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lara [203]
3 years ago
8

5x + 3y = -4 y - 2x = 6 By substitution

Mathematics
1 answer:
Assoli18 [71]3 years ago
4 0

Answer:

Hello!

Solve the following system of equations by the substitution method. 5x = y + 6 2x - 3y = 4 What is the value of the y-coordinate?

Solving:

5x = y + 6 (I)

2x - 3y = 4 (II)

god i hope i helped if i did tell me so in not plz still tell me and i will make it better see ya

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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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1 year ago
The sides of an open lot are measured in feet. Which unit could you use to describe the
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square feet

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Area has units of squared length.

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3 years ago
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A crane is rented at $1000 per day plus a charge per hour of use. The crane was used for 7 hours on a day, and the total charge
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The equation can be (3450-1000)<span>÷7=350.</span>
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3 years ago
In a theater, there are 4 long rows of chairs,each with an equal number of chairs There are 5 ahort rows of chairs,each with an
Hoochie [10]
<span>There are 4 long rows and 5 short rows in the theater. x represents the number of chairs in each long row and y represents the number of chairs in each short row.

So, total number of chairs in 4 long rows= 4x
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Multiply x^2+5•x^3+7 <br> I’m getting x^5+5x^3+7x^2+35 But I’m not sure if I’m right
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Answer:

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To put into standard form, rearrange from highest power to lowest power:

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