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2 years ago

13

the PTA makes a $5.00 profit on each school sweatshirt sell. If they made a profit of $2,170.00, how many sweatshirts did they s

ell?

1 answer:

Helga [31]2 years ago

5 0

It is 434 because 2170 ÷5 equals 434

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What is a good calculator that will give you the points to linear inequality systems?

satela [25.4K]

Answer:

I would just recommend you using M A T H W A Y and paying for the measly little $9.99 for the step-by-step answers.

Step-by-step explanation:

Or desmos would work but I would highly recommend m a t h w a y

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2 years ago

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

Please help me pleaseee

devlian [24]

I’m pretty sure it’s CB since it’s going the opposite direction!! :)

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2 years ago

What is the best deal 2.50 for 1 pint or 4.50 for 1 quart

Sonbull [250]

$4.50 depending on hum much you use

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3 years ago

the October meeting of the yearbook club had 21 people attend. That was 3 times as many people as the number of people who came

kolbaska11 [484]

October meeting is 3 times more than the number of people at September meeting.
Sept meeting = 21 ÷ 3 = 7

7 people were at the September meeting.

7 0

2 years ago

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