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3 years ago

15

At a local fair, a hamburger cost $2.50, and a drink cost $1.50. Write an expression that represents the cost of x number of ham

burgers and y number of drinks.

2 answers:

TEA [102]3 years ago

8 0

Answer:

2.50x + 1.50y = z

Step-by-step explanation:

z is the cost of the hamburgers and drinks.

x and y represent the number of hamburgers and drinks.

faltersainse [42]3 years ago

3 0

Answer:

y= 2.50

Step-by-step explanation:

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Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t ≥ 0. Then the integral ℒ{f(t)} = ∞ e−

poizon [28]

$f(t)=\begin{cases}\cos t&\text{for }0\le t$

The Laplace transform is then

$\mathcal L_s\{f(t)\}=\displaystyle\int_0^\infty f(t)e^{-st}\,\mathrm dt=\int_0^\pi e^{-st}\cos t\,\mathrm dt$

Let $I$ denote the integral we want to compute. Integrating by parts, setting

$u=e^{-st}\implies\mathrm du=-se^{-st}\,\mathrm dt$

$\mathrm dv=\cos t\,\mathrm dt\implies v=\sin t$

gives

$\displaystyle I=e^{-st}\sin t\bigg|_{t=0}^{t=\pi}+s\int_0^\pi e^{-st}\sin t\,\mathrm dt$

Integrate by parts again, setting

$u=e^{-st}\implies\mathrm du=-se^{-st}\,\mathrm dt$

$\mathrm dv=\sin t\,\mathrm dt\implies v=-\cos t$

Then

$\displaystyle I=e^{-st}\sin t\bigg|_{t=0}^{t=\pi}+s\left(-e^{-st}\cos t\bigg|_{t=0}^{t=\pi}-s\int_0^\pi e^{-st}\cos t\,\mathrm dt\right)$

$I=e^{-st}(\sin t-s\cos t)\bigg|_{t=0}^{t=\pi}-s^2I$

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3 years ago

A particle is moving with the given acceleration function and initial conditions. Find the velocity function and the position fu

Lerok [7]

Answer:

The velocity function is the particle is $v(t)=-2\cos (t)-4\sin (t)-1$ .

Step-by-step explanation:

The acceleration function of a moving particle is

$a(t)=2\sin (t)-4\cos (t)$

The initial conditions are v(0) = −3, s(0) = 5.

Integrate the acceleration function with respect to time to find the velocity function.

$\int a(t)=\int (2\sin (t)-4\cos (t))dt$

$v(t)=-2\cos (t)-4\sin (t)+C_1$

Use the initial condition v(0) = −3 to find the value of C₁.

$-3=-2\cos (0)-4\sin (0)+C_1$

$-3=-2(1)-4(0)+C_1$

$-3=-2+C_1$

$-3+2=C_1$

$-1=C_1$

So the velocity function is the particle is

$v(t)=-2\cos (t)-4\sin (t)-1$

Integrate the acceleration function with respect to time to find the position function.

$\int v(t)=\int (-2\cos (t)-4\sin (t)-1)dt$

$s(t)=-2\sin (t)+4\cos (t)-t+C_2$

Use the initial condition s(0) = 5 to find the value of C₂.

$5=-2\sin (0)+4\cos (0)-(0)+C_2$

$5=-2(0)+4(1)+C_2$

$5=4+C_2$

$1=C_2$

So, the position function is the particle is $s(t)=-2\sin (t)+4\cos (t)-t+1$ .

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Hope that this helps!

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3 years ago