A buoy floating in the ocean is bobbing in simple harmonic motion with period 5 seconds and amplitude 3ft . Its displacement d from sea level at time t=0 seconds is −3ft , and initially it moves upward. (Note that upward is the positive direction.) Give the equation modeling the displacement d as a function of time t .

d = 3sin(2π/5 t + 3π/2)

Step-by-step explanation:

Equation for simple harmonic motion is:

d = A sin(2π/T t + B) + C

where A is the amplitude,

T is the period,

B is the horizontal shift (phase shift),

and C is the vertical shift.  

Given that A = 3, T = 5, and C = 0:

d = 3 sin(2π/5 t + B)

At t = 0, the buoy is at d = -3:

-3 = 3 sin(2π/5 (0) + B)

-1 = sin(B)

3π/2 = B  

d = 3sin(2π/5 t + 3π/2)

Notice you can also use cosine instead of sine and get a different phase shift.

d = 3 cos(2π/5 t + π)

You can even use phase shift properties to simplify:

d = -3 cos(2π/5 t)

Any of these answers are correct.

341

step-by-step explanation:

all you have to do is 9x31 (which equals 279) and then 20x31 (which equals 620). then you have to subtract. 620-279=341.

26 is 33.33% of 78

step-by-step explanation:

26 is what percent of 78?

26 is p% of 78

equation: y = p% * x

solving our equation for p

p% = y/x

p% = 26/78

p = 0.3333

convert decimal to percent:

p% = 0.3333 * 100 = 33.33%