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3 years ago

Given the arithmetic sequence an = 4 + 8(n − 1), what is the domain for n?

Mathematics

1 answer:

tatiyna3 years ago

6 0

The domain should be all Natural numbers

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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

The central angle of a circle is equal in measure to one radian when the corresponding arc length is equal to which of the follo

irinina [24]

The formula to find the arc length L is
L = r*theta
where r is the radius and theta is the central angle in radians (this formula will not work if theta is in degrees)

If the central angle is 1 radian, then theta = 1 and
L = r*theta
L = r*1
L = r
So the arc length is the same as the radius

Answer: Choice A) The radius of the circle

5 0

3 years ago

Read 2 more answers

Indicate which two quadrants “theta” could terminate if sin theta = 4/5

Nitella [24]

Answer:

1st and 2nd quadrants

Step-by-step explanation:

You have sine is positive since it is 4/5.

Sine is the y-coordinate.

On the coordinate plane y is positive in the 1st and 2nd quadrants.

8 0

3 years ago

What is the order of rotational symmetry of a regular octagon?

SSSSS [86.1K]

Answer:

Answer: I do not know the answer

Step-by-step explanation:

5 0

2 years ago

PLEASE HELP WILL MARK BRAINLIEST!!<br> What is the value of j?

pickupchik [31]

Answer:

Step-by-step explanation:

simply

<em>the square represents 90 degrees and 90 - 61 is 21</em>

4 0

3 years ago