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2 years ago

1. The area of a rectangular carpet is X² + X - 2. HINT: Area = length X breadth

Mathematics

1 answer:

Ainat [17]2 years ago

6 0

Answer:

look above

Step-by-step explanation:

hopeit hepls

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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

Can someone answer this i’ll give u a cookie PLEASE I NEED IT NOW

AleksandrR [38]

Answer:

its c

Step-by-step explanation:

4 0

3 years ago

What is the multiple of 9 but is also a factor of 9

Natali5045456 [20]

Answer:

the answer i believe is 3

4 0

3 years ago

Read 2 more answers

If you answer the question correct and show steps i will mark you brainiest

olasank [31]

Im pretty sure x=4
because, if LO BISECTS NLM then it splits it in half, and if one of the halves is 4 then the other also should be.
im so sorry if its wrong

5 0

3 years ago

Bill and his dad are building a deck on the back of their house. The scale on the building plan is 1 in. = 4 ft. If the length o

choli [55]

Answer:

14 feet

Step-by-step explanation:

4 x 3 = 12ft

4 / 2

2 + 12

answer is 14 ft

8 0

3 years ago