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4 years ago

6

Which would most likely leave behind well sorted sediments?

Advanced Placement (AP)

2 answers:

Anarel [89]4 years ago

6 0

I believe it would be c.

stiks02 [169]4 years ago

4 0

Answer:

C. ocean waves

Explanation:

The wave waves are generated by the wind. As it begins to blow over the ocean's surface, it will increase its roughness, forming waves of very small amplitude (around the centimeter) called capillary waves. The longer the period during which the wind blows and the more intense it is, the greater the height of the waves that form.

This movement of seawater ends up moving small sediments that may be trapped at the bottom of the ocean or could be floating in the water. When the wave hits the surface it carries these sediments and then places them in several different places.

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2. Find the solution of each differential equation. (a) y/2y-8y = 0 (b) 25y/- 20y + 4y = 0 (c) y + 2y + 2y = 0 2. Find the solut

jek_recluse [69]

Each of these ODEs is linear and homogeneous with constant coefficients, so we only need to find the roots to their respective characteristic equations.

(a) The characteristic equation for

$y'' - 2y' - 8y = 0$

is

$r^2 - 2r - 8 = (r - 4) (r + 2) = 0$

which arises from the ansatz $y = e^{rx}$ .

The characteristic roots are $r=4$ and $r=-2$ . Then the general solution is

$\boxed{y = C_1 e^{4x} + C_2 e^{-2x}}$

where $C_1,C_2$ are arbitrary constants.

(b) The characteristic equation here is

$25r^2 - 20r + 4 = (5r - 2)^2 = 0$

with a root at $r=\frac25$ of multiplicity 2. Then the general solution is

$\boxed{y = C_1 e^{2/5\,x} + C_2 x e^{2/5\,x}}$

(c) The characteristic equation is

$r^2 + 2r + 2 = (r + 1)^2 + 1 = 0$

with roots at $r = -1 \pm i$ , where $i=\sqrt{-1}$ . Then the general solution is

$y = C_1 e^{(-1+i)x} + C_2 e^{(-1-i)x}$

Recall Euler's identity,

$e^{ix} = \cos(x) + i \sin(x)$

Then we can rewrite the solution as

$y = C_1 e^{-x} (\cos(x) + i \sin(x)) + C_2 e^{-x} (\cos(x) - i \sin(x))$

or even more simply as

$\boxed{y = C_1 e^{-x} \cos(x) + C_2 e^{-x} \sin(x)}$

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