An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
To find the number of electrons flowing through a device delivering 15.0 A for 30 seconds, we calculate the total charge using Q = I × t , yielding 450 C . Dividing this charge by the charge of one electron ( 1.602 × 1 0 − 19 C ), we estimate that approximately 2.81 × 1 0 21 electrons flow through the device. Thus, around 2.81 quintillion electrons pass in that time period.
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The Alternate Interior Angles Theorem justifies that ∠3 ≅ ∠5 and ∠1 ≅ ∠4 .
Congruent angles have equal measures, justifying m ∠1 = m ∠4 and m ∠3 = m ∠5 .
Angle addition and the definition of a straight line justify m ∠4 + m ∠2 + m ∠5 = 18 0 ∘ .
Substitution leads to m ∠1 + m ∠2 + m ∠3 = 18 0 ∘ .
m ∠1 + m ∠2 + m ∠3 = 18 0 ∘
Explanation
Analyze the problem The problem provides a proof outline for the theorem that the sum of the interior angles of a triangle is 18 0 ∘ . We need to fill in the missing justifications for two steps in the proof.
Justify the third statement The third statement, ' ∠3 ≅ ∠5 and ∠1 ≅ ∠4 ', states that angle 3 is congruent to angle 5, and angle 1 is congruent to angle 4. This is justified by the Alternate Interior Angles Theorem, since line DE is parallel to AC.
Justify the fourth statement The fourth statement, ' m ∠1 = m ∠4 and m ∠3 = m ∠5 ', states that the measure of angle 1 equals the measure of angle 4, and the measure of angle 3 equals the measure of angle 5. This is justified because congruent angles have equal measures.
Conclusion Therefore, the missing justifications are the Alternate Interior Angles Theorem and the statement that congruent angles have equal measures.
Examples
Understanding that the sum of angles in a triangle is 180 degrees is fundamental in many real-world applications. For example, when constructing a bridge, engineers use triangles for structural support. Knowing the angles of these triangles is crucial for ensuring the bridge's stability and proper weight distribution. Similarly, in architecture, calculating angles is essential for designing roofs, walls, and other structural elements that must fit together precisely and safely.
