Exercise 1

Due Tuesday 9/6

This exercise is a quick math refresher to help you brush up on a few techniques we'll use during the first half of the semester.

1. Please graph the two equations below and solve algebraically for the (x,y) point where they intersect.  An asterisk is used to denote multiplication: 10*x is 10 times x. Be sure to label the axes, show the numerical value of each intercept, and indicate the slope of each line.

y = 200 - 10*x

x + 1 = 0.05*y

2. Make a copy of your graph from part (1) and draw a horizontal line through the intersection of the two equations. Then calculate the area of the triangle between the line you just drew and the y = 200 - 10*x equation, and to the right of the y-axis.

3. Graph the three equations below and solve algebraically for the coordinates of the three points where pairs of lines intersect. As in part (1), be sure to label the graph thoroughly.

y = 1000 - 10*x

y = 200 + 10*x

x = 20

4. Calculate the area of the triangle formed by the lines in part (3).

5. Variables y1 and y2 both depend on x as shown by the equations below. Please solve algebraically for the equation of a new variable, y3, which also depends on x and is equal to the sum of y1 and y2. Graph all three equations (one equation per graph) showing the intercepts and slope of each one.

y1 = 10 - x

y2 = 20 - 2*x

6. Finally, make a copy of the graphs you drew for part (5) and add the line below to each one. Then calculate the areas of the three triangles that lie below the equations from part (5), to the right of the x = 5 line, and above the x-axis. What do you notice about the area of the third triangle compared to the areas of the other two?

x = 5

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