Doubly ionized lithium Li2+ (Z = 3) and triply ionized beryllium
Be3+ (Z = 4) each emit a line spectrum. For a certain series of
lines in the lithium spectrum, the shortest wavelength is 40.5 nm.
For the same series of lines in the beryllium spectrum, what is the
shortest wavelength?
Find the probability of each of the following, if Z~N(μ = 0,σ =
1).
a) P(Z < -1.88)
b) P(Z > 1.51) =
c) P(-0.61 < Z < 1.54) =
d) P(| Z | >1.78) =
e) P(Z < -1.27) =
f) P(Z > 1.02) =
g) P(-0.69 < Z < 1.78) =
h) P(| Z | >1.86) =
Find the dual problem for each of the following primal
problems.
a): min z=6x1+8x2 st: 3x1+x2>=4 5x1+2x2>=7 x1,x2>=0
b): max z=8x1+3x2-2x3 st: x1-6x2+x3>=2 5x1+7x2-2x3=-4
x1<=0,x2<=0,x3 unrestricted
For each of the following functions, find the extreme value of z
(this can be either max or min), subject to a given constraint by
the method of direct substitution.
(a) z = xy, subject to the constraint x2 +
y2 = 16 (Note that there are four solutions.)
(b) z = 3x2 − 10xy + 12y2 , subject to the
constraint y = 20 − 1/2 x
(c) z = xy, subject to the constraint x − y =...
3. For each of the following relations on the set Z of integers,
determine if it is reflexive, symmetric, antisymmetric, or
transitive. On the basis of these properties, state whether or not
it is an equivalence relation or a partial order.
(a) R = {(a, b) ∈ Z 2 ∶ a 2 = b 2 }.
(b) S = {(a, b) ∈ Z 2 ∶ ∣a − b∣ ≤ 1}.
find the point lying on the intersection of the plane, x +
(1/4)y + (1/3)z = 0 and the sphere x 2 + y 2 + z 2 = 25 with the
largest z-coordinate. (x,y,z)=(_)