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Jobisdone [24]
3 years ago
13

Which property is illustrated by the following statement? 5z + 1 = 1 + 5z

Mathematics
1 answer:
xenn [34]3 years ago
7 0
It is the commutative property of addition
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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
6÷2(1+2)= _____ whats the answer to this
GalinKa [24]

Answer:

9

Step-by-step explanation:

You do parenthesis first so 1+2=3

Then you do division 6 divided by 2=3

Then you will multiply 3 by 3 so 9

This is known as pemdas

P=parenthesis

E=exponents

MD=multiplication and division you do it left to right so if division is in front of multiplication then you do division

As=Addition and subtraction is also left to right

8 0
2 years ago
Read 2 more answers
A circular garden has a diameter of 6 yards. What is the area of the garden?
Salsk061 [2.6K]

Answer:

d.

Step-by-step explanation:

3 0
3 years ago
What is the measure of angle c?​
s344n2d4d5 [400]

Answer:

50 degrees

Step-by-step explanation:

Okay! So first off, because this is NOT a right triangle, we can't use soh cah toa. That means we can either use the law of sines or the law of cosines.

Because we only have sides here and no angles, we are forced to use the law of cosines.

c^2 = a^2 + b^2 − 2ab cos(C)

c = 6

b = 7.5

a = 6.5

36 = 6.5^2 + 7.5^2 - 2(6.5)(7.5)cos(C)

36 = 98.5 - 97.5cos(C)

-62.5 = -97.5cos(C)

0.641 = cos(C)

angle C = cos^-1(0.641)

angle C = 50.13 which is around 50 degrees

Remember! A dumb thing i always used to do in geometry was use radians instead of degrees, be sure to use degrees here because you are looking for degrees. Radians are for things involving not degrees, but PI.

5 0
3 years ago
(word sentence) Pooky eats three cans of cat food each day. How long will 27 cans of food last?
pshichka [43]

ANSWER:

9 days

Solution:

\frac{27\text{ cans}}{3\text{ cans per day}}\text{ = 9 days}

5 0
1 year ago
Read 2 more answers
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