“Assassin” is a real-life game in which a group of players all try individually to find and touch (or “kill”) one other player. You can use a linked list to represent this “kill ring” of players in the game:

If a “kill” is made, the ring adjusts by removing that person from the list. For example, the following occurs if Sally kills Jim:

Write a program that models a game of Assassin. The game reads the names of the initial kill ring from a file and puts them into a linked list in random order. Then the game repeatedly prompts for the name of a person that has been killed. The game continues until only one player remains and is declared the winner. The program should also have methods for printing the current contents of the kill ring and printing a “graveyard” of all players who have been killed.

Prove the given set of functions forms a fundamental set of solutions to the corresponding homogeneous equation. Then determine $g(x)$ so that $y_P$ is a solution to the given differential equation. Finally, for this $g(x)$, determine the solution to the initial value problem for the given initial conditions. $\left\{x, x^2\right\},(1 / 2) x^2 y^{\prime \prime}-x y^{\prime}+y=g(x), y_P=e^x$; $y(1)=1, y^{\prime}(1)=0$

Jung is editing a digital photograph that is 640 pixels wide and 480 pixels high on his computer monitor. a. If Jung zooms in on the photo on his monitor 150%, what are the dimensions of the image? b. Suppose that Jung is going to use the photograph in a design and wants the image to be 32 pixels wide. What scale factor should he use? c. Jung resizes the photograph so it is 600 pixels high. What scale factor did he use?

Find an SVD of each matrix in the below Exercise.

$$\left[\begin{array}{rr}-3 & 0 \\ 0 & -2\end{array}\right]$$

Find an SVD of each matrix in the below Exercise.

$$\left[\begin{array}{rr}-2 & 0 \\ 0 & 0\end{array}\right]$$

Consider the initial value problem y''+y=fk(t),y(0)=0,y'(0)=0,where fk(t)=[u4−k(t)−u4+k(t)]/2k with 0<k≤1.(a) Find the solution y=φ(t,k)of the initial value problem.(b) Calculate lim k→0+φ(t,k) from the solution found in part (a).(c) Observe that lim k→0+fk(t)=δ(t−4). Find the solutionφ0(t)of the given initial value problem with fk(t)replaced byδ(t−4). Is it true thatφ0(t)=lim k→0+φ(t,k)?(d) Plotφ(t,1/2),φ(t,1/4), andφ0(t)on the same axes. Describe the relation betweenφ(t,k)andφ0(t).

(a) Find the solution of the given initial value problem.(b) Draw a graph of the solution.y''+2y'+3y=sint+δ(t−3π);y(0)=0,y'(0)=0

Bob works at a construction company. He has an equally likely chance to be assigned to work for different crews every day. He can be assigned to work on crews building apartments, condominiums, or houses. If he works 18 days a month, how many times should he expect to be assigned to the house crew? See the earlier example.

Explain the meaning of each of the following terms. geography, hemisphere, equator, prime meridian, latitude, longitude.

Prove $y_1$ is a solution to the homogeneous equation. Then use the reduction of order technique introduced in subsection $4.2 .2$ to determine a second linearly independent solution.

$$(1+x) y^{\prime \prime}+x y^{\prime}-y=0, y_1=e^{-x}$$

use the method of variation of parameters to find a particular solution of the given differential equation. y” − 5y' + 6y = 2et

Solve each system of equations algebraically.

$$\begin{array}{l} x+4 y=3 \\ 2 x-3 y=17 \end{array}$$

For each of the following cases, either explain why the case cannot occur or give an example to show how it can.

(a). Two negative numbers whose product is greater than both numbers

(b). Two negative numbers whose product is in between the two numbers

($c$). Two negative numbers whose product is less than both numbers

The characteristic polynomial of the differential equation has distinct real roots. Find the general solution of the differential equation.

$$y^{\prime \prime}+8 y^{\prime}=0$$