Assignment 18
This material is simply an extension of previous assignments involving inequalities. Here's a simple example: Suppose I have two positive numbers, x and y. These numbers must be such that their sum less than 20, but greater than 10. There are four conditions being described here.
OK, can you use the language of mathematics and describe what has just been written. I hope so! You should realize that the set of points being described are in the first quadrant between the parallel lines y = -x + 20 and y = -x + 10. Let me emphasize that this is an AND situation. The four conditions constitute a compound conditional statement that will be true only if all four conditions must be satisfied. The point (3,-4) does not make the compound conditional statement true because the second stated condition fails. The point (2,6) does not make the compound conditional statement true because the fourth stated condition fails. The point (6,8) does satisfy the compound conditional statement, since all four stated conditions are true. MATH IS A LANGUAGE. LEARN IT, AND USE IT PROPERLY. MATH IS POWER.
Problem: Describe the region defined by the constraints x > 5 Solution (with communication): This is a rectangular region in the first quadrant with an area equal to 3x10 = 30 (square units). The rectangle is bordered by the lines x = 5, x = 8, y = 1, and y = 8. The border of the rectangle is not in the described region. Review thought: The constraints could be written 5 < x < 8 and 1 < y < 11. Problem: Construct a system of inequalities describing all points below the line containing (0,4) and (2,10), and above the line containing (3, -2) and (14, -2). Solution (with communication): The line containing (0,4) and (2,10) has slope = 3. The equation of this line is y = 3x + 4. The line containing (3,-2) and (14,-2) is horizontal. It has equation y = -2. The requested constraints are y < 3x + 4 |