A scientist studies the population of an insect colony. She begins her study with 10,000 insects in the colony and measures the
1 answer:
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has characteristic equation
with roots at . Then the characteristic solution is
For the particular solution, consider the ansatz , whose first and second derivatives vanish. Substitute
and its derivatives into the equation:
Then the general solution to the equation is
With , we have
and with ,
Then the particular solution to the equation is
Answer:
see below
Step-by-step explanation:
(a) the graph is symmetrical about the horizontal axis. It has a maximum value of r = 3 at θ = π.
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(b) The graph is symmetrical about both the horizontal and the vertical axis. It has a maximum value of r = 1 at θ = 0 and θ = π. (Note this curve has subtle differences from the inner loop of the above curve.)
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<em>About how</em>
As with any graphing problem, when doing it by hand, one chooses enough points to give the general shape of the curve. In some cases, quite a few points may be required. It is often helpful to use a spreadsheet for calculating the point values. Here, we've graphed the equations using "technology"--a graphing calculator.
