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Additional resources for Precalculus: Mathematics for Calculus, 6th Edition
10 zero t 1 determine 18 while t ϭ zero, then „ ϭ four. 5102 ϩ 28 ϭ 28, so 10, 282 is at the line. whilst t ϭ 2, then „ ϭ four. 5122 ϩ 28 ϭ 37, so 12, 372 is at the line. the road that's made up our minds by way of those issues is proven in determine 18. (b) The slope is m ϭ four. five; it represents the speed of switch of water point with admire to time. which means the water point raises four. five toes in line with yr. The „-intercept is 28 and happens whilst t ϭ zero, so it represents the water point whilst the dam was once built. NOW attempt workout sixty nine instance 12 ■ Linear dating among Temperature and Elevation (a) As dry air strikes upward, it expands and cools. If the floor temperature is 20 ЊC and the temperature at a peak of one km is 10 ЊC, show the temperature T (in ЊC) when it comes to the peak h (in km). (Assume that the connection among T and h is linear. ) Copyright 2010 Cengage studying. All Rights Reserved. is probably not copied, scanned, or duplicated, in entire or partially. because of digital rights, a few 3rd social gathering content material will be suppressed from the book and/or eChapter(s). Editorial assessment has deemed that any suppressed content material doesn't materially impact the final studying event. Cengage studying reserves the proper to take away extra content material at any time if next rights regulations require it. part 1. 10 | traces a hundred and fifteen (b) Draw the graph of the linear equation. What does its slope signify? (c) what's the temperature at a top of two. five km? Temperature decreases with elevation answer (a) simply because we're assuming a linear courting among T and h, the equation needs to be of the shape T ϭ mh ϩ b the place m and b are constants. whilst h ϭ zero, we're on condition that T ϭ 20, so 20 ϭ m102 ϩ b b ϭ 20 hence, we now have T ϭ mh ϩ 20 whilst h ϭ 1, we've T ϭ 10, so 10 ϭ m112 ϩ 20 m ϭ 10 Ϫ 20 ϭ Ϫ10 T the mandatory expression is 20 T ϭ Ϫ10h ϩ 20 T=_10h+20 10 zero 1 three (b) The graph is sketched in determine 19. The slope is m ϭ Ϫ10ЊC/km, and this represents the speed of swap of temperature with appreciate to distance above the floor. So the temperature decreases 10ЊC in step with kilometer of peak. (c) At a top of h ϭ 2. five km the temperature is h T ϭ Ϫ1012. fifty two ϩ 20 ϭ Ϫ25 ϩ 20 ϭ Ϫ5 °C determine 19 ■ NOW attempt workout seventy three 1. 10 workouts recommendations four. (a) The slope of a horizontal line is of the horizontal line passing via 12, 32 is 1. we discover the “steepness,” or slope, of a line passing via issues by way of dividing the variation within the -coordinates of . The equation (b) The slope of a vertical line is . The equation of the vertical line passing via 12, 32 is those issues by means of the adaptation within the -coordinates. So the road passing in the course of the issues 10, 12 and 12, fifty two has slope . talents 2. A line has the equation y ϭ 3x ϩ 2. (a) This line has slope 5–12 . (b) Any line parallel to this line has slope . (c) Any line perpendicular to this line has slope three. The point-slope kind of the equation of the road with slope three passing during the aspect eleven, 22 is . . ■ locate the slope of the road via P and Q. five. P10, 02 , Q14, 22 6.