1. Set L = 5 mH, C = 8 µF, R = 0 Ω,
and Q...
1. Set L = 5 mH, C = 8 µF, R = 0 Ω,
and Q = 2E-6 C. Measure the maximum current through the circuit,
and the period of the oscillation.
Now increase the inductance of the inductor by 50% to 7.5 mH
calculate max current = ________ A period T =
________ s.
2. Reset to L = 5 mH, C = 8
µF, keep R = 0 Ω, and Q = 2E-6 C.
Keeping the charge on the...
2. Let A = {p, q, r, s}, B = {k, l, m, n}, and C...
2. Let A = {p, q, r, s}, B = {k, l, m, n}, and C = {u, v, w},
Define f : A→B by f(p) = m, f(q) = k, f(r) = l, and f(s) = n, and
define g : B→C by g(k) = v, g(l) = w, g(m) = u, and g(n) = w. Also
define h : A→C by h = g ◦ f. (a) Write out the values of h. (b) Why
is it that...
Question 1: Roll two fair dice. Then the sample space S is the
following.
S =...
Question 1: Roll two fair dice. Then the sample space S is the
following.
S =
(1,1) (1,2) (1,3) (1,4) (1,5) (1,6)
(2,1) (2,2) (2,3) (2,4) (2,5) (2,6)
(3,1) (3,2) (3,3) (3,4) (3,5) (3,6)
(4,1) (4,2) (4,3) (4,4) (4,5) (4,6)
(5,1) (5,2) (5,3) (5,4) (5,5) (5,6)
(6,1) (6,2) (6,3) (6,4) (6,5) (6,6)
Let E be the event that the sum of the dice is odd, let F be the
event that the first die lands on 1,
and let G...
2.
Let A, B, C be subsets of a universe U.
Let R ⊆ A ×...
2.
Let A, B, C be subsets of a universe U.
Let R ⊆ A × A and S ⊆ A × A be binary relations on
A.
i. If R is transitive, then R−1 is transitive.
ii. If R is reflexive or S is reflexive, then R ∪ S is
reflexive.
iii. If R is a function, then S ◦ R is a function.
iv. If S ◦ R is a function, then R is a function
Let S = {A, B, C, D, E, F, G, H, I, J} be the set...
Let S = {A, B, C, D, E, F, G, H, I, J} be the set consisting of
the following elements:
A = N, B = 2N , C = 2P(N) , D = [0, 1), E = ∅, F = Z × Z, G = {x
∈ N|x 2 + x < 2}, H = { 2 n 3 k |n, k ∈ N}, I = R \ Q, J =
R.
Consider the relation ∼ on S given...
2. Define a relation R on pairs of real numbers as follows: (a,
b)R(c, d) iff...
2. Define a relation R on pairs of real numbers as follows: (a,
b)R(c, d) iff either a < c or both a = c and b ≤ d. Is R a
partial order? Why or why not? If R is a partial order, draw a
diagram of some of its elements.
3. Define a relation R on integers as follows: mRn iff m + n is
even. Is R a partial order? Why or why not? If R is...
2. Consider a ten-sided die of which the sides display the
numbers 1, 2, 3, and...
2. Consider a ten-sided die of which the sides display the
numbers 1, 2, 3, and 4 according to this table:
side of die 1 2 3 4 5 6 7 8 9 10 number displayed 1 1 1 1 2 2 2 3 3
4
Rolling two such dice is an experiment with the sample space S =
(1,1) (1,2) (1,3) (1,4) (2,1) (2,2) (2,3) (2,4) (3,1)
(3,2) (3,3) (3,4) (4,1) (4,2) (4,3)...
Consider permutations of the 26-character lowercase alphabet
Σ={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.
In how many of these permutations do
a,b,c...
Consider permutations of the 26-character lowercase alphabet
Σ={a,b,c,d,e,f,g,h,i,j,k,l,m,n,o,p,q,r,s,t,u,v,w,x,y,z}.
In how many of these permutations do
a,b,c occur consecutively and in that
order?
In how many of these permutations does a appear before
b and b appear before c?