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3 years ago

10 + 5 + 5 ( 10 + 10 )

Mathematics

1 answer:

Shalnov [3]3 years ago

8 0

Answer:

The answer is 115 you do parentheses first and multiply 5 by the number in the parentheses and then add

Step-by-step explanation:

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(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

3 years ago

Hey, this question is really simple but im a little tired and can't seem to get it.. 25 points and brainliest- please help out.

Nimfa-mama [501]

Answer:1/3

Step-by-step explanation:

It’s 4/12 so divide both numbers by 4 is 1/3

5 0

3 years ago

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A bottle of italian salad contains 0.7 grams of sugar. How many milligrams of sugar are in 6 bottles of italian salad dressing

tatyana61 [14]

Answer:

420mg

Step-by-step explanation:

0.7x6 = 0.42g which is 420mg

1g = 1000mg

8 0

3 years ago

The neighborhood swimming pool drains at a rate of 99 gallons every 3 hours. At this rate, how many gallons are

Ivahew [28]

Answer:

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Step-by-step explanation:

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3 years ago

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A scale drawing of a lake has a scale of 1 cm to 80 m. If the actual width was f the lake is 1,000 m, what is the width of the l

Veseljchak [2.6K]

Answer:

12,5 centimeters.

Step-by-step explanation:

We take the following proportion

$\frac{1 cm}{80m} = \frac{x}{1000m}$

Which becomes:

$1000 = 80x$

And then, we clear out the variable x:

$\frac{1000}{80}=\frac{100}{8}=\frac{50}{4}=12,5$

And this means that the width of the lake on the scale drawing will be 12.5 cm.

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3 years ago