Author: Anonymous

Convert \(r=4\) from a polar to a cartesian equation.

Determine a unit vector pointing in the direction of \(\langle 3,4\rangle \).

What is the equation associated with the following ellipse?

Determine the symmetries of \(r=5\cos(3\theta)\).

Write \(sin(x+\frac{11\pi}{6}\) in terms of \(sin(x)\) and \(cos(x)\).

Determine the coordinates of the center of the hyperbola \(\frac{y^2}{49}-\frac{x^2}{32}=1\)

Below in the left-side column are a list of “checks” that balance out our branches of government.  Correctly identify the two branches that are associated with that “check” in the right-side column. 

Which device generally connects an internal network to external networks (such as from an Ethernet to the Internet)?

A router with IP address 138.76.29.7 manages a NAT translation table for a private network. The router uses ports starting from 8000. Each time a new connection is needed, it increments by one. For example, if a host in the private network with address 10.0.0.5:5000 sends a message to 132.239.8.45:80 then the entry in the NAT table would be filled in as shown in row (i) below. The next time the router will use 8001 as the port to establish a new connection and so on.  All connections are TCP. Complete the NAT Table for the following events:a) Host 10.0.0.101:6000 sends a message to 206.190.36.45:80 b) Host 10.0.0.200:7000 opens a TCP/HTTP session to 144.229.10.5:443. Private Address Private Port External Address External Port Transport Protocol (i) 10.0.0.5 5000 132.76.29.7 8000 TCP b) [Privateb] [PrivatePortb] [Externalb] [ExternalPortb] TCP c)  [Privatec] [PrivatePortc] [Externalc] [ExternalPortc] TCP/HTTPS  

A router with external IP address 203.45.67.89 performs NAT for a private network. The NAT algorithm always starts assigning internal‑host public ports at 9000 and increments by one for each new outbound TCP connection. For example, if a host in the private network with address 10.1.2.3:4000 sends a message to 217.21.3.11 : 443 on a TCP  connection, then the entry in the NAT table would be filled in as shown in row (i) below. Complete the NAT Table for the following events:a) host 10.1.2.10:4000 attempts to open a TCP connection to 198.51.100.5:80. b) host 10.1.2.3:4000 initiates a new TCP connection to 140.113.200:22 Private Address Private Port External Address External Port Transport Protocol (i) 10.1.2.3 4000 203.45.67.89 9000 TCP a) [Privatea] [PrivatePorta] [Externala] [ExternalPorta] TCP b)  [Privateb] [PrivatePortb] [Externalb] [ExternalPortb] TCP/HTTPS