EXAMPLE 1 Useful driving math Suppose you are driving along a highway at a con- stant speed and you record the number of seconds it takes to travel between two consecu- tive mile markers. If it takes 60 seconds to travel one mile, then your average speed is 1 mi/60 s or 60 mi/hr. Now suppose you travel one mile in 60 + x seconds; for ex- ample, if it takes 62 seconds, then x = 2, and if it takes 57 seconds, then x = -3. In this case, your average speed over one mile is 1 mi/(60 + x) s. Because there are 3600 s in 1 hr, the function 3600 s(x) 3600(60 + x)-1 60 + x gives your average speed in mi/hr if you travel one mile in x seconds more or less than 60 seconds. For example, if you travel one mile in 62 seconds, then x = 2 and your aver- age speed is s(2) - 58.06 mi/hr. If you travel one mile in 57 seconds, then x = -3 and your average speed is s(-3) = 63.16 mi/hr. Because you don't want to use a calculator while driving, you need an easy approximation to this function. Use linear approximation to derive such a formula.

EXAMPLE 1 Useful driving math Suppose you are driving along a highway at a con- stant speed and you record the number of seconds it takes to travel between two consecu- tive mile markers. If it takes 60 seconds to travel one mile, then your average speed is 1 mi/60 s or 60 mi/hr. Now suppose you travel one mile in 60 + x seconds; for ex- ample, if it takes 62 seconds, then x = 2, and if it takes 57 seconds, then x = -3. In this case, your average speed over one mile is 1 mi/(60 + x) s. Because there are 3600 s in 1 hr, the function 3600 s(x) 3600(60 + x)-1 60 + x gives your average speed in mi/hr if you travel one mile in x seconds more or less than 60 seconds. For example, if you travel one mile in 62 seconds, then x = 2 and your aver- age speed is s(2) - 58.06 mi/hr. If you travel one mile in 57 seconds, then x = -3 and your average speed is s(-3) = 63.16 mi/hr. Because you don't want to use a calculator while driving, you need an easy approximation to this function. Use linear approximation to derive such a formula.

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter7: Conic Sections And Quadratic Systems

Section7.1: The Circle And The Parabola

Problem 3SC

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