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Galina-37 [17]
3 years ago
10

Use appropriate algebra and theorem 7.2.1 to find the given inverse laplace transform. (write your answer as a function of t.) −

1 1 s2 − 720 s7

Mathematics
1 answer:
aleksley [76]3 years ago
4 0
When it comes to laplace equations, there are transformation equations to follow. Generally, when you want to transform a laplace equation, you change the equation from f(t) to F(s). If you do the reverse, it is called the reverse laplace equation.

Based on the given, the useful transformation equation is shown in the attached picture.

When the term is s^2, that must mean that the equation is 1!/s^(1+1) to yield 1/s^2. This means that n=1. Taking the reciprocal s^2 must be equal to 1/t. Thus, for the first term, -11s^2 is equal to -11/t. For the second term, n must be equal to 6 so that 6!/s^(6+1) would yield 720/s^7. Thus, 720s^7 is equal to 1/t^6. 

Hence, the transformed equation is -11/t - 1/t^6

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A scientist is investigating whether percent concentration can be used to predict density in apple juice. A scientist selected a
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Answer:

The most appropriate inference procedure for the investigation is;

a. A linear regression t-interval for the slope

Step-by-step explanation:

Given that the slope of an horizontal line is zero, we have that there is no change in the y (dependent) variable when there is a change in the x-variable, therefore, it is important to find the true relationship between the two variables, 'x', and 'y'

The confidence interval of the slope is calculated and analyzed to determine if it excludes or includes, 0, such that, if the confidence interval exclude 0, then, it is unlikely that the slope is 0, therefore, there the relationship between the variables, 'x', and 'y' is significant

Therefore, a linear regression t-interval for the slope is most appropriate.

3 0
3 years ago
Find the average rate of change of f(x)=-x^2+2x+2 from x=2 to x=6. Simplify your answer as much as possible.
Eduardwww [97]

Answer:

- 6

Step-by-step explanation:

The average rate of change of f(x) in the closed interval [ a, b ] is

\frac{f(b)-f(a)}{b-a}

Here [ a, b ] = [ 2, 6 ] , then

f(b) = f(6) = - 6² + 2(6) + 2 = - 36 + 12 + 2 = - 22

f(a) = f(2) = - 2² + 2(2) + 2 = - 4 + 4 + 2 = 2 , then

average rate of change = \frac{-22-2}{6-2} = \frac{-24}{4} = - 6

8 0
3 years ago
Choose the graph that represents the linear equation y = 2x + 1
amid [387]

Answer:

The third option is the answer.

Step-by-step explanation:

In the formula <em>y = mx + b</em>, using the equation given,

  • <em>m = 2</em>, which means that the line goes up <em>2 units and right 1 unit</em>.
  • <em>b = 1</em>, which means that the <em>y-intercept</em>, or where the line touches the y-axis, is <em>1</em>.
8 0
2 years ago
4x+6=2x+10 find value of x makes equation true
forsale [732]

Answer:

x = 2

Step-by-step explanation:

4x + 6 = 2x + 10 \\  \\ 4x - 2x = 10 - 6 \\  \\ 2x = 4 \\  \\ x =  \frac{4}{2}  \\  \\ x = 2

5 0
3 years ago
Read 2 more answers
If f(x) = 2x - 8 and g(x) = x4, what is (gºf)(5)?​
Readme [11.4K]

Answer:

(g°f)x =16 when x = 5

Step-by-step explanation:

It might be easier to understand if you wrote this the other acceptable way.

g(x) = x^4

f(x) = 2x - 8

g(f(x))  means that in g(x) wherever you see and x you put f(x)

g(f(x)) = (f(x) ) ^ 4 Now put in the general value for f(x)

g(2x - 8) = (2x - 8)^4

You really don't want to expand this (although it would give you the right answer eventually).

g(2*5 - 8) = (2 * 5 - 8)^4

g(2*5 - 8) = (10 - 8)^4

g(2*5 - 8) = 2^4

Answer 16

8 0
3 years ago
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