For the following exercises, the rectangular coordinates ( x , y , z ) of a point are given. Find the spherical coordinates ( ρ , θ , φ ) of the paint. Express the measure of the angles in degrees rounded to the meanest integer. 390. ( − 1 , 2 , 1 )
For the following exercises, the rectangular coordinates ( x , y , z ) of a point are given. Find the spherical coordinates ( ρ , θ , φ ) of the paint. Express the measure of the angles in degrees rounded to the meanest integer. 390. ( − 1 , 2 , 1 )
For the following exercises, the rectangular coordinates
(
x
,
y
,
z
)
of a point are given. Find the spherical coordinates
(
ρ
,
θ
,
φ
)
of the paint. Express the measure of the angles in degrees rounded to the meanest integer.
1- Let A = {A1, A2, ...), in which A, A, = 0, when i j.
a) Is A a π-system? If not, which element(s) should be added to A to become a π-system?
b) Prove that σ(A) consists of the finite or countable unions of elements of A; i.c., A E σ(A) if and
only if there exists finite or countable sequence {n} such that A = U₁An (Hint: Let F be such
class; prove that F is a σ-filed containing A.)
c) Let p ≥ 0 be a sequence of non-negative real numbers with Σip₁ = 1. Using p₁'s, how do you
construct a probability measure on σ(A)? (Hint: use extension theorem.)
2- Construct an example for which P(lim sup A,) = 1 and P(lim inf An) = 0.
3. Let
f(z) =
sin (22) + cos (T2)
2(22+1)(z+1)
Compute f(z)dz over each of the contours/closed curves C1, C2, C3 and C4 shown
below.
Don't use any Al tool
Don't send the same
previous answer that
was Al generated
L
10
-c
x
show ur answer
pe
n and paper then take
Send ur answer in pe
n and paper don't rep
uted ur self down
PLEASE SOLVE STEP BY STEP WITHOUT ARTIFICIAL INTELLIGENCE OR CHATGPT
SOLVE BY HAND STEP BY STEP
4.- A beer at an unknown temperature is introduced into a refrigerator that has a constant temperature of 1°C. After 20 minutes, the temperature of the beer is 10°C, and after 40 minutes, the temperature of the beer is 6°C.
a) Determine the temperature at which the beer was placed inside the refrigerator.b) How long will it take for the beer to reach 2°C?
Elementary Statistics: Picturing the World (7th Edition)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, subject and related others by exploring similar questions and additional content below.