# At a Glance - Constants

Constants are quantities that do not change. They're like crotchety old curmudgeons, forever stuck in their ways.

• 3, 57, 299, 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're given. Joey makes d · t dollars in a day, since that's his pay 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 = mc2. If E and m are the energy and mass of an object (depending on what the object is), and c is the speed of light, which letter represents a constant?

#### 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.