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Dmitrij [34]
3 years ago
10

Consider the absolute value function f (x) = -|x + 2| - 2 . The vertex of the function is .

Mathematics
1 answer:
mezya [45]3 years ago
5 0
The answer would be c
Hope this helps!
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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

brainly.com/question/14487937

#SPJ4

6 0
1 year ago
What is the volume of 12 inches by 2 inches by 12 inches
Orlov [11]

Answer:

288in^3

Step-by-step explanation:

formula for volume is l*w*h

substitute the variables for 12*2*12=288

Thus the answer is 288in^3

7 0
3 years ago
Read 2 more answers
Which fraction is the largest?
Alexeev081 [22]

Answer:

17/30

Step-by-step explanation:

7 0
3 years ago
CONSTRUCTED RESPONSE
Digiron [165]

The fraction for the above ratio is 5/9

Where 5- no of cups of bread crumbs needed; 9= pounds of ground beef needed

Step-by-step explanation:

Anything that can be represented in the x/y form constitutes the fraction.

The above statement can be represented in the fraction form as 5/9. It means that for every 9 pounds of ground beef, 5 cups of bread crumbs are needed.

The above fraction provides the ratio in the form of cups of bread crumb/ pound of ground beef required. Where 5 represents the number of cups of bread crumbs required, 9 represents the pound of ground beef needed for the same.

3 0
3 years ago
Can someone please help me answer this?
ozzi
For this problem i got

7 0
3 years ago
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