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Scilla [17]
3 years ago
6

Use the Laplace transform to solve differential equation

Mathematics
1 answer:
Inessa [10]3 years ago
4 0
Using Laplace transform we have:L(x')+7L(x) = 5L(cos(2t))sL(x)-x(0) + 7L(x) = 5s/(s^2+4)(s+7)L(x)- 4 = 5s/(s^2+4)(s+7)L(x) = (5s - 4s^2 -16)/(s^2+4)
=> L(x) = -(4s^2 - 5s +16)/(s^2+4)(s+7) 
now the boring part, using partial fractions we separate 1/(s^2+4)(s+7) that is:(7-s)/[53(s^2+4)] + 1/53(s+7). So:
L(x)= (1/53)[(-28s^2+4s^3-4s^2+35s-5s^2+5s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]L(x)= (1/53)[(4s^3 -37s^2 +40s)/(s^2+4) + (-4s^2+5s-16)/(s+7)]
denoting T:= L^(-1)and x= (4/53) T(s^3/(s^2+4)) - (37/53)T(s^2/(s^2+4)) +(40/53) T(s^2+4)-(4/53) T(s^2/s+7) +(5/53)T(s/s+7) - (16/53) T(1/s+7)
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<img src="https://tex.z-dn.net/?f=%5Csqrt%7B%5Cfrac%7B-140%7D%7B%5Csqrt%7B28%7D%20%7D" id="TexFormula1" title="\sqrt{\frac{-140}
Zanzabum

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This is the answer

8 0
2 years ago
A point R (-2,5) is mapped to point R',as described by a translation of 6 units to the rights and 7 units down.Mark R' on the co
laila [671]

Answer:

(4, -2)

Step-by-step explanation:

Given a point R (-2,5), if the point R' is described by a translation of 6 units to the rights and 7 units down, then the coordinate of R' will be;

6 units to the rights is towards the positive x axis

7 units down is towards the negative y axis

R' = (-2+6, 5-7)

R' = (4, -2)

Hence the coordinate point of R' on the plane is (4, -2)

4 0
3 years ago
Sarai is mixing a solution. She pours all the liquid from a full small beaker into a larger beaker. The liquid fills the large b
n200080 [17]

Answer:

2000 ml

Step-by-step explanation:

Given: Sarai pours all the liquid from a full small beaker into a larger    beaker.

           The liquid fills the large beaker to 15% of its capacity.

            The small beaker holds 300 ml.

Lets assume capacity of large beaker to hold be "x".

As given, Sarai pours all the liquid from a full small beaker into a larger beaker

∴ 15\% \times x= 300\ ml

⇒ 0.15x= 300

Dividing both side by 0.15

⇒x= \frac{300}{0.15}

∴ x= 2000\ ml

Hence, the large beaker can hold 2000 ml of liquid.

3 0
3 years ago
When the center of Earth is 3.8 × 105 kilometers from the center of the moon, the force of gravity between Earth and the moon is
kow [346]
I think the answer to you question is 35 i might be wrong tho but it may work.
7 0
3 years ago
In a smoking survey among boys between the ages of 12 and 17, 78% prefer to date nonsmokers, 1% prefer to date smokers, and 21%
Ganezh [65]

Answer:

i think it is a

Step-by-step explanation:

4 0
3 years ago
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