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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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PLEASE HELP SUPER EASY!!!
Effectus [21]

A1. 12 i.e option D

A2. 3n-7 i.e option A

A3. -6n+20 i.e option D

A4. -70 i.e option C

Step-by-step explanation:

aₙ = a₁ + (n - 1) × d  

aₙ = the nᵗʰ term in the sequence

a₁ = the first term in the sequence

d = the common difference between terms

Using the above formula to solve the first part, we have :

  • -8 = a₁ + (2-1) × 5
  • -13 = a₁
  • a₆ = -13 + (6-1) × 5
  • a₆ = 12

For the second part, we have :

  • aₙ = -4 + (n-1)×3
  • aₙ = -4 + 3n -3
  • aₙ = 3n-7

For the third part, we have :

  • a₁=14 ; d=-6
  • aₙ = 14 + (n-1)×(-6)
  • aₙ = -6n + 20

For the fourth part, we have :

  • aₙ = 14 + (15-1)×(-6)
  • aₙ = -70
7 0
3 years ago
Select the correct answer.
maks197457 [2]
The answer to this question has to be D. 42.75 square inches.
7 0
2 years ago
which values of x and y are solutions to the open sentence? 4y ≥ 3x 2 a. x = 3, y = 0 b. x = 4, y = 3 c. x = 6, y = 5 d. x = 7,
boyakko [2]
4y ≥ 3x + 2

Plugging in the values in the options, then the required values are when x = 6 and y = 5, then
4(5) ≥ 3(6) + 2
20 ≥ 18 + 2
20 ≥ 20
8 0
3 years ago
Solve for x - PLEASE NEED HELP, this is my 3rd time posting it.
mafiozo [28]

Answer:

x=58

Step-by-step explanation:

First, remember that the maximum degree of an angle totals 360°.

Since we already have 294°, this means that what is left must total 360\textdegree - 294\textdegree= 66\textdegree.

Therefore, this means that our two smaller angles must equal 66°. So:

(36)+(x-28)=66

Solve for x. Add on the left:

x+8=66

Subtract 8 from both sides. Therefore, the value of x is:

x=58

6 0
3 years ago
What would 672,831 be rounded to the nearest hundred
maks197457 [2]

Answer:

672,800

Step-by-step explanation:

672,800 672800

8 0
3 years ago
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