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m_a_m_a [10]
3 years ago
6

Please help me with this question​

Mathematics
1 answer:
aivan3 [116]3 years ago
5 0

Step-by-step explanation:

the answer is

1) £30

2) £ 270

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Answer:

Step-by-step explanation:

\frac{d^2 y}{dt^2} +12\frac{dy}{dt} +32y = 10e^{-2t} where f(x) is replaced by y

Take Laplace on both sides

s^2 Y -s(0)-0 +12s Y-0+32Y = \frac{10}{s+2} \\Y(s^2+12s+32) =  \frac{10}{s+2}\\Y =  \frac{10}{(s+2)(s+4)(s+8)}

We can resolve into partial fraction to get Y = L(y)

Let this equals

\frac{A}{s+2} +\frac{B}{s+4} +\frac{C}{s+8} \\10 = A(s+4)(s+8) + B(s+2)(s+8) +Cs+4)(s+2) \\

Solving we get

s=-9

24C = 10 or C =5/12

s=-2:  A=10/12=5/6

s=-4: B = -5/4

Taking inverse Laplace

y(t) = \frac{-5e^{-4t} }{4} + \frac{5e^{-8t} }{12} +\frac{-5e^{-2t} }{6}

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3 years ago
Hi, I don't need this really fast, but I really don't understand how to do surface area and lateral surface area with rectangula
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The surface area is the area that describes the material that will be used to cover a geometric solid. When we determine the surface areas of a geometric solid we take the sum of the area for each geometric form within the solid.

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