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juin [17]
2 years ago
10

Solve by completing the square: x^2+18x+45=0

Mathematics
1 answer:
MrRa [10]2 years ago
5 0

Answer:

 x = -3 , - 15

Step-by-step explanation:

<em>Given:</em>

<em>x² + 18x + 45 = 0</em>

<em>Solve:</em>

<em />x_{1,\:2}=\frac{-18\pm \sqrt{18^2-4\cdot \:1\cdot \:45}}{2\cdot \:1}

Simplify

-18\pm \sqrt{18^2-4\cdot \:1\cdot \:45=12

x_{1,\:2}=\frac{-18\pm \:12}{2\cdot \:1}

Separate the solution

x_1=\frac{-18+12}{2\cdot \:1},\:x_2=\frac{-18-12}{2\cdot \:1}

x_1=\frac{-18+12}{2\cdot \:1}=-3

x_2=\frac{-18-12}{2\cdot \:1}=-15

Thus, the answer are:

x=-3,\:x=-15

<u><em>Kavinsky</em></u>

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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 ]

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Step-by-step explanation:

a)

Given that;

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N = 947.213 OR 52.786

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N = 947 OR 53

Therefore Equilibrium point : [ 947, 53 ]

b)

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

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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

so N = 53  is unstable equilibrium

The capacity k=1000

If the population is less than 53 then the population will become extinct but since the capacity is equal to 1000 then the population will not go extinct.

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