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shutvik [7]
2 years ago
10

Pls help for number 6

Mathematics
1 answer:
Vlad1618 [11]2 years ago
7 0
A: 45x + 30y = 1350
Since we don’t know how many adults and children are in the group, we use x and y

b: x-intercept= 30 y-intercept=45
To find the x-intercept you need to isolate the variable. 45x/45 = x
Then you do the same thing to the other side. 1350/45 = 30
So x=30
Same thing with the y-intercept.
30y/30 = y 1350/30 = 45
y=45 (Not really sure what it means by “what they represent” but I thinks it’s that there are 30 adult tickets and 45 children tickets )

c: so our points are (30,0) and (0,45) so you would graph that.
To find how many children tickets were bought if there were 20 adult tickets just look at the photo I put. I don’t know how to explain this.


Hope this helps

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

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<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]$ \\\\

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Read more about Laplace tranoform

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