Asound wave is given the following equation:

y= 8 sin(512πt) where t= time in seconds.

how many cycles will occur between t=2 and t=3.5 seconds?

384

Step-by-step explanation:

Standard equation of a sine wave is:

y = A sin(2πf x + B) + C

where A is the amplitude, f is the frequency, B is the phase shift, and C is the vertical offset.

In this case:

2πf = 512π

f = 256

This means there are 256 cycles per second.  The number of cycles between t = 2 and t = 3.5 is:

(3.5 − 2) × 256

384

Length = 20 cm

Width = 7 cm

Step-by-step explanation:

Given that :-

The perimeter of a rectangle is 54 cm. Its length and width if the length is represented by 3x + 2 and the width is represented by 2x – 5.

To find :-

Find the measures of length and width

Solution :-

To calculate the measures of length and width of rectangle . we gave given in question that perimeter of rectangle is 54 cm and length is represented by 3x + 2 and width is represented by 2x-5.

Using Formula :-

Perimeter of rectangle = 2 ( l + b )

Where,

l is the length and w is the width of rectangle.Perimeter = 54 cm

Substitute the values

54 cm = 2 ( 3x + 2 + 2x - 5 )

Combine like terms

54 cm = 2 ( 3 x + 2 x + 2 - 5)

54 cm = 2 ( 5 x -3)

Simplify both sides of the equation.

54 = 2( 5x− 3 )

54 = (2)(5x) + (2)(−3). .. ( Distribute )

54 = 10x +−6

54 = 10x −6

Flip the equation.

10x −6 = 54

Add 6 to both sides.

10x −6 + 6 = 54 + 6

10x = 60

Divide both sides by 10.

10x / 10 = 60 / 10

x = 6

Therefore ,

Length = 3x + 2 =3 ×6 + 2 = 18 + 2 = 20 cm

Width = 2x- 5 = 2 × 6 - 5 = 12 - 5 = 7 cm