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shepuryov [24]
3 years ago
15

Spruce budworms are a major pest that defoliates balsam fir. They are preyed upon by birds. A model for the per capita predation

rate is given by f(N)=aNk2+N2 where N denotes the density of spruce budworms and a and k are positive constants. Find f′(N), and determine when the per capita predation rate is increasing and when it is decreasing.

Mathematics
1 answer:
xenn [34]3 years ago
8 0

Answer:

f'(N) = a(k² - N²)/(k² + N²)

The function increases in the interval

(-k < N < k)

And the function decreases everywhere else; the intervals given as

(-∞ < N < -k) and (k < N < ∞)

Step-by-step explanation:

f(N)=aN/(k²+N²)

The derivative of this function is obrained using the quotient rule.

Then to determine the intervals where the function is increasinumber and decreasing,

The function increases in intervals where f'(N) > 0

and the function decreases in intervals where f'(N) < 0.

This inequality is evaluated and the solution obtained.

The solution is presented in the attached image.

Hope this Helps!!!

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Explain an example of how taking an amount (for example, $20), decreasing it by 40% and then increasing that amount by 40% does
Likurg_2 [28]

Answer:

See below

Step-by-step explanation:

What we can do is try it out.

20*0.6=12

since 0.6 is left

now we increase 12 by 40, or multiply it by 1.4

12*1.4= 16.8

See what is happening here is that at first when we are decreasing it by 40 percent, we are taking 40 percent of 20. However, when we increase that amount by 40 percent, we are now increasing 40 percent of 20 by 40 percent, or increasing 16 by 40 percent. Therefore, we will not get the original amount.

4 0
3 years ago
2 movie tickets and 1 popcorn cost $29.4 movie tickets and 4 popcorns cost $68. So how much would 3 movie tickets and 5 popcorns
Arisa [49]

Answer:

3 movie tickets would cost 44.8 5 popcorns would cost 85

Step-by-step explanation:

29.4 divided by 2 equals 14.7

29.4 plus 14.7 equals 44.8

68 divided by 4 17

68 plus 17 equals 85

4 0
3 years ago
Can someone please help i am very stuck :
Oliga [24]
The answer is
the first one is x= 18.98 
a^2+b^2=c^2
8 cm^2+17 cm^2= x^2 
64+289=x^2
√x^2= √353
x=18.89
<span><span>the second one is x= 18.7
a^2+b^2=c^2
7 m^2+ x^2= 20 m^2
49 m+x^2=400 m
-49            -49
  </span></span>√x^2=√352
<span><span>x= 18.7
Hope this helps!</span></span>
5 0
3 years ago
A squirrel is 5.0 m away from you while moving at a constant velocity of 3m/s away from you. How far away is the squirrel after
Vladimir [108]
20 meters away.......
5 0
3 years ago
What is the area (in square units) of the region under the curve of the function f(x)=x+3, on the interval from x=1 to x=3 ?
aleksandrvk [35]

Answer:

10 square units

Step-by-step explanation:

We want to find the area under the curve f(x)=x+3 from x=1 to x=3.

We use definite integrals to find this area.

\int\limits^3_1 {x+3} \, dx

We integrate to obtain:

\frac{x^2}{2}+3x|_1^3

We evaluate the limits to get:

\frac{3^2}{2}+3(3)-(\frac{1^2}{2}+3(1))

4.5+9-0.5-3=10

Therefore the area under the curve from x=1 to x=3 is 10 square unit.

8 0
3 years ago
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