Express the following propositions in symbolic form, and identify the principal connective: i.Either Karen is studying computing and Ketsi is not studying mathematics, or Ketsi is studying mathematics. ii.It is not the case case that if it is sunny then i will carry an umbrella.

let us also assign to n the orientation in the direction of increasing x value. then compute surface integral over n of the vector field k on R^3 plane given by h(x,y,z)= (y,0,z)_(x,y,z)

A car travels at 108 kph from A to B for t seconds, applies the brakes for 4 seconds between B and C to give the car a constant deceleration and a speed of 72 kph at C, and finally travels at this speed from C to D, also for t seconds. If the total horizontal distance from A to D is 3100 m, determine the distance between A and B.

The popularity of fads and fashions often decays exponentially. One example is ticket sales for a popular movie. The table shows the total money spent per weekend on tickets in the United States and Canada for the movie The Da Vinci Code.
$\begin{array}{cc}\text{Weekend in 2006}& \text{Ticket Sales (millions)}\\ \text{May 19—May 21}& \text{77.1}\\ \text{May 26—May 28}& \text{34.0}\\ \text{June 2—June 4}& \text{18.6}\\ \text{June 9—June 11}& \text{10.4}\\ \text{June 16—June 18}& \text{5.3}\\ \text{June 23—June 25}& \text{4.1}\\ \text{June 30—July 2}& \text{2.3}\end{array}$
a) Use a graphing calculator to create a scatter plot of the data.

b) Draw a quadratic curve of best fit. - Press STAT, cursor over to display the CALC menu, and select 5:QuadReg. - Press VARS, and cursor over to display the Y-VARS menu. Select 1:Function and then select 1:Y1. - Press ENTER to get the QuadReg screen, and press GRAPH.

c) Draw an exponential curve of best fit. - Press STAT, cursor over to display the CALC menu, and select 0:ExpReg. - Press VARS, and cursor over to display the Y-VARS menu. Select 1:Function and then select 2:Y2. - Press ENTER to get the ExpReg screen, and press GRAPH.

d) Examine the two curves. Which curve of best fit best models the data?