Show all of your work, even though the question may not explicitly remind you to do so. Clearly label any functions, graphs, tables, or other objects that you use. Justifications require that you give mathematical reasons, and that you verify the needed conditions under which relevant theorems, properties, definitions, or tests are applied. Your work will be scored on the correctness and completeness of your methods as well as your answers. Answers without supporting work will usually not receive credit.

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A particle moves along the l-axis so that its position at time t>0 is given by x(t) = (t^2 - 9)/(3t^2 + 8)

(a) Is the particle moving toward the origin or away from the origin at time t = 2 ?
(b) The acceleration of the particle is given by a (t). Write an expression for a (t), and find the Value of a(2)
(c) what position does the particle approach as(t) approaches infinity?

  (a) at t=2, the particle is moving toward the origin

  (b) a(t) = 70(8 -9t^2)/(3t^2 +8)^3; a(2) = -0.245

  (c) the particle approaches x = 1/3 as t gets large

Step-by-step explanation:

(a) The function x(t) is negative for -3 < t < 3, so at t = 2, the particle is to the left of the origin.

The velocity of the particle is given by the derivative of the position function:

Then, at t=2, the expression is positive, indicating the particle is moving toward the origin.

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(b) The acceleration is the derivative of the velocity, so is ...

Then at t=2, the acceleration is ...

  a(2) = 70(8 -9·4)/(3·4+8)^3 = 70(-28)/8000

  a(2) = -0.245

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(c) As t gets large, the value of x(t) approaches t^2/(3t^2) = 1/3.

the population of other specie of birds will decline or other specie of birds will find some alternate source of food to survive.

explanation:

according to the competitive exclusion principle, which is also known as gause's law, two specie living in the same niche and feeding on the same resource cannot co-exist stably.

as we have well studied the theory of natural selection which states that only those organisms survive which have better tendency to compete for food and adapt to the environmental conditions.

coming towards the question, what wi ll happen when one species outcompetes the other for the small fish , the other specie will not get enough food and will start to die or decline in population. eventually either other specie needs to find another alternative food source for itself or migrate at some other location where there is less competition otherwise it will just not exist anymore at that niche.

hope it !

table a is wierd

step-by-step explanation:

6*f