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4 years ago

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Why does Y equal Mxb?

1 answer:

Deffense [45]4 years ago

7 0

It's just the slope formula.

y = mx + b

The "m" is the slope.

The "b" is the y-intercept.

The y and the x don't change.

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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

2 years ago

What is the exponent in the expression 7^6 ? 6 7 13 42

Illusion [34]

The exponent is 6, since 7^6 is the same as (see picture).

5 0

3 years ago

Read 2 more answers

Bryanna is thinking of two numbers. Their sum is −7. One of the numbers is 11. Write an

Kryger [21]

Answer:

-18 is the answer please brainlist

Step-by-step explanation:

6 0

3 years ago

Monica took a survey of her classmates' hair and eye color. The results are in the table below.

jolli1 [7]

Answer:

let R represent red hair

let G represent green eyes

<em>from</em><em> </em><em>Baye's</em><em> </em><em>theorem</em><em>:</em>

<em> $P( \frac{R}{G} ) = \frac{P(RnG)}{P(G)}$ </em>

P(RnG) = 5

$P(G) = { \sum}(green \: hair) \\ = (3 + 5 + 5) \\ = 13$

Therefore:

$P( \frac{R}{G} ) = \frac{5}{13} \\ = 0.385$

The conditional relative frequency = 0.385

4 0

3 years ago

The Japanese 5 yen coin has a hole in the middle.

alexandr402 [8]

Answer:

Subtract the two diameters and multiply by 0.5

Step-by-step explanation:

Calculating the Radius of the hole gives distance to the inner edges WHILE the Radius of the coin gives us the distance to the outer edges.

By subtracting the output we can then get the difference between both distances.

If hole diameter = 5mm and coin diameter = 22mm

Difference = [(22 - 5)mm] ÷ 2

17mm / 2 = 8.5mm

5 0

3 years ago