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zhuklara [117]
2 years ago
7

F(x) = sqrt(- 2x) Determine for each value whether it is in the domain of f or not.

Mathematics
1 answer:
Gnoma [55]2 years ago
4 0

Answer:

only -2 is in the domain

Step-by-step explanation:

For negative values under the sqrt, there is no real answer, hence

-2x ≥ 0

only for x=-2 this is the case.

The domain represents all the valid input values for x.

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Suppose a population grows according to the logistic equation but is subject to a constant total harvest rate of H. If N(t) is t
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Answer:

a) Equilibrium point : [ 947, 53 ]

b) N = 947 is stable equilibrium, N = 53  is unstable equilibrium

c) N0, the population will not go extinct

Step-by-step explanation:

a)

Given that;

r = 2, k = 1000, H = 100

dN/dT = R(1 - N/k)N - H

so we substitute

dN/dt = 2( 1 - N/1000)N - 100

now for equilibrium solution, dN/dt = 0

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N = 1000 ± √(-1000)² - 4(1)(50000)) / 2(1)

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approximately

N = 947 OR 53

Therefore Equilibrium point : [ 947, 53 ]

b)

g(N) = 2( 1 - N/1000)N - 100

= 2N - N²/500 - 100

g'(N) = 2 - N/250

SO AT 947

g'(N) = g'(947) =  2 - 947/250 = -1.788 which is less than (<) 0

so N = 947 is stable equilibrium

now AT 53

g'(N) = g"(53) = 2 - 53/250 = 1.788 which is greater than (>) 0

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The capacity k=1000

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