An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Simplified the fraction − 16 24 to 2 − 3 .
Identified that a number to the left on a number line is smaller.
Calculated the length of the line segment between 1 2 1 and − 2 2 1 as 4 units.
Recognized the line segment from a vertex to the midpoint of the opposite side as a median.
Determined the circumcentre in a right-angled triangle lies at the mid-point of the hypotenuse. 1. d, 2. b, 3. a, 4. c, 5. d
Explanation
Problem Analysis Let's analyze each multiple-choice question step by step.
Simplifying the fraction Question 1: The simplest form of − 16 24 is To simplify the fraction, we find the greatest common divisor (GCD) of 24 and 16, which is 8. Then, we divide both the numerator and the denominator by 8: − 16 ÷ 8 24 ÷ 8 = − 2 3 = 2 − 3 So the correct answer is (d).
Understanding Number Line Question 2: On a number line, a number lying to the left of the given number is On a number line, numbers decrease as you move from right to left. Therefore, a number to the left of a given number is smaller. So the correct answer is (b).
Calculating Length on Number Line Question 3: On a number line, the length of the line segment joining 1 2 1 and − 2 2 1 is First, convert the mixed numbers to improper fractions: 1 2 1 = 2 3 and − 2 2 1 = − 2 5 .
The length of the line segment is the absolute difference between the two numbers: ∣ 2 3 − ( − 2 5 ) ∣ = ∣ 2 3 + 2 5 ∣ = ∣ 2 8 ∣ = ∣4∣ = 4 So the correct answer is (a).
Identifying Triangle Median Question 4: A line segment that joins a vertex to the mid-point of the opposite side is called By definition, a line segment joining a vertex to the midpoint of the opposite side of a triangle is called a median. So the correct answer is (c).
Locating Circumcentre in Right Triangle Question 5: In a right-angled triangle, the circumcentre lies In a right-angled triangle, the circumcentre is located at the midpoint of the hypotenuse. So the correct answer is (d).
Final Answers The answers to the multiple-choice questions are:
(d) 2 − 3
(b) smaller
(a) 4 units
(c) median
(d) mid-point of hypotenuse
Examples
These concepts are fundamental in geometry and number theory. For example, simplifying fractions is used in everyday calculations, understanding number lines helps in visualizing numerical relationships, and knowing properties of triangles is essential in architecture and engineering.
The electric device carrying a current of 15.0 A for 30 seconds transports approximately 2.81 × 1 0 21 electrons. This calculation was made by first determining the total charge and then utilizing the charge of a single electron to find the total number of electrons. The relationships between current, time, and charge are key to understanding this process.
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