A dress which costs $180 is being sold at a discount of 10%. The amount of the discount is

(5) Find the Laplace transform of the following time functions: (a) f(t) = 20.5 + 10t + t 2 + δ(t), where δ(t) is the unit impul

Aloiza [94]

Answer

(a) $F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

Step-by-step explanation:

(a) $f(t) = 20.5 + 10t + t^2 +$ δ(t)

where δ(t) = unit impulse function

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 f(s)e^{-st} \, dt$

where a = ∞

=> $F(s) = \int\limits^a_0 {(20.5 + 10t + t^2 + d(t))e^{-st} \, dt$

where d(t) = δ(t)

=> $F(s) = \int\limits^a_0 {(20.5e^{-st} + 10te^{-st} + t^2e^{-st} + d(t)e^{-st}) \, dt$

Integrating, we have:

=> $F(s) = (20.5\frac{e^{-st}}{s} - 10\frac{(t + 1)e^{-st}}{s^2} - \frac{(st(st + 2) + 2)e^{-st}}{s^3} )\left \{ {{a} \atop {0}} \right.$

Inputting the boundary conditions t = a = ∞, t = 0:

$F(s) = \frac{20.5}{s} - \frac{10}{s^2} - \frac{2}{s^3}$

(b) $f(t) = e^{-t} + 4e^{-4t} + te^{-3t}$

The Laplace transform of function f(t) is given as:

$F(s) = \int\limits^a_0 (e^{-t} + 4e^{-4t} + te^{-3t} )e^{-st} \, dt$

$F(s) = \int\limits^a_0 (e^{-t}e^{-st} + 4e^{-4t}e^{-st} + te^{-3t}e^{-st} ) \, dt$

$F(s) = \int\limits^a_0 (e^{-t(1 + s)} + 4e^{-t(4 + s)} + te^{-t(3 + s)} ) \, dt$

Integrating, we have:

$F(s) = [\frac{-e^{-(s + 1)t}} {s + 1} - \frac{4e^{-(s + 4)}}{s + 4} - \frac{(3(s + 1)t + 1)e^{-3(s + 1)t})}{9(s + 1)^2}] \left \{ {{a} \atop {0}} \right.$

Inputting the boundary condition, t = a = ∞, t = 0:

$F(s) = \frac{-1}{s + 1} - \frac{4}{s + 4} - \frac{4}{9(s + 1)^2}$

3 0

2 years ago

A box of 8 snack bars costs $24.72. A single snack bar costs $3.47. What is the savings on each snack bar if you buy a box of 8

sweet [91]

You would save $3.04

4 0

3 years ago

Read 2 more answers

What is the answer????????? help

fenix001 [56]

80

adding up the numbers 30,20,5,25

maybe im wrong but i hope it helps...

8 0

2 years ago

Carla drops a carton of eggs. out of 12 eggs, 7 eggs are cracked. as a decimal, what fraction of the eggs are not cracked? [roun

anyanavicka [17]

There are 5 eggs which remained. In a fraction, the eggs which are not cracked is expressed as 5/12. Converting it to decimals, the answer is 0.4166667. Since the answer only requires 2 decimal places, the number has to be rounded off to the hundredths place. Since 6 is more than 5, the value of the hundredths place is added by 1. Hence the final answer is 0.42.

4 0

3 years ago

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Forty students took a statistics exam having a maximum of 50 points. The distribution of score is given in the stem-and-leaf plo

Aneli [31]

Based on the fact that Tess's score was 25 in the statistics exam as shown by the stem-and-leaf plot, her Tess's percentile was 30th.

<h3>What was Tess's percentile?</h3>

Tess's percentile depends on the number of people whose scores she is above.

When looking at the stem-and-leaf plot, we see that Tess's score of 25 is the 13th score.

Her percentile is therefore:

= (13 - 1) / 40

= 12 / 40

= 30th percentile

Rest of the question is:

Tess’s score was 25. What was her percentile?

Find out more on percentile scores at brainly.com/question/24245405

#SPJ1

5 0

1 year ago