### Understanding Linear Equations: Practical Application**Question 4:**A drill is used to dig down into the earth. The depth to which the drill has reached is given at two different time intervals. - After 2 hours, the drill is 12 meters below the surface.- After 5 hours, the drill is 30 meters below the surface.**Problem Statement:**Which equation represents the depth of the drill in meters, $ y $, after $ x $ hours of drilling?**Options:**a. $ y = 12x $b. $ y = -12x $c. $ y = 6x $d. $ y = -6x $**Solution Explanation:**To find the correct equation, consider the following:1. **Determine the Depth Change:** Compare the depth at different times; from 2 hours to 5 hours, the depth changes from 12 meters to 30 meters. - Depth change = 30 meters - 12 meters = 18 meters. 2. **Determine the Time Change:** - Time change = 5 hours - 2 hours = 3 hours. 3. **Calculate the Rate of Change (Slope):** - Slope = Depth change / Time change = 18 meters / 3 hours = 6 meters per hour. However, since the drill is moving downwards, this should be considered a negative slope, representing descent. - Thus, slope = -6 meters/hour. 4. **Verify the Equation:** - The equation with this slope consistent with the given changes in depth aligns with option d: \[ y = -6x \]Therefore, the solution to the problem is **d. $ y = -6x $**. This equation accurately represents the depth of the drill after $ x $ hours of drilling.

Answered: Image /qna-images/answer/5885ceb1-25a7-4d5c-b1ae-c64ad23b152b.jpg

4. A drill is used to dig down into the earth. After 2 hours, the drill is 12 meters below the surface. After 5 hours, the drill is 30 meters below the surface. Which equation represents the depth of the drill in meters, y, after x hours of drilling? y = 12x b. у %3D-12х a. C. y = 6x d. y=-6x

4. A drill is used to dig down into the earth. After 2 hours, the drill is 12 meters below the surface. After 5 hours, the drill is 30 meters below the surface. Which equation represents the depth of the drill in meters, y, after x hours of drilling? y = 12x b. у %3D-12х a. C. y = 6x d. y=-6x

Algebra and Trigonometry (6th Edition)

6th Edition

ISBN:9780134463216

Author:Robert F. Blitzer

Publisher:Robert F. Blitzer

ChapterP: Prerequisites: Fundamental Concepts Of Algebra

Section: Chapter Questions

Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...

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Cylinders

A cylinder is a three-dimensional solid shape with two parallel and congruent circular bases, joined by a curved surface at a fixed distance. A cylinder has an infinite curvilinear surface.

Cones

A cone is a three-dimensional solid shape having a flat base and a pointed edge at the top. The flat base of the cone tapers smoothly to form the pointed edge known as the apex. The flat base of the cone can either be circular or elliptical. A cone is drawn by joining the apex to all points on the base, using segments, lines, or half-lines, provided that the apex and the base both are in different planes.

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