An electric device delivers a current of [tex]$15.0 A$[/tex] for 30 seconds. How many electrons flow through it?
Answer (2)
Calculate the area of each section using the appropriate formula for its shape: rectangle, right triangle, square, and trapezoid.
Determine the population density for each section by dividing the number of trees by the area.
Compare the calculated densities to order the sections from least to greatest.
The population densities from least to greatest are: A < C < D < B .
Explanation
Problem Analysis We are given the number of trees and the shape of four sections of a forest. We need to find the population density (trees per square mile) for each section and order them from least to greatest.
Calculate the Area of Each Section First, we need to calculate the area of each section.
Section A is a rectangle with length 60 miles and width 75 miles. The area of a rectangle is given by: A re a = l e n g t h × w i d t h A re a A = 60 × 75 = 4500 s q u a re mi l es
Section B is a right triangle with legs 60 miles and 70 miles. The area of a right triangle is given by: A re a = 2 1 × ba se × h e i g h t A re a B = 2 1 × 60 × 70 = 2100 s q u a re mi l es
Section C is a square with side length 60 miles. The area of a square is given by: A re a = s i d e × s i d e A re a C = 60 × 60 = 3600 s q u a re mi l es
Section D is a trapezoid with bases 50 miles and 70 miles and a height of 50 miles. The area of a trapezoid is given by: A re a = 2 1 × ( ba s e 1 + ba s e 2 ) × h e i g h t A re a D = 2 1 × ( 50 + 70 ) × 50 = 2 1 × 120 × 50 = 3000 s q u a re mi l es
Calculate the Population Density of Each Section Next, we calculate the population density for each section using the formula: De n s i t y = A re a N u mb er o f T rees
Section A: De n s i t y A = 4500 450 , 000 = 100 t rees / s q u a re mi l e
Section B: De n s i t y B = 2100 250 , 000 = 119.05 t rees / s q u a re mi l e
Section C: De n s i t y C = 3600 400 , 000 = 111.11 t rees / s q u a re mi l e
Section D: De n s i t y D = 3000 350 , 000 = 116.67 t rees / s q u a re mi l e
Order the Population Densities Finally, we order the population densities from least to greatest: De n s i t y A < De n s i t y C < De n s i t y D < De n s i t y B 100 < 111.11 < 116.67 < 119.05 So the order of the sections from least to greatest population density is A, C, D, B.
Final Answer The population densities in order from least to greatest are: A < C < D < B.
Examples
Understanding population density is crucial in urban planning and environmental conservation. For instance, knowing the tree density in different forest sections helps forest rangers manage resources effectively, such as allocating personnel for fire prevention or tracking the spread of diseases. Similarly, in urban areas, population density informs decisions about infrastructure development, like building schools or hospitals, ensuring resources are distributed according to the population's needs.
Approximately 2.81 × 10^21 electrons flow through the electric device when a current of 15.0 A is delivered for 30 seconds.
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