduce to that? Well, if
R
is constant in
82. coordinates at the origin,
r
is zero but theta can be
83. So, you're asking about whether the delta
r
is actually strictly
84. linearity. I am saying high, but
r
can be from negative one to positive one. The closer
85. Right? With our bases being smaller—well... the absolute value of
r
—being less than
86. Whereas in Australian English, we wouldn't pronounce the
R
at the ends of words.
87. g sub Z of
r
is the expected value of e to the rZ.
88.
r
. The other one is v delta t.
89. as err in Dutch err with a thrill so it's Pardon. Pardon. Pardon. with double
r
, rrr.
90. setting x equals
r
cosine theta, y equals
r
sine theta.
91. they put the '
r
on the end.
92. partial
r
? And that is going to be,
93. So this is now
r
squared cos squared theta, right?
94. And we evaluate this at
r
equals 0.
95.
r
, and v delta t, magnitude of the cross product.
96. The supremum over t, again in
R
, so this guy is
97. we can write this as dr/dt cross v plus
r
cross dv/dt,
98. SENATOR JOHN KENNEDY (
R
-LA): Criminal? MATTHEW PETERSEN: No.
99. Depending on your native language, this may sound like an
R
to you.
100. Actually, delta
r
is not strictly tangent to anything.
101. Python,
R
, all other would have those.
102. the rejection region
r
psi, which
103. even registers when it comes to
R
&D as
104. If
r
is less than a, the whole thing goes to 0.
105. from xy to
r
theta. But, we can also switch from
r
106. equals a constant. OK,
r
cross v has constant
107. Minus, this is
r
squared sine squared theta.
108. Also we have
R
-insertion.
109. If
r
is bigger than alpha, this exponent is bigger than
110. I mean, this inequality here is true for all
r
, for all
r
111.
r
over g of
r
squared.
112. I have 2r*cos(theta) times
r
*sin(theta).
113. And then we have
r
, which is simply the distance between
114. There there's no
R
there unless the next word begins with a vowel.
115. it means d by dt of
r
cross v is the zero vector.
116. If I tell you
R
cross v is constant, you might be expected
117. delta
r
, which is the change in position vector a various
118.
r
minus
r
times a?
119. If I switch from x, y, rectangular coordinates, to
r
,
120. instead of using x and y, you will use coordinates
r
,
121. and it is repeated
r
times-- so x minus alpha to the
r
-th power
122. Its second derivative of other values or
r
you have to
123. I look at some particular value of
r
.
124. y with respect to
r
, theta.
125. the case. Well, if I do
R
times i hat --
126. (-x,-y). And if I applied
R
four times,
127. y, in fact, you can plug these in as a function of
r
and theta.
128.
R
&D whether it's pharmaceuticals or the
129. dr/ds means position vector
r
means you have the origin,
130. y/
r
. The inverse trig function therefore you are putting in the y/
r
and you are looking
131. Now, it says show that if
R
has constant length then they are
132. vector
R
. And it asks you how do we find
133. For example, if you compute
R
squared,
134. This is gamma of
r
.
135. times cos(theta), v equals
r
times sin(theta),
136. that
r
cross v equals a constant vector, OK?
137. single form because we are saying
r
cross v has constant
138. So, we'll multiply that by just pi,
r
squared, to get
139. And when
r
is greater than 0 for this one and less than 0
140. Much like it's sister subreddits,
r
/Let'sNotMeet's stories vary from creepy to downright terrifying,
141. It's gX to the n of
r
times e to the minus rna.
142. we have a position vector,
r
, that will depend on some
143. As long as these encounters continue to happen,
r
/Let'sNotMeet will continue to grow, stories
144. Some people have difficulty with some of the letters, like "n" and "
r
".
145. is we assume length
R
is constant.
146. SENATOR JOHN KENNEDY (
R
-LA): Bench? MATTHEW PETERSEN: No.
