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A construction worker is digging holes for a fence. The supervisor has asked him to dig the holes 35" deep. Since the height of the fence posts can be adjusted the supervisor conveyed that the depth of his holes could be off by no more than 2". a. On the number line below, represent all possible depths (in inches) that the holes can be. ++++. 15 20 25 30 35 40 45 Clear All Draw: b. Write an inequality (without using absolute value) to represent all possible values for z, the depth (in inches) of the holes. Preview c. Complete the following absolute value inequality to represent all possible values for z, the depth (in inches) of the holes.

A construction worker is digging holes for a fence. The supervisor has asked him to dig the holes 35" deep. Since the height of the fence posts can be adjusted the supervisor conveyed that the depth of his holes could be off by no more than 2". a. On the number line below, represent all possible depths (in inches) that the holes can be. ++++. 15 20 25 30 35 40 45 Clear All Draw: b. Write an inequality (without using absolute value) to represent all possible values for z, the depth (in inches) of the holes. Preview c. Complete the following absolute value inequality to represent all possible values for z, the depth (in inches) of the holes.

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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**Educational Exercise: Representing Depths and Inequalities** **Scenario:** A construction worker is tasked with digging holes for a fence. The supervisor has specified that the holes should be dug 35 inches deep. However, due to adjustable fence post heights, the holes' depth can vary by up to 2 inches. **Tasks:** a. **Graph Representation:** - On the number line, depict all possible depths (in inches) the holes can be. Since the depth is 35 inches plus or minus 2 inches, the holes can range from 33 inches to 37 inches. b. **Inequality Without Absolute Value:** - Write an inequality to represent all potential values for \( x \), where \( x \) is the depth (in inches) of the holes. - Example of entering inequality notation: \( 33 \leq x \leq 37 \) c. **Absolute Value Inequality:** - Use absolute value to write an inequality that encapsulates all possible values for \( x \). - Complete the expression for \( |x - 35| \leq 2 \). **Input Instructions:** - **Box 1:** Draw the possible range on the graph, which spans from 33 to 37 inches. - **Box 2:** Enter the inequality notation. Use a combined interval like \( 33 \leq x \leq 37 \). - **Box 3:** Express an answer as a formula, for example, \( 3x^2+1 \). - **Box 4:** Enter a value as a number or computation, e.g., \( 5/3, 2.2172 \). **Notes:** - Use \( DNE \) for results that do not exist. - Use \( \infty \) for infinity. This exercise aids in understanding how to represent constraints and variations in a practical context using mathematical inequalities and visual tools.
Transcribed Image Text:**Educational Exercise: Representing Depths and Inequalities** **Scenario:** A construction worker is tasked with digging holes for a fence. The supervisor has specified that the holes should be dug 35 inches deep. However, due to adjustable fence post heights, the holes' depth can vary by up to 2 inches. **Tasks:** a. **Graph Representation:** - On the number line, depict all possible depths (in inches) the holes can be. Since the depth is 35 inches plus or minus 2 inches, the holes can range from 33 inches to 37 inches. b. **Inequality Without Absolute Value:** - Write an inequality to represent all potential values for \( x \), where \( x \) is the depth (in inches) of the holes. - Example of entering inequality notation: \( 33 \leq x \leq 37 \) c. **Absolute Value Inequality:** - Use absolute value to write an inequality that encapsulates all possible values for \( x \). - Complete the expression for \( |x - 35| \leq 2 \). **Input Instructions:** - **Box 1:** Draw the possible range on the graph, which spans from 33 to 37 inches. - **Box 2:** Enter the inequality notation. Use a combined interval like \( 33 \leq x \leq 37 \). - **Box 3:** Express an answer as a formula, for example, \( 3x^2+1 \). - **Box 4:** Enter a value as a number or computation, e.g., \( 5/3, 2.2172 \). **Notes:** - Use \( DNE \) for results that do not exist. - Use \( \infty \) for infinity. This exercise aids in understanding how to represent constraints and variations in a practical context using mathematical inequalities and visual tools.
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