We now summarize some important strategies that you have been using and will need to apply when confronting applied problems in this and future courses in mathematics: • Read and re-read

the problem statement until you have identified the relevant quantities in the situation and can visualize how they are related. Make note of which two varying quantities are to be related. • Define variables to represent the varying quantities to be related. • Represent the relevant fixed and varying quantities in a drawing-for example, the fixed length of a race using a solid line, Usain's distance from the starting line using a dashed vector with an arrow on one end, etc. If distances, heights, areas, etc. are defined in terms of some elapsed time t, express these quantities in terms of t--for example, if Benny walks at a constant speed of 2 meters per second from his front door, his distance from his front door is 2t meters. (As t, the number of seconds since he started walking, varies, so does 2t, Benny's distance from his front door in meters.) Remember that when expressing a dependent quantity's value, r (the remaining length of a burning candle in inches). "in terms of another (independent) quantity's value, t (the time elapsed in hours since the candle started burning), our goal is to write an expression using the independent variable, t, that computes the value of the dependent variable, r. As an example, let's consider the situation when the original height of the candle is 18 inches tall and the candle burns at a constant rate of 3 inches per hour. original length barned length 18 3t remaining length in terms of burned length After constructing this expression, we can assign its value to the dependent variable, r, and write: r = 18 - 3t When building the expression using (in terms of) t, we use operations to combine t with constant quantities (e.g., fixed distances or fixed rates) so that the new expression represents the value of r./nDetermine if the following statements are true or false. a. Select an answer b. Select an answer The values of the independent and dependent quantities in a formula vary together. When defining m in terms of n, our goal is to write an expression using n that determines the value of m. c. Select an answer Making a drawing of the quantities described in a problem context is often necessary for visualizing how quantities described in the problem are related. d. Select an answer When asked to define the values of the dependent quantity, y, "in terms of the values of the independent quantity, z, our goal is to construct an expression using the independent variable, z, that we can use to determine (or represent) the value of the dependent (or output) variable, y. Submit