147. Its second derivative at
r
equals 0 is pretty easy.
148. partial
r
plus partial f over partial y times partial y over
149. tell your class about
R
. And others.
150. (Begin video segment.) SENATOR JOHN KENNEDY (
R
-LA): Have you ever tried a jury trial?
151. And
R
. I've just had a email saying,
152. SENATOR JOHN KENNEDY (
R
-LA): Civil? MATTHEW PETERSEN: No.
153. theta. y sub
r
is sine;
154. So some examples of
R
insertion.
155. Sorry, so it's approximately equal to
r
cross v magnitude
156. If you take the derivative of this with respect to
r
,
157. It also applies for dot-product. That is dR by dt dot
R
plus
R
158. the length of delta
r
is not exactly the length along the
159. It is
r
^n -- for the nth pair,
r
^n times cos(n*theta),
160.
R
/Let'sNotMeet: On par with
r
/Creepy and
r
/NoSleep,
r
/Let'sNotMeet is a subreddit containing user-submitted
161. gX of
r
exists for
r
less than alpha in this case.
162. That means
R
is perpendicular to v.
163. This guy here is exactly what we get when we multiply
R
by i.
164. The derivative with respect to
r
of the logarithm of g of
r
165. For example, an "n" or an "
r
", if you don't make it properly it could look like another
166. And the other one,
r
is less than 0.
167. And this is where the sup for t in
R
of Fn of t.
168. We're not looking at what goes on around
r
equals 0.
169. So if gX of
r
is e to the rX, then e to the e to the
r
Sn--
170. theta, polar coordinates, x is
r
*cos(theta).
171. press
R
to run, ooh
172. Here we have AW as in LAW vowel followed by the
R
consonant.
173. The derivative with respect to
r
of the logarithm of g of
r
174. But now, it's become
r
, or anything.
175. na is this e to the n times gamma x of
r
minus ra.
176. It's true for all
r
for which this moment-generating
177. Partial x over partial theta is negative
r
sine theta.
178. e-s-c-
r
-i-m-a
179. STUDENT QUESTION: when you said
R
equals that
180. And, delta
r
is approximately T times delta s.
181. Usually, I say it as "fo(
r
)".
182. contains
r
and v. So, what's the direction of the
183. Well, if you optimize it over
r
, It's essentially
184. and I want to express it in terms of the polar coordinates
r
185. Well, if you optimize it over
r
, It's essentially
186. If
r
is bigger than alpha, this exponent is bigger than
187. And the area is going to be pi
r
squared.
188. And so that means d by dt of
R
dot
R
is zero.
189. when
r
changes with time.
190. SENATOR JOHN KENNEDY (
R
-LA): OK. MATTHEW PETERSEN: Yes.
191. the derivative of
R
dot
R
? Well, remember we have a
192.
r
value (the absolute value of
r
)... less than 1. And so, this geometric series that
193. terms of
r
. So, this would let us switch
194. Well, we'll have a small change. Let me call that vector delta
r
195. Yeah, tell me all the subspaces of
R
^3.
196. So now we can solve this for
r
, the radius,
197. equals (1 over
r
) times dx dy. And then we'd have,
198.
r
equals 2, so I have alpha to the n and n alpha to the n.
199. And the area is going to be pi
r
squared.
200. That is what it says,
R
has constant length.
201. And so that means
R
dot v is zero.
202.
R
^4 would be identity. OK, questions?
203. we just have g prime of
r
squared
204. I heard", so the vowel sound changes: "ear", "er": "hear", "heard", it's spelt "h-e-a-
r
"
205. So
r
here is the risk-free interest rate.
206. partial
r
. That will end up being actually
207. which is somewhere out there, and the vector
r
is here.
208. of course, to replace
r
by its formula in xy coordinates.
209.
R
^3, three-dimensional space.
210. Gamma of
r
at 0, it's the log of the moment-generating
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