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zmey [24]
3 years ago
14

Inverse laplace of [(1/s^2)-(48/s^5)]

Mathematics
1 answer:
Katen [24]3 years ago
7 0
**Refresh page if you see [ tex ]**

I am not familiar with Laplace transforms, so my explanation probably won't help, but given that for two Laplace transform F(s) and G(s), then \mathcal{L}^{-1}\{aF(s)+bG(s)\} = a\mathcal{L}^{-1}\{F(s)\}+b\mathcal{L}^{-1}\{G(s)\}

Given that \dfrac{1}{s^2} = \dfrac{1!}{s^2} and -\dfrac{48}{s^5} = -2\cdot\dfrac{4!}{s^5}

So you have \mathcal{L}^{-1}\left\{\dfrac{1}{s^2} - 2\cdot\dfrac{4!}{s^5}\right\} = \mathcal{L}^{-1}\left\{\dfrac{1}{s^2}\right\} - 2\mathcal{L}^{-1}\left\{\dfrac{4!}{s^5}\right\}

From Table of Laplace Transform, you have \mathcal{L}\{t^n\} = \dfrac{n!}{s^{n+1}} and hence \mathcal{L}^{-1}\left\{\dfrac{n!}{s^{n+1}}\right\} = t^n

So you have \mathcal{L}^{-1}\left\{\dfrac{1}{s^2}\right\} - 2\mathcal{L}^{-1}\left\{\dfrac{4!}{s^5}\right\} = \boxed{t-2t^4}.

Hope this helps...
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2. A circle of radius 12 units is divided into 8 congruent slices.
adelina 88 [10]

Answer:

a: 18pi

b: 3pi

Step-by-step explanation:

part a:

total area = 12^2*pi = 144pi

144pi/8 = 18pi

part b:

total circumference = 12*2*pi = 24pi

24pi/8 = 3pi

3 0
3 years ago
Which is the graph of f (x) = 4 (1/2) Superscript x?
miss Akunina [59]

Answer:

Option (2) is correct graph.

Step-by-step explanation:

Given:

The function to graph is given as:

f(x)=4(\frac{1}{2})^x

Now, the above function is an exponential function of the form f(x)=ka^x

Where, 'k' and 'a' are constants.

The range of an exponential function is always greater than 0.

The domain is all real numbers.

Now, for graphing it, we need to find some points on it and its end behaviour.

Now, for x = 0, the function value is given as:

f(0)=4(\frac{1}{2})^0=4

So, (0, 4) is a point on the graph.

Now, for x = 1, the function value is given as:

f(1)=4(\frac{1}{2})^1=4\times\frac{1}{2}=2

So, (1, 2) is another point on the graph.

Now, for x = 2, the function value is given as:

f(2)=4(\frac{1}{2})^2=4\times\frac{1}{4}=1

So, (2, 1) is another point on the graph.

Now, as 'x' tends to ∞, the function value tends to:

f(x\to\infty)=4\cdot\frac{1}{2}^{\infty}=\frac{4}{\infty}=0

So, as

x\to\infty,f(x)\to0\\\\x\to-\infty,f(x)\to\infty

Now, from among all the options, only option (2) fulfills all the conditions given above.

So, option (2) is correct graph.

5 0
3 years ago
Number 5 am stuck pls help
Norma-Jean [14]

Answer:

im going to be honest i havent done this since las year and so i dont remember the value of that line outside but i think its 70*

Step-by-step explanation:

reason is because the c is originally 180* but it has more of and angle so the angles obv increases and you can get the angle by multiplying 70*times 7x and divide by 3

i say 3 because of the amount of angles in a triangle and the line outside if i remember correctly is the "angles" of a triangle  and that would be your answer

4 0
2 years ago
One angle of a triangle measures 65°. The other two angles are in a ratio of 3:20. What are the measures of those two angles?
Nataly_w [17]

Answer:

15° and 100°

Step-by-step explanation:

65 + 3x + 20x = 180

23x = 115

x = 5

3 × 5 = 15, 20 × 5 = 100. So the other two angles measure 15° and 100°.

3 0
2 years ago
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a_sh-v [17]

Answer:

slope: -3/4    y-intercept: 3   equation: y=(-3/4)x+3

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