Lee has a jar of 100 pennies. She adds groups of 10 pennies to the jar. She adds 5 groups. What numbers does she say?

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

In college math class of 50 student are 23 are boys 27 are girls on the final exam 15 boys and 14 girls made an A. What is the p

Mila [183]

Answer:

The probability of choosing an A student is 58% (0.58 or 29/50)

Step-by-step explanation:

The fact that 23 students are boys and 27 are girls is irrelevant to the question so we can ignore that.

There are 50 students in all and out of these students 15 boys and 14 girls made an A.

We can first add 15+14 which equals 29. So 29 students out of 50 made in A on the exam.

29/50 equals 0.58 or 58%.

3 0

3 years ago

Plzzzzzss answer quickly !!!!!

xz_007 [3.2K]

Answer:

3.3 m

Step-by-step explanation:

The formula used to solve for leg a of a right triangle is a= sqrt(c^2-b^2). This is replaced by sqrt(6^2-5^2) for your equation. If you work this out, it equals about 3.32, and you have to round it to the nearest tenth, so the answer is 3.3 m.

4 0

3 years ago

Nine million, twenty three thousand in digits

Anna007 [38]

Answer:

the answer to your question is 9,023,000.

I hope this helps you, have a wonderful day!

7 0

3 years ago

Read 2 more answers

The sides of a triangle are in the ratio 5 : 12 : 13. What is the length of each side of the triangle if the perimeter of the tr

Ganezh [65]

Answer:

2.5, 6 and 6.5 inches.

Step-by-step explanation:

5 + 12 + 13 = 30

So the shortest side = 5/30 * 15 = 1/6 * 15

= 2.5 inches.

The longest = 13 / 30 * 15 = 13/2

= 6.5 inches,

and the third = 12/30 * 15

= 6 inches.

4 0

3 years ago