1. 4.2 from textbook consider the following transfer function: (a) what is the steady-state gain? (b) what is the time constant? (c) if u(s) = 4/s, what is the value of the output y(t) when t → [infinity]? (d) for the same input, what is the value of the output when t = 10? what is the output when expressed as a fraction of the new steady-state value? (e) if u(s) = (1 – e-s)/s, the unit rectangular pulse, what is the output when t → [infinity]? (f) if u(t) = δ(t), the unit impulse at t = 0, what is the output when t → [infinity]? (g) if u(t) = 5 sin 2t, what is the value of the output when t → [infinity]?

step-by-step explanation:

u = -(6/7)w

step-by-step explanation:

place all values with 'u' on one side of the equation.

4u + 8w = - 3u + 2w

4u + 3u = 2w - 8w

further simplify the equation by solving the addition and subtraction.

7u = - 6w

make 'u' the independent variable by placing its co-efficient on the right-hand side.

u = - (6/7)w

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step-by-step explanation:

a cube has 6 sides

the probability of getting 5 on the first cube is 1/6 since only one side of the cube has 5 on it.

there are 3 sides of the cube with even number on it [2,4,6]

therefore the probability of getting even number is 3/6

for both events to happen together, the probability would be

1/6 x 3/6 = 12/36

which simplifies to 1/12