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Get Full Access to Precalculus With Trigonometry: Concepts And Applications - 1 Edition - Chapter 10-5 - Problem 11
Get Full Access to Precalculus With Trigonometry: Concepts And Applications - 1 Edition - Chapter 10-5 - Problem 11

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# Geology Problem: Figure 10-5d shows an underground rock formation that slants up and ISBN: 9781559533911 468

## Solution for problem 11 Chapter 10-5

Precalculus with Trigonometry: Concepts and Applications | 1st Edition

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Problem 11

Geology Problem: Figure 10-5d shows an underground rock formation that slants up and outcrops at ground level along a line in a field. The x- and y-axes run along perpendicular fence lines. A point on the outcropping is (200, 300, 0), where distances are in meters. A vector normal to the plane of the underground formation is = 30 17 + 11 . Figure 10-5d a. Find an equation of the plane surface of the underground rock formation. b. If you follow the outcropping line to the fences, which axis will it cross first, the x-axis or the y-axis? At what point will it meet the fence? c. If a well is drilled vertically starting at the point (70, 50, 0), how deep will it be when it first encounters the rock formation? d. The angle between the plane of the rock formation and the plane of the ground is called a dihedral angle. Geologists call this angle the dip of the formation. It is equal to the angle between the normal vectors to the two planes or to the supplement of this angle. Find the acute dip angle.

Step-by-Step Solution:

Geology Problem: Figure 10-5d shows an underground rock formation that slants up and outcrops atground level along a line in a field. The x- and y-axes run along perpendicular fence lines. A point onthe outcropping is (200, 300, 0), where distances are in meters. A vector normal to the plane of theunderground formation is = 30 17 + 11 . Figure 10-5d a. Find an equation of the plane surface of theunderground rock formation. b. If you follow the outcropping line to the fences, which axis will itcross first, the x-axis or the y-axis At what point will it meet the fence c. If a well is drilledvertically starting at the point (70, 50, 0), how deep will it be when it first encounters the rockformation d. The angle between the plane of the rock formation and the plane of the ground is calleda dihedral angle. Geologists call this angle the dip of the formation. It is equal to the angle betweenthe normal vectors to the two planes or to the supplement of this angle. Find the acute dip angle. Step By Step SolutionStep 1 of 4: (a) Equation of the plane: The normal vector to the plane is: The equation of the plane is written as: Substituting the values of x, y and z :Therefore the equation of the plane is:

Step 2 of 4

Step 3 of 4

##### ISBN: 9781559533911

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