Ask question

Ask question

All categories

3 years ago

13

Jessica packed 1-inch cubes into a box with a volume of 144 cubic inches how many layers of 1-inc cubes did Jessica pack

1 answer:

alexdok [17]3 years ago

7 0

Maybe 3 or 6 or 8, the formula for the volume of a rectangular prism = a * b * c. A<span>, B, C are the length, width, and height. and 3*6*8=144</span>

You might be interested in

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

Answer The Question and get 50 Points + Brainliest !!!!

Hatshy [7]

Answer:

Well i mean i know i am is college but i have not learned it yet. sorry :(

Step-by-step explanation:

7 0

2 years ago

Hi sorry im slow could anyone help ?

vivado [14]

Step-by-step explanation:

your answer is 60

hope it helps :)

6 0

3 years ago

Read 2 more answers

The sum of thee consecutive ODD integers is -21

Svetach [21]

15252 is the correct a set

5 0

3 years ago

Read 2 more answers

a club has two membership levels gold and silver gold members pay 10$ per year and silver members pay 5 per year.The Club collec

Oliga [24]

Answer:

A

Step-by-step explanation:

CAUSE MATH

I GOT THE SAME QUESTION AND GOT IT CORRECT. YEET :))))))))

6 0

3 years ago