Ambassadors from countries A, B, C, D, E, and F are to be seated around a circular conference table. Friendly relations among the various countries are described as follows: A has friendly relations with B and F. B has friendly relations with A, C, and E. C has friendly relations with B, D, E, and F. E has friendly relations with B, C, D, and F. All friendly relations are mutual. Using vertices to represent countries and edges to represent friendly relations, draw a graph that models the information given. Then use a Hamilton circuit to devise a seating arrangement around the table so that the ambassadors from B and E are seated next to each other, and each ambassador represents a country that has friendly relations with the countries represented by the ambassadors next to him or her.

Let R be the relation on the set {1, 2, 3, 4, 5} containing the ordered pairs (1, 3), (2, 4), (3, 1), (3, 5), (4, 3), (5, 1), (5, 2), and (5, 4). Find R^2 , R^3 , R^4 , R^5 , and R^6 .

Let A = {1, 2, 3, 4, 6}, and let R be the relation on A defined by “x divides y”, written as x|y. A. Write R as a set of ordered pairs.

determine whether each point lies on the graph of the equation. Equation y = x^3 - 3x + 2 Points (2, 0)

Evaluate the integral:

$$\int_{\pi / 4}^{\pi / 2}\left(1+e^{\cot \theta}\right) \csc ^{2} \theta d \theta$$

For 80% of lectures, Professor X arrives on time and starts lecturing with delay T=0. When Professor X is late, the starting time delay T is uniformly distributed between 0 and 300 seconds. Find the CDF and PDF of T.

Let R be the relation on the set {0, 1, 2, 3} containing the ordered pairs (0, 1), (1, 1), (1, 2), (2, 0), (2, 2), and (3, 0). Find the a) reflexive closure of R. b) symmetric closure of R.

Let $p$ and $q$ be distinct primes: Suppose that $H$ is a proper subset of the integers and H is a group under addition that contains exactly three elements of the set $\left\{p, p+q, p q, p^{q}, q^{p}\right\}$. Determine which of the following are the three elements in H.

a. $p q, p^{q}, q^{p}$.

b. $p+q, p q, p^{q}$.

c. $p, p+q, pq$.

d. $p, p^{q}, q^{p}$,

e. $p, p q, p^{q}$

Determine whether or not each of the following relations is a function. If a relation is a function, find its range. a) $\{(x, y) | x, y \in Z, y=x 2+7\},$ a relation from Z to Z b) $\{(v, y) | x_{t} y \in R, y 2=x),$ a relation from R to R c) $\left\{(v, y)\left|x_{t} y \in R, y=3 x+11\right.\right.,$ a relation from R to R d) $\{(x, y) | x, y \in Q, x 2+y 2=1\},$ a relation from Q to Q e) $\mathscr{R}$ is a relation from A to B where $|\mathrm{A}|=5,|\mathrm{B}|=6,$ and $|\mathscr{R}|=6,$

The laser in a DVD player emits light at a wavelength of 640 nm. The laser in a Blu-Ray player emits light at 405 nm. What are the photon energies of each laser, in eV?

How does the kinematic viscosity of (a) liquids and (b) gases vary with temperature?

Determine whether the relation R on the set of all people is reflexive, symmetric, antisymmetric, and/or transitive, where (a, b) ∈ R if and only if

a) a is taller than b.

b) a and b were born on the same day.

c) a has the same first name as b.

d) a and b have a common grandparent.

The uranium ores of the Athabasca Basin deposits of Saskatchewan, Canada, are unusually pure, containing up to 70, uranium oxides. Why doesn’t this uranium ore undergo an explosive chain reaction?

A projectile is fired at an inclination of $45^{\circ}$ to the horizontal, with a muzzle velocity of 100 feet per second.The height h of the projectile is modeled by $h(x)=\frac{-32 x^{2}}{(100)^{2}}+x$ where x is the horizontal distance of the projectile from the firing point. Find the maximum height of the projectile.