Explanation Given: p ( r ) = 52 ( 1 + r 2 ) − 2 gorillas per square kilometer Calculation: We have been given that, radius considered=5 km and radial population density = p ( r ) = 52 ( 1 + r 2 ) − 2 gorillas per square kilometer which varies from centre of clearing 0 to radius considered 5. To calculate the population in the given circle, thin rings inside the circle are considered, as shown below, Now, if we straightened out each ring we get rectangular strips, with length as the circumference of that ring 2πr (r is radius of the ring) and breadth as the difference in radius dr Therefore, area of ring = 2πr*dr square km Therefore, Population of ring = area of ring* radial population density Therefore, total population, P in thousands = sum of (area of ring*radial population density) = integral of 2πrdr* radial population density p(r) P = ∫ 0 5 2 π r p ( r ) d r P = 2 π ∫ 0 5 r p ( r ) d r P = 2 π ∫ 0 5 r 52 ( 1 + r 2 ) − 2 d r P = 2 π × 52 ∫ 0 5 r ( 1 + r 2 ) − 2 d r L e t , u = 1 + r 2 d u = 2 r d r r d r = d u 2 P = 104 π

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Chapter 6.2, Problem 30E

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To calculate: the number of gorillas within a 5km radius of the clearing if the radial population density is $p (r) = 52 {(1 + r^{2})}^{- 2}$ gorillas per square kilometer

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Chapter 6.2, Problem 29E

Chapter 6.2, Problem 31E

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Chapter 6 Solutions

CALCULUS 4E (LL) W/ ACHIEVE ACCESS

Ch. 6.1 - Prob. 1PQ Ch. 6.1 - Prob. 2PQ Ch. 6.1 - Prob. 3PQ Ch. 6.1 - Prob. 4PQ Ch. 6.1 - Prob. 5PQ Ch. 6.1 - Prob. 6PQ Ch. 6.1 - Prob. 1E Ch. 6.1 - Prob. 2E Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E

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the number of gorillas within a 5km radius of the clearing if the radial population density is p ( r ) = 52 ( 1 + r 2 ) − 2 gorillas per square kilometer

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To calculate: the number of gorillas within a 5km radius of the clearing if the radial population density is p(r)=52(1+r2)−2 gorillas per square kilometer

Want to see the full answer?

Chapter 6 Solutions

To calculate: the number of gorillas within a 5km radius of the clearing if the radial population density is $p (r) = 52 {(1 + r^{2})}^{- 2}$ gorillas per square kilometer