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2.38. Sketch the plots described below and calculate the equations for y(x) from the given information. The plots are all straight lines. Note that the given coordinates refer to abscissa and ordinate values, not x and y values. [The solution of Part (a) is given as an example.] a. A plot of In y versus x on rectangular coordinates passes through (1.0, 0.693) and (2.0, 0.0) (i.e., at the first point x 1.0 and In y = 0.693). Solution: In y bx + In a = y = aebæ (In y2 – In y1)/(x2 – x1) (0 – 0.693)/(2.0 – 1.0) = –0.693 In a In y1 – bx1 = 0.693 + (0.693) (1.0) = 1.386 = a = el.386 = 4.00 y = 4.00e-0.693x b. A semilog plot of y (logarithmic axis) versus x passes through (1, 2) and (2, 1). c. A log plot of y versus æ passes through (1, 2) and (2, 1). Answer d. A semilog plot of xy (logarithmic axis) versus y/x passes through (1.0, 40.2) and (2.0, 807.0). e. A log plot of y² /x versus (x - 2) passes through (1.0, 40.2) and (2.0, 807.0).

2.38. Sketch the plots described below and calculate the equations for y(x) from the given information. The plots are all straight lines. Note that the given coordinates refer to abscissa and ordinate values, not x and y values. [The solution of Part (a) is given as an example.] a. A plot of In y versus x on rectangular coordinates passes through (1.0, 0.693) and (2.0, 0.0) (i.e., at the first point x 1.0 and In y = 0.693). Solution: In y bx + In a = y = aebæ (In y2 – In y1)/(x2 – x1) (0 – 0.693)/(2.0 – 1.0) = –0.693 In a In y1 – bx1 = 0.693 + (0.693) (1.0) = 1.386 = a = el.386 = 4.00 y = 4.00e-0.693x b. A semilog plot of y (logarithmic axis) versus x passes through (1, 2) and (2, 1). c. A log plot of y versus æ passes through (1, 2) and (2, 1). Answer d. A semilog plot of xy (logarithmic axis) versus y/x passes through (1.0, 40.2) and (2.0, 807.0). e. A log plot of y² /x versus (x - 2) passes through (1.0, 40.2) and (2.0, 807.0).

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 92E
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The problem that is listed below need to be solved and you may access that problem via viewing them through the attached images in this request. **Question Number #2.38**

2.38. Sketch the plots described below and calculate the equations for y(x) from the given information. The plots are all straight lines. Note that the given coordinates refer to abscissa and ordinate values, not x and y values. [The solution of Part (a) is given as an example.] a. A plot of In y versus x on rectangular coordinates passes through (1.0, 0.693) and (2.0, 0.0) (i.e., at the first point x 1.0 and In y = 0.693). Solution: In y bx + In a = y = aebæ (In y2 – In y1)/(x2 – x1) (0 – 0.693)/(2.0 – 1.0) = –0.693 In a In y1 – bx1 = 0.693 + (0.693) (1.0) = 1.386 = a = el.386 = 4.00 y = 4.00e-0.693x b. A semilog plot of y (logarithmic axis) versus x passes through (1, 2) and (2, 1). c. A log plot of y versus æ passes through (1, 2) and (2, 1). Answer d. A semilog plot of xy (logarithmic axis) versus y/x passes through (1.0, 40.2) and (2.0, 807.0). e. A log plot of y² /x versus (x - 2) passes through (1.0, 40.2) and (2.0, 807.0).
Transcribed Image Text:2.38. Sketch the plots described below and calculate the equations for y(x) from the given information. The plots are all straight lines. Note that the given coordinates refer to abscissa and ordinate values, not x and y values. [The solution of Part (a) is given as an example.] a. A plot of In y versus x on rectangular coordinates passes through (1.0, 0.693) and (2.0, 0.0) (i.e., at the first point x 1.0 and In y = 0.693). Solution: In y bx + In a = y = aebæ (In y2 – In y1)/(x2 – x1) (0 – 0.693)/(2.0 – 1.0) = –0.693 In a In y1 – bx1 = 0.693 + (0.693) (1.0) = 1.386 = a = el.386 = 4.00 y = 4.00e-0.693x b. A semilog plot of y (logarithmic axis) versus x passes through (1, 2) and (2, 1). c. A log plot of y versus æ passes through (1, 2) and (2, 1). Answer d. A semilog plot of xy (logarithmic axis) versus y/x passes through (1.0, 40.2) and (2.0, 807.0). e. A log plot of y² /x versus (x - 2) passes through (1.0, 40.2) and (2.0, 807.0).
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