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2 years ago

Explain the answer with briefs steps

Mathematics

1 answer:

aliina [53]2 years ago

6 0

Step-by-step explanation:

steps are in picture above.

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Leno4ka [110]

Answer:

$\frac{s^2-25}{(s^2+25)^2}$

Step-by-step explanation:

Let's use the definition of the Laplace transform and the identity given: $\mathcal{L}[t \cos 5t]=(-1)F'(s)$ with $F(s)=\mathcal{L}[\cos 5t]$ .

Now, $F(s)=\int_0 ^{+ \infty}e^{-st}\cos(5t) dt$ . Using integration by parts with u=e^(-st) and dv=cos(5t), we obtain that $F(s)=\frac{1}{5}\sin(5t)e^{-st} |_{0}^{+\infty}+\frac{s}{5}\int_0 ^{+ \infty}e^{-st}\sin(5t) dt=\int_0 ^{+ \infty}e^{-st}\sin(5t) dt$ .

Using integration by parts again with u=e^(-st) and dv=sin(5t), we obtain that

$F(s)=\frac{s}{5}(\frac{-1}{5}\cos(5t)e^{-st} |_{0}^{+\infty}-\frac{s}{5}\int_0 ^{+ \infty}e^{-st}\sin(5t) dt)=\frac{s}{5}(\frac{1}{5}-\frac{s}{5}\int_0^{+ \infty}e^{-st}\sin(5t) dt)=\frac{s}{5}-\frac{s^2}{25}F(s)$ .

Solving for F(s) on the last equation, $F(s)=\frac{s}{s^2+25}$ , then the Laplace transform we were searching is $-F'(s)=\frac{s^2-25}{(s^2+25)^2}$

3 0

3 years ago

Find the equation of the line which passes through the point (−2,−5) and is parallel to the line −3x+5y=−4.

leonid [27]

-3x+5y=-4
5y=3x-4
Y=3/5x-4/5

When it parallel to the line y=3/5x-4/5

It can be y=-3/5x+b

-5=6/5+b

B=-5-6/5=-25/5-6/5=-31/5

Y=-3/5x-31/5

3/5x+y=-31/5

Multiply 5

3x+5y=-31

4 0

3 years ago

Read 2 more answers

What is the p(3,1,2) on rolls of a die

Anna35 [415]

Number 3 is 1/6 to role a 1 on the second roll is 1/36= 1/6 X 1/6
to get 2 on the third role is 1/216 so the probability is 1/216

3 0

3 years ago

3a+11=7a-13 with shown work

DaniilM [7]

3a+11=7a-13

move 7a to the other side

sign changes from +7a to -7a

3a-7a+11= 7a-7a-13( combine like terms)

3a-7a+11= -13

-4a+11= -13

move 11 to the other side

sign changes from +11 to -11

-4a+11-11= -13-11

-4a= -13-11

-4a= -24

divide both sides by -4 to get a by itself

-4a/-4= -24/-4

Answer: a= 6

4 0

3 years ago

What is the distance from the pier to the lighthouse?

bezimeni [28]

Answer:

$\sqrt{58}$

Step-by-step explanation:

PL^2 =7^2 +3^2

PL^2=49+9

PL=

$\sqrt{58}$

4 0

3 years ago

Explain the answer with briefs steps​

Explain the answer with briefs steps