A Tank with a dimension of length (L) x width (B) x
height (H) of 4m x 2m x 2m is filled with 1m depth of water and
with oil to the fullest. Density of oil ρm= 801 kg/m3. The tank is
open.
1.Calculate and draw pressure distribution on tank wall
2.Calculate force on the length and width side of tank wall, also
on the bottom of the tank Given: ρwater= 1000 kg/m3 , g = 9,81
m/sec2
Problem 1. At time t = 0 the state of a particle in one dimension (1D) is given by ψ(x, 0) = A x 2 + a 2 Here a and A are some positive constants.
i) Find A
ii) Sketch the graph of the probability density of ψ
iii) Find the probability that the particle is within −a < x < a and − √ 2a < x < √ 2a
iv) Find the expectation value of the...
Let?:?2(R)⟶?1(R)bedefinedby?(?+?x+?x2)=(?+?)+(?−?)x,where
?, ?, ? are arbitrary constants.
a. DeterminethetransformationmatrixforT.(6pts)
b. Find the basis and the dimension of the Kernel of T. (10pts)
c. Find the basis and the dimension of the Range of T. (10pts)
d. Determine if T is one-to-one. (7pts)
e. DetermineifTisonto.(7pts)
Suppose the probability mass function of a random variable X is
given by
??x−1?pr(1−p)x−r, ifx=r,r+1,r+2,... f(x) = r−1
0, otherwise
If this is the case then we say X is distributed as a Negative
Binomial Random Variable with parameters r and p and we write X ∼
NegBin(r, p) (a) If we set r = 1, what distribution do we get? (b)
Explain what this random variable models and justify the formula.
(Hint: See Section 4.8.2 in Ross.) Math 241...
Question 1: Show that x = h + r cos t and y = k + r sin t
represents the equation of a circle.
Question 4: Find the area above the polar x-axis and enclosed by
r = 2−cos(θ).
Question 5: If r = f(θ) is a polar curve, find the slope of the
tangent line at a point (r0,θ0).