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2 years ago

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Describe the data for a correlational research study and explain how these data are different from the data obtained in experime

ntal and nonexperimental studies, which also evaluate relationships between two variables. A correlational study satisfies which conditions?

1 answer:

stepladder [879]2 years ago

8 0

Answer:

Step-by-step explanation:

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Consider the initial value problem y′+5y=⎧⎩⎨⎪⎪0110 if 0≤t<3 if 3≤t<5 if 5≤t<[infinity],y(0)=4. y′+5y={0 if 0≤t<311 i

rosijanka [135]

It looks like the ODE is

$y'+5y=\begin{cases}0&\text{for }0\le t$

with the initial condition of $y(0)=4$ .

Rewrite the right side in terms of the unit step function,

$u(t-c)=\begin{cases}1&\text{for }t\ge c\\0&\text{for }t$

In this case, we have

$\begin{cases}0&\text{for }0\le t$

The Laplace transform of the step function is easy to compute:

$\displaystyle\int_0^\infty u(t-c)e^{-st}\,\mathrm dt=\int_c^\infty e^{-st}\,\mathrm dt=\frac{e^{-cs}}s$

So, taking the Laplace transform of both sides of the ODE, we get

$sY(s)-y(0)+5Y(s)=\dfrac{e^{-3s}-e^{-5s}}s$

Solve for $Y(s)$ :

$(s+5)Y(s)-4=\dfrac{e^{-3s}-e^{-5s}}s\implies Y(s)=\dfrac{e^{-3s}-e^{-5s}}{s(s+5)}+\dfrac4{s+5}$

We can split the first term into partial fractions:

$\dfrac1{s(s+5)}=\dfrac as+\dfrac b{s+5}\implies1=a(s+5)+bs$

If $s=0$ , then $1=5a\implies a=\frac15$ .

If $s=-5$ , then $1=-5b\implies b=-\frac15$ .

$\implies Y(s)=\dfrac{e^{-3s}-e^{-5s}}5\left(\frac1s-\frac1{s+5}\right)+\dfrac4{s+5}$

$\implies Y(s)=\dfrac15\left(\dfrac{e^{-3s}}s-\dfrac{e^{-3s}}{s+5}-\dfrac{e^{-5s}}s+\dfrac{e^{-5s}}{s+5}\right)+\dfrac4{s+5}$

Take the inverse transform of both sides, recalling that

$Y(s)=e^{-cs}F(s)\implies y(t)=u(t-c)f(t-c)$

where $F(s)$ is the Laplace transform of the function $f(t)$ . We have

$F(s)=\dfrac1s\implies f(t)=1$

$F(s)=\dfrac1{s+5}\implies f(t)=e^{-5t}$

We then end up with

$y(t)=\dfrac{u(t-3)(1-e^{-5t})-u(t-5)(1-e^{-5t})}5+5e^{-5t}$

3 0

3 years ago

Find the HCF of 64 and 80.

Varvara68 [4.7K]

Answer:

64=2✖️2✖️2✖️2✖️2✖️2

80=2✖️2✖️2✖️2✖️2✖️5

Common factors=2✖️2✖️2✖️2

As HCF= Product of common factors

HCF =2✖️2✖️2✖️2

HCF=16

Step-by-step explanation:

I hope this will help you:)

7 0

3 years ago

Read 2 more answers

Someone, please help me with this.<br> Correct answers get brainiest

Phantasy [73]

Answer:

3

-3

sqrt(9)

-sqrt(9)

Step-by-step explanation:

What number multiplied by itself will give you 9

3*3 =9

-3*-3 =9

sqrt(9) * sqrt(9) = sqrt(81) = 9

-sqrt(9) * -sqrt(9) = + sqrt(81) =9

7 0

2 years ago

Read 2 more answers

4 - 10q = -2q + 10 - 9 q

andrew-mc [135]

Answer:

q = 6

Step-by-step explanation:

Isolate the variable by dividing each side by factors that don't contain the variable.

3 0

2 years ago

Read 2 more answers

Help me please !!!!!!!

AfilCa [17]

Use the given times and velocities to make two points: (1,4) and (2,2)

Part A:

Slope is the change in Y over the change in X from the two pints you made:

Slope = (2-4) / (2-1 )= -2

Now you have the slope, calculate the Y-intercept

y = -2x + b

Using (1,4)

4 = -2(1) + b = 4 =-2 +b. b = 6

Equation is: y = -2x+6

Part B:

using the above equation replace x with 1, 2, 3, and 4 and solve for the Y

then plot those onto a graph

6 0

2 years ago