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3 years ago

Only answer this if you have an explanation and if you know what the answer is.

Mathematics

1 answer:

Pavlova-9 [17]3 years ago

6 0

The answer is C. The explanation in the previous comment section is correct

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Use the laplace transform to solve the given initial-value problem. y' 5y = e4t, y(0) = 2

Basile [38]

The Laplace transform of the given initial-value problem

$y' 5y = e^{4t}, y(0) = 2$ is mathematically given as

$y(t)=\frac{1}{9} e^{4 t}+\frac{17}{9} e^{-5 t}$

<h3>What is the Laplace transform of the given initial-value problem? y' 5y = e4t, y(0) = 2?</h3>

Generally, the equation for the problem is mathematically given as

$&\text { Sol:- } \quad y^{\prime}+s y=e^{4 t}, y(0)=2 \\\\&\text { Taking Laplace transform of (1) } \\\\&\quad L\left[y^{\prime}+5 y\right]=\left[\left[e^{4 t}\right]\right. \\\\&\Rightarrow \quad L\left[y^{\prime}\right]+5 L[y]=\frac{1}{s-4} \\\\&\Rightarrow \quad s y(s)-y(0)+5 y(s)=\frac{1}{s-4} \\\\&\Rightarrow \quad(s+5) y(s)=\frac{1}{s-4}+2 \\\\&\Rightarrow \quad y(s)=\frac{1}{s+5}\left[\frac{1}{s-4}+2\right]=\frac{2 s-7}{(s+5)(s-4)}\end{aligned}$

$\begin{aligned}&\text { Let } \frac{2 s-7}{(s+5)(s-4)}=\frac{a_{0}}{s-4}+\frac{a_{1}}{s+5} \\&\Rightarrow 2 s-7=a_{0}(s+s)+a_{1}(s-4)\end{aligned}$

$put $s=-s \Rightarrow a_{1}=\frac{17}{9}$$

$\begin{aligned}\text { put } s &=4 \Rightarrow a_{0}=\frac{1}{9} \\\Rightarrow \quad y(s) &=\frac{1}{9(s-4)}+\frac{17}{9(s+s)}\end{aligned}$

In conclusion, Taking inverse Laplace tranoform

$L^{-1}[y(s)]=\frac{1}{9} L^{-1}\left[\frac{1}{s-4}\right]+\frac{17}{9} L^{-1}\left[\frac{1}{s+5}\right]$ \\\\$

$y(t)=\frac{1}{9} e^{4 t}+\frac{17}{9} e^{-5 t}$

Read more about Laplace tranoform

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6 0

1 year ago

A data set includes data from 500 random tornadoes. The display from technology available below results from using the tornado l

lisov135 [29]

Answer:

The null and alternative hypothesis are:

$H_0:\mu =2.6\\H_a:\mu >2.6$

There is sufficient evidence to support the claim that the mean tornado length is greater than 2.6 miles

Step-by-step explanation:

Consider the provided information.

The claim that the mean tornado length is greater than 2.6 miles.

If there is no statistical significance in the test then it is know as the null which is denoted by $H_0$ , otherwise it is known as alternative hypothesis which denoted by $H_a$ .

Therefore, the required null and alternative hypothesis are:

$H_0:\mu =2.6\\H_a:\mu >2.6$

significance level α =0.05

From the given table the test statistic T=2.230166

P-value is 0.0131

0.0131<0.05

P value is less than the significance level, so reject the null hypothesis.

There is sufficient evidence to support the claim that the mean tornado length is greater than 2.6 miles

6 0

3 years ago

A fair spinner has 10 equal sections: 3 red, 3 blue and 4 green.

Natalka [10]

Answer:

Step-by-step explanation:

cool ok byeeeeeeeeeee

6 0

3 years ago

Difference of 8 Let's dig into this and find out for sure. First think of two numbers that have a difference of 8. Type the LARG

Serhud [2]

Answer:

Step-by-step explanation:

We need to find 2 numbers that have a difference of 8.

Let take's 16 and 8.

As we know :

⇒ 16 - 8

⇒ <u>8</u>

<u />

The larger of these 2 numbers is <u>16</u>

5 0

1 year ago

Select whether the number is rational, irrational, or imaginary. 1/4

rjkz [21]

Because 1/4 is a fractional number, it is also a ratio which means it is Rational. :)

7 0

3 years ago

Read 2 more answers