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Vera_Pavlovna [14]
3 years ago
14

Please answer the question.

Mathematics
1 answer:
Maksim231197 [3]3 years ago
7 0

Answer:

Every number is rational except for pi

Step-by-step explanation:

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When both variables increase together, a line can be made to represent their constant rise. This means that there is a positive correlation between the two, as one increases or decreases with the other.

The answer is A. positive correlation.
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Help will give Brainly points
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Answer:

Use the SINE RULE:

\frac{a}{ \sin( \alpha ) } =  \frac{b}{ \sin( \beta ) }

\frac{6}{ \sin(60) }  =  \frac{x}{ \sin(90) }

x =  \sin(90)  \times  \frac{6}{ \sin(60) }

x = 6.93

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9x5000x9x how many thousands
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Step-by-step explanation:

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Which of the following functions best describes this graph?
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3 years ago
Use the laplace transform to solve the given system of differential equations. dx dt + 3x + dy dt = 1 dx dt − x + dy dt − y = et
blagie [28]

Let X(s) and Y(s) denote the Laplace transforms of x(t) and y(t).

Taking the Laplace transform of both sides of both equations, we have

\dfrac{dx}{dt} + 3x + \dfrac{dy}{dt} = 1 \implies \left(sX(s) - x(0)\right) + 3X(s) + \left(sY(s) - y(0)\right) = \dfrac1s \\\\ \implies (s+3) X(s) + s Y(s) = \dfrac1s

\dfrac{dx}{dt} - x + \dfrac{dy}{dt} = e^t \implies \left(sX(s) - x(0)\right) - X(s) + \left(sY(s) - y(0)\right) = \dfrac1{s-1} \\\\ \implies (s-1) X(s) + s Y(s) = \dfrac1{s-1}

Eliminating Y(s), we get

\left((s+3) X(s) + s Y(s)\right) - \left((s-1) X(s) + s Y(s)\right) = \dfrac1s - \dfrac1{s-1} \\\\ \implies X(s) = \dfrac14 \left(\dfrac1s - \dfrac1{s-1}\right)

Take the inverse transform of both sides to solve for x(t).

\boxed{x(t) = \dfrac14 (1 - e^t)}

Solve for Y(s).

(s - 1) X(s) + s Y(s) = \dfrac1{s-1} \implies -\dfrac1{4s} + s Y(s) = \dfrac1{s-1} \\\\ \implies s Y(s) = \dfrac1{s-1} + \dfrac1{4s} \\\\ \implies Y(s) = \dfrac1{s(s-1)} + \dfrac1{4s^2} \\\\ \implies Y(s) = \dfrac1{s-1} - \dfrac1s + \dfrac1{4s^2}

Taking the inverse transform of both sides, we get

\boxed{y(t) = e^t - 1 + \dfrac14 t}

7 0
1 year ago
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