Find the inverse Laplace transform of F (s)=2/s^3

Mathematics

1 answer:

IceJOKER [234]2 years ago

4 0

Recall that for integers <em>n</em> > -1,

$L_s\left\{t^n\right\} = \dfrac{n!}{s^{n+1}}$

Then

$\displaystyle L^{-1}_t\left\{\frac2{s^3}\right\} = L^{-1}_t\left\{\frac{2!}{s^{2+1}}\right\} = \boxed{t^2}$

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Given two central angles in any two circles, the ratio of the arc length to the radius of each corresponding circle is equal if

krok68 [10]

First, we have
s1/r1 = s2/r2

The question also states the fact that
s/2πr = θ/360°

Rearranging the second equation, we have
s/r = 2πθ/360°

Then we substitute it to the first equation
s1/r1 = 2πθ1/360°
s2/r2 = 2πθ2/360°

which is now
2πθ1/360° = 2πθ2/360°

By equating both sides, 2π and 360° will be cancelled, therefore leaving
θ1 = θ2

6 0

3 years ago

Which function represents g(x), a reflection of f(x) = 6(one-third) Superscript x across the y-axis?

Rasek [7]

The function $g(x)=6(3)^{x}$ represents a reflection of $f(x)=6(\frac{1}{3})^{x}$ across the y-axis ⇒ 3rd answer

Step-by-step explanation:

Let us revise the reflection across the axes

If the function f(x) reflected across the x-axis, then its image is g(x) = - f(x)
If the function f(x) reflected across the y-axis, then its image is g(x) = f(-x)

∵ $f(x)=6(\frac{1}{3})^{x}$

∵ g(x) is the image of f(x) after reflection across the y-axis

- From the rule above reflection across the y-axis changes the sign of x

∴ $g(x)=6(\frac{1}{3})^{-x}$

∵ $(a)^{-n}=(\frac{1}{a})^{n}$

∵ $(\frac{1}{a})^{-n}=(a)^{n}$

∴ $(\frac{1}{3})^{-x}=(3)^{x}$

∴ $g(x)=6(3)^{x}$

The function $g(x)=6(3)^{x}$ represents a reflection of $f(x)=6(\frac{1}{3})^{x}$ across the y-axis

Learn more:

You can learn more about reflection in brainly.com/question/5017530

#LearnwithBrainly

7 0

3 years ago

Read 2 more answers

The manufacturing of a ball bearing is normally distributed with a mean diameter of 22 millimeters and a standard deviation of .

Misha Larkins [42]

Answer:

0.1507 or 15.07%.

Step-by-step explanation:

We have been given that the manufacturing of a ball bearing is normally distributed with a mean diameter of 22 millimeters and a standard deviation of .016 millimeters. To be acceptable the diameter needs to be between 21.97 and 22.03 millimeters.

First of all, we will find z-scores for data points using z-score formula.

$z=\frac{x-\mu}{\sigma}$ , where,