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2 years ago

Mar 19, 1:51:44 PM

Mathematics

1 answer:

saveliy_v [14]2 years ago

4 0

Answer:

selected variable divided by total

variables

4/29

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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

Whats the answer for 6×6

Tatiana [17]

The correct answer is 64 bc 6 times 6 is 64

7 0

3 years ago

Read 2 more answers

Every time you conduct a hypothesis test, there are four possible outcomes of your decision to reject or not reject the null hyp

almond37 [142]

Answer:

1. A. You allow the passenger to board his flight when the passenger has a weapon.

2. B. You select the passenger for further inspection when the passenger has no weapon.

Explanation:

1. Remember, a Type I error in simple words means that the assumption "the passenger has a weapon" (null hypothesis) is actually true, but the airport security screener incorrectly concluded it is false. In other words, he assumed the passenger had no weapon and allowed the passenger to board his flight when he actually did have one.

2. While, a Type II error means that the assumption "the passenger has a weapon" (null hypothesis) is actually false, but the airport security screener incorrectly concluded it is true. In other words, he assumed the passenger had a weapon and selected the passenger for further inspection when he actually didn't have one.