An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Convert the inequality x ≤ − 1 to interval notation: ( − ∞ , − 1 ] .
Convert the inequality x < 3.4 to interval notation: ( − ∞ , 3.4 ) .
Convert the inequality xg t r g e q 2 5 to interval notation: [ 2 5 , ∞ ) .
The final answer is: a) ( − ∞ , − 1 ] , b) ( − ∞ , 3.4 ) , c) [ 2 5 , ∞ ) .
Explanation
Understanding the Problem We are given three inequalities and we need to express them using interval notation. Interval notation is a way to write sets of real numbers.
Converting Inequality a) to Interval Notation For the inequality x ≤ − 1 , this means that x can be any number less than or equal to − 1 . In interval notation, this is written as ( − ∞ , − 1 ] . The parenthesis indicates that − ∞ is not included, and the square bracket indicates that − 1 is included.
Converting Inequality b) to Interval Notation For the inequality x < 3.4 , this means that x can be any number less than 3.4 , but not equal to 3.4 . In interval notation, this is written as ( − ∞ , 3.4 ) . The parenthesis indicates that 3.4 is not included.
Converting Inequality c) to Interval Notation For the inequality x ≥ 2 5 , this means that x can be any number greater than or equal to 2 5 . In interval notation, this is written as [ 2 5 , ∞ ) . The square bracket indicates that 2 5 is included, and the parenthesis indicates that ∞ is not included.
Final Answer Therefore, the inequalities in interval notation are: a) ( − ∞ , − 1 ] b) ( − ∞ , 3.4 ) c) [ 2 5 , ∞ )
Examples
Interval notation is used in many areas of mathematics, including calculus and analysis. For example, when describing the domain and range of a function, interval notation is often used. Suppose you are analyzing the temperature range in a city over a month. If the temperature never went below 10 degrees Celsius and never exceeded 30 degrees Celsius, you could express this range in interval notation as [ 10 , 30 ] . This notation provides a concise way to communicate the boundaries of the temperature range.
The total charge delivered by a 15.0 A current over 30 seconds is 450.0 C. This corresponds to approximately 2.81 x 10^21 electrons flowing through the device. Therefore, around 2.81 x 10^21 electrons pass through the device in that time period.
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