An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?

Approximately 2.81 x 10^21 electrons flow through the electric device when it delivers a current of 15.0 A for 30 seconds. This is calculated using the total charge and the charge of a single electron. Understanding these relationships is essential in physics, particularly in electrical circuits.
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Answered by Anonymous | 2025-07-05

Calculate n for Row 1 using the interior angle sum formula: ( n − 2 ) × 18 0 ∘ = 34 0 ∘ , resulting in n ≈ 3.89 .
Calculate the interior angle sum and each interior angle for Row 2 using n = 14 , giving an interior angle sum of 216 0 ∘ and each interior angle as approximately 154.2 9 ∘ .
Calculate n for Row 10 using each interior angle of 12 0 ∘ , resulting in n = 6 , and then find the interior angle sum as 72 0 ∘ .
Calculate n for Row 11 using each interior angle of 156. 4 ∘ , resulting in n ≈ 15.25 , and then find the interior angle sum as approximately 2385.7 6 ∘ .

Explanation

Problem Analysis and Strategy The problem is to complete a table related to the properties of regular polygons. The table includes columns for the number of sides ( n ), the interior angle sum, and the measure of each interior angle in a regular polygon. We will use the formulas for the interior angle sum, which is ( n − 2 ) × 18 0 ∘ , and the measure of each interior angle in a regular polygon, which is n ( n − 2 ) × 18 0 ∘ ​ , to fill in the missing values in the table.

Row 1 Calculations For Row 1, we are given that the interior angle sum is 34 0 ∘ . We can use the formula for the interior angle sum to find the number of sides n :
( n − 2 ) × 18 0 ∘ = 34 0 ∘ n − 2 = 180 340 ​ = 9 17 ​ n = 9 17 ​ + 2 = 9 17 ​ + 9 18 ​ = 9 35 ​ ≈ 3.89 Now we can find each interior angle by dividing the interior angle sum by n :
n 34 0 ∘ ​ = 9 35 ​ 34 0 ∘ ​ = 340 \tImes 35 9 ​ = 35 3060 ​ = 7 612 ​ ≈ 87.4 3 ∘

Row 2 Calculations For Row 2, we are given that the number of sides is n = 14 . We can use the formula for the interior angle sum to find the interior angle sum: ( n − 2 ) × 18 0 ∘ = ( 14 − 2 ) × 18 0 ∘ = 12 × 18 0 ∘ = 216 0 ∘ Now we can find each interior angle by dividing the interior angle sum by n :
14 216 0 ∘ ​ = 7 1080 ​ ≈ 154.2 9 ∘

Row 10 Calculations For Row 10, we are given that each interior angle is 12 0 ∘ . We can use the formula for each interior angle to find the number of sides n :
n ( n − 2 ) × 18 0 ∘ ​ = 12 0 ∘ ( n − 2 ) × 180 = 120 n 180 n − 360 = 120 n 60 n = 360 n = 6 Now we can find the interior angle sum using the formula: ( n − 2 ) × 18 0 ∘ = ( 6 − 2 ) × 18 0 ∘ = 4 × 18 0 ∘ = 72 0 ∘

Row 11 Calculations For Row 11, we are given that each interior angle is 156. 4 ∘ . We can use the formula for each interior angle to find the number of sides n :
n ( n − 2 ) × 18 0 ∘ ​ = 156. 4 ∘ ( n − 2 ) × 180 = 156.4 n 180 n − 360 = 156.4 n 23.6 n = 360 n = 23.6 360 ​ = 236 3600 ​ = 59 900 ​ ≈ 15.25 Now we can find the interior angle sum using the formula: ( n − 2 ) × 18 0 ∘ = ( 59 900 ​ − 2 ) × 18 0 ∘ = ( 59 900 ​ − 59 118 ​ ) × 180 = 59 782 ​ \tImes 180 = 59 140760 ​ ≈ 2385.7 6 ∘

Final Results In summary: Row 1: n = 9 35 ​ ≈ 3.89 , Each interior angle ≈ 87.4 3 ∘ Row 2: Interior angle sum = 216 0 ∘ , Each interior angle ≈ 154.2 9 ∘ Row 10: n = 6 , Interior angle sum = 72 0 ∘ Row 11: n = 59 900 ​ ≈ 15.25 , Interior angle sum ≈ 2385.7 6 ∘


Examples
Understanding the properties of polygons is crucial in various fields, such as architecture and engineering. For example, when designing a building with a polygonal base, architects need to calculate the interior angles to ensure structural stability and aesthetic appeal. Knowing the relationship between the number of sides and the interior angles allows for precise planning and construction, resulting in visually stunning and structurally sound buildings.

Answered by GinnyAnswer | 2025-07-05