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Elena-2011 [213]
3 years ago
11

Jake cuts a length of 1,12 from a 3-meter board.how long is the board now ?

Mathematics
1 answer:
iren [92.7K]3 years ago
7 0
1,12-3 = -1.88
That should be the answer

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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
Help???????!!!!!!!??????
Musya8 [376]
I think you divde the fractions
8 0
3 years ago
Factor completely.<br> 25+70x+49x^2=
weeeeeb [17]

Answer:

(7x+5)(7x+5)

Step-by-step explanation:

Factor 25+70x+49x2

49x2+70x+25

=(7x+5)(7x+5)

Answer:

(7x+5)(7x+5)

Hope this helps!

8 0
3 years ago
The length of a rectangle is 22 feet longer than the width. the perimeter is 1616 feet. find the dimensions of the rectangle.
NemiM [27]
So we can setup variable equations for this:
so we're given that the length is 22feet longer than the width!
so as an expression length is equal to 22+w
and width as an expression is just w
so the formula for the perimeter for a rectangle is 2l+2w=perimeter
so fill it in now!
1616=2(22+w)+2w
1616=44+2w+2w
1616=44+4w
1572=4w
divide by four..
w=393
and length is simply 22 more than that as stated in the question!
so length is 415
dimensions are: 415x393
7 0
3 years ago
What is the grates common factor of 15 and 64??
Rashid [163]

Answer:

The gcf of 15 and 64 can be obtained like this: The factors of 15 are 15, 5, 3, 1. The factors of 64 are 64, 32, 16, 8, 4, 2, 1. The common factors of 15 and 64 are 1, intersecting the two sets above. In the intersection factors of 15 ∩ factors of 64 the greatest element is 1. Therefore, the greatest common factor of 15 and 64 is 1.

Hope this helped!

Good luck :p

~Emmy <3



7 0
3 years ago
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