The average number of newspapers for sale in an airport stand is 15. SD is 6. The average age of the pilots is 36 and SD is 4. W
1 answer:
Answer:
The average age of pilots has a lower coefficient of variation, so it is the most consistent data set.
Step-by-step explanation:
The coefficient of variation is used to measure consistency of a data set. It is the standard deviation divided by the mean. The higher the coefficient of variation, the more variable, that is, the least consistent the data set is.
The average number of newspapers for sale in an airport stand is 15. SD is 6.
The consistency is:
The average age of the pilots is 36 and SD is 4.
The consistency is:
The average age of pilots has a lower coefficient of variation, so it is the most consistent data set.
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Take the Laplace transform of both sides:
L[y'' - 4y' + 8y] = L[δ(t - 1)]
I'll denote the Laplace transform of y = y(t) by Y = Y(s). Solve for Y :
(s²Y - s y(0) - y'(0)) - 4 (sY - y(0)) + 8Y = exp(-s) L[δ(t)]
s²Y - 4sY + 8Y = exp(-s)
(s² - 4s + 8) Y = exp(-s)
Y = exp(-s) / (s² - 4s + 8)
and complete the square in the denominator,
Y = exp(-s) / ((s - 2)^2 + 4)
Recall that
L⁻¹[F(s - c)] = exp(ct) f(t)
In order to apply this property, we multiply Y by exp(2)/exp(2), so that
Y = exp(-2) • exp(-s) exp(2) / ((s - 2)² + 4)
Y = exp(-2) • exp(-s + 2) / ((s - 2)² + 4)
Y = exp(-2) • exp(-(s - 2)) / ((s - 2)² + 4)
Then taking the inverse transform, we have
L⁻¹[Y] = exp(-2) L⁻¹[exp(-(s - 2)) / ((s - 2)² + 4)]
L⁻¹[Y] = exp(-2) exp(2t) L⁻¹[exp(-s) / (s² + 4)]
L⁻¹[Y] = exp(2t - 2) L⁻¹[exp(-s) / (s² + 4)]
Next, we recall another property,
L⁻¹[exp(-cs) F(s)] = u(t - c) f(t - c)
where F is the Laplace transform of f, and u(t) is the unit step function
To apply this property, we first identify c = 1 and F(s) = 1/(s² + 4), whose inverse transform is
L⁻¹[F(s)] = 1/2 L⁻¹[2/(s² + 2²)] = 1/2 sin(2t)
Then we find
L⁻¹[Y] = exp(2t - 2) u(t - 1) • 1/2 sin(2 (t - 1))
and so we end up with
y = 1/2 exp(2t - 2) u(t - 1) sin(2t - 2)
Answer:
172.70 sq. ft.
Step-by-step explanation:
The surface area of a circular cone is
r = radius of base l = slant height
r = 4.4 and l = 8.1
SA = 3.14(19.36) + 111.9096
= 60.7904 + 111.9096
= 172.70 sq. ft.