An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (1)
The problem provides three inequalities relating Darius's height ( d ) and William's height ( w ):
$d
Analyze each statement to determine if it must be true based on the given inequalities.
The statements that must be true are:
Darius is at least 36 inches tall ($d
William's height is less than 68 inches ( w < 68 ).
Darius is no more than 4 inches taller than twice William's height ($d
The final answer consists of these three statements.
Explanation
Understanding the Problem We are given a system of linear inequalities that describe the possible heights of Darius, d , and William, w , in inches. The inequalities are:
d ≥ 36
w < 68
d ≤ 4 + 2 w
We need to determine which three statements about their heights must be true based on these inequalities.
Analyzing the Statements Let's analyze each statement:
Darius is at least 36 inches tall. This statement corresponds to the inequality d ≥ 36 , which is given. So, this statement must be true.
Darius is at most 36 inches tall. This statement contradicts the inequality d ≥ 36 . So, this statement is false.
William's height is less than 68 inches. This statement corresponds to the inequality w < 68 , which is given. So, this statement must be true.
William's height is at least 68 inches. This statement contradicts the inequality w < 68 . So, this statement is false.
Darius is less than 4 inches taller than twice William's height. This translates to d < 4 + 2 w . The given inequality is d ≤ 4 + 2 w . Since d can be equal to 4 + 2 w , this statement is not necessarily true.
Darius is no more than 4 inches taller than twice William's height. This translates to d ≤ 4 + 2 w , which is the same as the given inequality. So, this statement must be true.
Identifying the True Statements Based on the analysis, the following statements must be true:
Darius is at least 36 inches tall.
William's height is less than 68 inches.
Darius is no more than 4 inches taller than twice William's height.
Final Answer Therefore, the three statements that must be true are:
Darius is at least 36 inches tall.
William's height is less than 68 inches.
Darius is no more than 4 inches taller than twice William's height.
Examples
Understanding inequalities can help in various real-life scenarios. For instance, when planning a budget, you might have constraints on how much you can spend on different categories (e.g., groceries, rent, entertainment). Inequalities can help you model these constraints and find feasible spending plans that satisfy all your requirements. Similarly, in manufacturing, inequalities can be used to ensure that products meet certain quality standards or performance criteria. This problem demonstrates how inequalities can be used to define and analyze constraints in a given situation.
