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4 years ago

Select the correct answer What is |-2.24|?

Mathematics

1 answer:

KengaRu [80]4 years ago

4 0

Answer:

2.24

Step-by-step explanation:

when there are the lines outside of it, it will always become positive.

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In the division problem, what does the 8 represent in the quotient 3653÷13=281

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Question 6 of 10 f(x) = 5x + 1) – 3 g(x) = 4 Find (f - g)(x).

alexdok [17]

Answer:

Answer:

5x + 6

Step-by-step explanation:

(f-g)(x) is nothing but f(x) - g(x)

f(x) is |5x + 1| - 3 and g(x) is 4 so the equation is [|5x+1| - 3] - [4]

Once this is solved, the answer is 5x - 6. Since there's absolute value, remove the negative and change it to a positive to get the answer 5x + 6.

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2 years ago

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

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

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

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

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

So we have

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

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

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

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