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Geometry

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A biologist is researching the population density of lizards near a boulder in a desert. The biologist counts 15 lizards within a radius of 14 mi of the boulder.

What is the population density of lizards?

Use 3.14 for pi and round only your final answer to the nearest whole number.

jbouyer  May 7, 2017
#1
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A biologist is researching the population density of lizards near a boulder in a desert. The biologist counts 15 lizards within a radius of 14 mi of the boulder.

What is the population density of lizards?

Use 3.14 for pi and round only your final answer to the nearest whole number.

$$The \ population \ density \ of \ lizards \ is$$

$$= \frac{15\ lizards }{2\times 3.14 \times {14}^2 square\ miles} = ( \frac{15}{1230.88}=0.012)\frac{ lizards }{square\ mile}$$

$$\approx 1 \frac {1 lizard }{square \ mile}$$

!

asinus  May 8, 2017
edited by asinus  May 8, 2017
#2
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sine

$$= \frac{15\ lizards }{ 3.14 \times {14}^2 square\ miles} = ( \frac{15}{615.44}=0.0244)\frac{ lizards }{square\ mile}$$

$$\approx 1 \frac {1 lizard }{square \ mile}$$

asinus

Guest May 8, 2017
edited by Guest  May 8, 2017
#3
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This isn’t a sustainable population. It’s probably 1/4 mile radius.

15/(3.14*.252) = 76.43

76 lizards per square mile.

Guest May 8, 2017
#4
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Note that Density = $$\frac{\text{population}}{\text{area}}$$

As stated in the question, there are 15 lizards, and the area of the circle that surrounds the boulder is simply $$14^2\times\pi$$or $$196\pi$$Thus the answer is $$\frac{15}{196\pi} \approx \frac{1}{41.0293333}$$

LtLlipop123  May 8, 2017