Population distribution. In order to study the population distribution of a certain species of insect, a biologist has constructed an artificial habitat in the shape of a rectangle 16 feet long and 12 feet wide. The only food available to the insects in this habitat is located at its center. The biologist has determined that the concentration C of insects per square foot at a point d units from the food supply (see the figure) is given approximately by C = 10 − 1 10 d 2 What is the average concentration of insects throughout the habitat? Express C as a function of x and y , set up a double integral , and evaluate it. Figure of 51
Population distribution. In order to study the population distribution of a certain species of insect, a biologist has constructed an artificial habitat in the shape of a rectangle 16 feet long and 12 feet wide. The only food available to the insects in this habitat is located at its center. The biologist has determined that the concentration C of insects per square foot at a point d units from the food supply (see the figure) is given approximately by C = 10 − 1 10 d 2 What is the average concentration of insects throughout the habitat? Express C as a function of x and y , set up a double integral , and evaluate it. Figure of 51
Solution Summary: The author calculates the average concentration of insects throughout the habitat. The length and breadth of the rectangular shape of an artificial habitat are 16 and 12 feet.
Population distribution. In order to study the population distribution of a certain species of insect, a biologist has constructed an artificial habitat in the shape of a rectangle 16 feet long and 12 feet wide. The only food available to the insects in this habitat is located at its center. The biologist has determined that the concentration C of insects per square foot at a point d units from the food supply (see the figure) is given approximately by
C
=
10
−
1
10
d
2
What is the average concentration of insects throughout the habitat? Express C as a function of x and y, set up a double integral, and evaluate it.
Figure of 51
With differentiation, one of the major concepts of calculus. Integration involves the calculation of an integral, which is useful to find many quantities such as areas, volumes, and displacement.
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ilc 8.3 End-of-Unit Assessment, Op x
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Problem 2
A successful music app tracked the number of song downloads each day for a month for 4 music artists, represented by lines l, j, m,
and d over the course of a month. Which line represents an artist whose downloads remained constant over the month?
Select the correct choice.
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Sidebar
Tools
M
45
song downloads
days
d
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8
m
l
RA
9
>
КУ
Fullscreen
G
Save & Exit
De
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Q/Determine the set of points at which
-
f(z) = 622 2≥ - 4i/z12
i
and
differentiable
analytice
is:
sy = f(x)
+
+
+
+
+
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X
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9
The function of shown in the figure is continuous on the closed interval [0, 9] and differentiable on the open
interval (0, 9). Which of the following points satisfies conclusions of both the Intermediate Value Theorem
and the Mean Value Theorem for f on the closed interval [0, 9] ?
(A
A
B
B
C
D
Chapter 7 Solutions
Calculus for Business, Economics, Life Sciences, and Social Sciences (13th Edition)
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