Answer:
First, remember that a circle of radius R centered in the point (a, b) can be written as:
(x - a)^2 + (y - b)^2 = R^2
Suppose that we can model the yard as a rectangular coordinate axis.
And the tree is planted in the point (a, b)
If we want to have 15 feet in all directions around the base of the tree (15 ft around the point (a, b))
The section that must remain unplanted is:
(x - a)^2 + (y - b)^2 ≤ R^2
Where the ≤ symbol is used because all the interior of the circle must remain unplanted (border included)
Given differential equation, (D4 - 5D3 + 5D2 + 5D - 6)y = 0
=> For general solution of equation,
Solve D4 - 5D3 + 5D2 + 5D - 6 = 0
=> D4 - 5D3 + 6D2 - D2 + 5D - 6 = 0
=> D2 (D2 - 5D + 6) - (D2 - 5D + 6) = 0
=> (D2 - 5D + 6)(D2 - 1) = 0 ................................(1)
Now
D2 - 1 = (D - 1)(D + 1) and
Factors of D2 - 5D + 6
D2 - 5D + 6 = D2 - 2D - 3D + 6
= D(D - 2) - 3(D - 2)
= (D - 3)(D - 2)
Therefore, equation (1) implies
(D2 - 5D + 6)(D2 - 1) = (D - 3)(D - 2)(D - 1)(D + 1) = 0
=> D = 3, 2, 1, -1 or D = -1, 1,, 2, 3
=> General solution of differential equation is,<span>
=><span> y = C1 e-x + C2 ex + C3 e2x + C4 e3x</span> .
Hope it helps
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5 of seven are not minivans - > 5/7
5/7*161=115
