The last question the position d of a block that is attached to a spring is given by the formula d=6cos(pi/2 t) where t is in seconds. what is the maximum distance of the block from its equilibrium position (the position at which d = 0)? find the period of the motion.

Step-by-step explanation:

Waves have the form:

y = A sin (2π/T x + φ) + B

where A is the amplitude (the distance from the center of the wave to the max or min),

T is the period (time it takes for one cycle),

φ is the phase shift (moves the wave left or right),

and B is the offset (moves the wave up or down).

This can also be written with cosine.

Here, we have d = 6 cos(π/2 t).

The amplitude is A = 6, so the maximum distance from the equilibrium position is 6 units.

The period is:

2π / T = π/2

T = 4

So the period is 4 seconds.

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

hope this !