3 Given that the Laplace transform of x is F(3) 1
derive the
Laplace transform of xl without using the integral definition
4 Use the Laplace transform to volve each of the following equations.
(a) f(x) + f(x) = x where f(0) = 0
(b) f(x) -x) = where f(0) = -1
(c) '(x) + 48*(x) + 4) where 0 = 0 and (0) - 0
(d) 48" (x) - 9f(x) = -18 where f(0) = 0 and f(0) 0
3 Show that if F() - )
xxx then:
(a) () F() L()) m (*) - 110
Use part (a) to find
(b) 01 Lsin 2x) ir 11x cos3x)
(c) What would you say the mh derivative of Fs) is equal to?
4 Show that it (x)} F($) then La) F's - A) where is a
constant
Hunce hind
(a) (sinha)
(b) cosbx) where a and b are constants in both cases

Bob is putting books on a shelf and takes a break after filling 18 1/2 inches on the book shelf. the book shelf is now 2/3 full. how long is the entire bookshelf?

1. the manager of collins import autos believes the number of cars sold in a day (q) depends on two factors: (1) the number of hours the dealership is open (h) and (2) the number of salespersons working that day (s). after collecting data for two months (53 days), the manager estimates the following log-linear model: q 4 equation 1 a. explain, how to transform the log-linear model into linear form that can be estimated using multiple regression analysis. the computer output for the multiple regression analysis is shown below: q4 table b. how do you interpret coefficients b and c? if the dealership increases the number of salespersons by 20%, what will be the percentage increase in daily sales? c. test the overall model for statistical significance at the 5% significance level. d. what percent of the total variation in daily auto sales is explained by this equation? what could you suggest to increase this percentage? e. test the intercept for statistical significance at the 5% level of significance. if h and s both equal 0, are sales expected to be 0? explain why or why not? f. test the estimated coefficient b for statistical significance. if the dealership decreases its hours of operation by 10%, what is the expected impact on daily sales?

In terms of x, find an expression that represents the area of the shaded region. the outer square has side lengths of (x+5) and the inner square has side lengths of (x-2), as shown. area: a1 x + a2 square units submit