???? Help plz ?…. It’s a grade

Consider the initial value problem y′′+36y=2cos(6t),y(0)=0,y′(0)=0. y″+36y=2cos⁡(6t),y(0)=0,y′(0)=0. Take the Laplace transform

Bingel [31]

Recall the Laplace transform of a second-order derivative,

$L(y''(t)) = s^2Y(s)-sy(0)-y'(0)$

and the transform of cosine,

$L(\cos(at))=\dfrac s{a^2+s^2}$

Here, both $y(0)=y'(0)=0$ , so taking the transform of both sides of

$y''(t)+36y(t)=2\cos(6t)$

gives

$s^2Y(s)+36Y(s)=\dfrac{2s}{36+s^2}$

$\implies Y(s)=\dfrac{2s}{(s^2+36)^2}$

4 0

3 years ago

PLEASE HELP ME ASAP! THANK YOU

Daniel [21]

Answer:

The area of the sector of the circle is approximately

Step-by-step explanation:

The given parameters of the circle having a shaded sector are;

The radius of the circle, r = 4 meters

The measure of the arc bounding the sector = 135°

The area of a sector of a circle, 'A', is given as follows;

$A = \dfrac{\theta}{360 ^{\circ}} \times \pi \times r^2$

Therefore, the area, 'A' of the given sector of the circle, is given as follows;

$A = \dfrac{135 ^{\circ}}{360 ^{\circ}} \times \pi \times (4\ cm)^2 \approx 18.85 \ cm^2$

The area of the sector of the circle, with radius 4 cm and bounded by an arc, A ≈ 18.82 cm².

4 0

3 years ago

Last summer, 54,849 people went on a vacation. This year it is expected that an additional 9,499 people will take a summer vacat

ZanzabumX [31]

Answer:64,348

Step-by-step explanation:

please make brainliest

5 0

3 years ago

Jimmy invests $4,000 in an account that pays 5% annual interest, compounded semiannually. What is his balance, to the nearest ce

masha68 [24]

Answer:

$20,000 I think

Step-by-step explanation:

4,000

x 5

----------

20,000

4 0

3 years ago

Which systems of equations have infinite solutions 2x+5y=31 6x-y=13 or 2x+y=10 -6x=3y+7 or y=14-2x 6x+3y=42 or y=13-2x 4x-3y=-19

Lerok [7]

Answer:

y=14-2x; 6x+3y=42
2x+y=17; -6x=3y-51

Step-by-step explanation:

Dependent equations will have infinite solutions. One way to tell if a system of equations is dependent is to put all of the equations into standard form. Here, we can use the form ...

ax + by = c

where a, b, c are mutually prime integers and "a" is positive. When dependent equations are put in this form, they resolve to the same equation.

Here, the rearrangement is accomplished by putting the x- and y-terms on the same side of the equal sign, with the x-term having a positive coefficient. If necessary, the constant is put on the other side, and any common factors removed from all of them.

Then the sets of equations are ...

2x +5y = 31
6x -y = 13 . . . . not dependent

__

2x +y = 10
6x +3y = -7 . . . . not dependent

__

2x +y = 14
2x +y = 14 . . . . dependent

__

2x +y = 13
4x -3y = -19 . . . . not dependent

__

2x +y = 14
x +2y = 13 . . . . not dependent

__

2x +y = 17
2x +y = 17 . . . . dependent

__

The 3rd and 5th sets of equations are dependent, so have infinite solutions.

_____

The second set of equations is inconsistent, so has no solutions.

6 0

3 years ago