Question

2.2 inches per hour. When values are .1 The length of a burning candle I (in inches) decreases at a constant rate of the candle has been burning for 3.5 hours it is 8.3 inches long. These co-occurring represented by the point (3.5, 8.3) on the graph. a. Represen t "an increase in the time spent burning of 2 hours" as a vector from the given point on the graph what is the value of Δ/ (in inches) when the time spent burning increases b. Represent the change in the length of the candle, AI, that you found in part (b), as a vector from the given point on the graph Represent "a decrease in the time t spent burning of 1.8 hours" (that is, Ar1.8) as a vector from the given point on the graph. c. d. What is the value of Al (in inches) when the time spent burning is decreased by 1.8 hours (that is, Ar--1.8). Represent Al as a vector on the graph. Define a formula that relates the change in the length of the candle Δ/ in terms of the change in the number of hours the candle has been burning, Δ? e. Number of hours candie has been burming What was the original length of the candle (in inches) before it started burning? Explain how you determined this value and represent your reasoning on the graph f. On the axes in part (a), complete the graph that represents the length of the candle 1 (in inches) in terms of the number of hours spent burning t. Discuss in groups (or as a class) how r, 1, and are represented on this graph. Page 35 athnways Precalculus 2018 Carlson, Oehrtman, and Moore

Answer 1

Given that length of burning candle l decreases at constant rate of 2.2 inches per hour In coordinate from we writ eit as (t, l) Given point is (3.5, 8.3) (a) when there is increase in time spent burning of 2 hours, time would be 3.5 + 2 = 5.5 length decreases by 2.2 times 2 = 4.4 the form length 8.3 if would be 8.3 - 4.4 = 3.9 Delta = 4.4 point (5.5, 3.9) (b) we have change in length Delta I = 4.4 change in time Delta t = 2 (c) Given point (3.5, 8.3) Time is a decrease in time spent burning of 1.8 hours Delta t = -1.8 \r\n Time would be 3.5 - 1.8 = 1.7 d) Delta = -1.8 times 2.2 = -3.96 euro Delta = 2.2 Delta t (f) let I is initial length length is decreasing by 2.2 per hour thus in time 't' it would decrease by 2.2 t thus