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3 years ago

15

Can anyone do this? My teacher is out for a few months and sub tried to teach us this and it just did not work.

1 answer:

Marina86 [1]3 years ago

6 0

Graph the points that are givin

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Consider the system of differential equations dxdt=−4ydydt=−4x. Convert this system to a second order differential equation in y

koban [17]

$\dfrac{\mathrm dy}{\mathrm dt}=-4x\implies x=-\dfrac14\dfrac{\mathrm dy}{\mathrm dt}\implies\dfrac{\mathrm dx}{\mathrm dt}=-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}$

Substituting this into the other ODE gives

$-\dfrac14\dfrac{\mathrm d^2y}{\mathrm dt^2}=-4y\implies y''-16y=0$

Since $x(t)=-\dfrac14y'(t)$ , it follows that $x(0)=-\dfrac14y'(0)=4\implies y'(0)=-16$ . The ODE in $y$ has characteristic equation

$r^2-16=0$

with roots $r=\pm4$ , admitting the characteristic solution

$y_c=C_1e^{4t}+C_2e^{-4t}$

From the initial conditions we get

$y(0)=5\implies 5=C_1+C_2$

$y'(0)=16\implies-16=4C_1-4C_2$

$\implies C_1=\dfrac12,C_2=\dfrac92$

So we have

$\boxed{y(t)=\dfrac12e^{4t}+\dfrac92e^{-4t}}$

Take the derivative and multiply it by -1/4 to get the solution for $x(t)$ :

$-\dfrac14y'(t)=\boxed{x(t)=-\dfrac12e^{4t}+\dfrac92e^{-4t}}$

7 0

3 years ago

Which graphs are functional?

Daniel [21]

Answer:

2 and 5

Step-by-step explanation:

5 0

3 years ago

-45 divided by -9 .........

dmitriy555 [2]

5 because it’s a double negative which offsets the answer to be positive 5

7 0

2 years ago

Read 2 more answers

Need help please?????

Fantom [35]

Its C, sorry for the kinda late answer

7 0

3 years ago

A trough is filled with water. The trough holds 315 gallons. Each cubic foot of water contains about 7.5 gallons. The trough is

elena55 [62]

Answer:

The height of the trough is about 1.5 ft

Step-by-step explanation:

If each cubic foot of water contains about 7.5 gallons.

Then; 315 gallons is about $\frac{315}{7.5}=42ft^3$

Let h be the height of the trough, then

$7\times 4\times h=42$

This implies that;

$28h=42$

Divide both sides by 28 to get:

$h=\frac{42}{28}$

$\therefore h=1.5$

The height of the trough is about 1.5 ft

4 0

3 years ago