At a Glance - Constants
Constants are quantities that do not change. They are like crotchety old curmudgeons who are stuck in their ways.
- 3, 57, 2^{99}, and are constants.
- π and e are also constants.
We can also use letters to represent unknown constant values.
Sample Problem
Joey gets d dollars for each odd job he does for his Grandpa. His Grandpa literally told him he would pay him d dollars for each job, probably so that old coot could stiff his grandson when it came time to tell him how much d is. No matter what the job is, Joey is paid the same. If Joey does t odd jobs for his Grandpa in a day, how much money does Joey make that day?
We don't have any amounts, and therefore, we can only answer this question in terms of the variables we are given. Joey makes d · t dollars in a day, since this amount is how much he is paid per job times the number of jobs he does. Because Joey gets paid the same amount per job, d will never change; therefore, we call it a constant. The varying quantity in this problem is t, since the number of jobs Joey does per day will vary depending on what his Grandpa forces—pardon us—asks him to do.
Example 1
Consider Einstein's famous equation, E = mc^{2}. What do you know about it? |
Exercise 1
Mortimer Poindexter spends two hours every day running away from bullies. Some of the bullies he encounters are faster than others; therefore, he sometimes needs to run faster than at other times, but he is always chased for exactly two hours. (These bullies stick to a very rigid schedule.) Let s be the speed Mortimer runs (in miles per hour) and let d be the distance he travels (in miles) as he tries to make his escape. Is s a constant or a variable?
Exercise 2
Mortimer Poindexter spends two hours every day running away from bullies. Some of the bullies he encounters are faster than others; therefore, he sometimes needs to run faster than at other times, but he is always chased for exactly two hours. (These bullies stick to a very rigid schedule.) Let s be the speed Mortimer runs (in miles per hour) and let d be the distance he travels (in miles) as he tries to make his escape. Is d a constant or a variable?
Exercise 3
Mortimer Poindexter spends two hours every day running away from bullies. Some of the bullies he encounters are faster than others; therefore, he sometimes needs to run faster than at other times, but he is always chased for exactly two hours. (These bullies stick to a very rigid schedule.) Let s be the speed Mortimer runs (in miles per hour) and let d be the distance he travels (in miles) as he tries to make his escape. Express in symbols the relationship between d and s.