Aweight is attached to a spring that is oscillating up and down. it takes 3 sec. for the spring to complete one cycle, and the distance from the highest to lowest point is 4 in. what equation models the position of the weight at time t seconds?

a. y=2sin(pi/3 t)

b. y=4sin(pi/3 t)

c. y=2sin(2pi/3 t)

d. y=4sin(2pi/3 t)

e. y=2sin(3pit)

f. y=4sin(3pit)

Option C.

Step-by-step explanation:

The equation that models the position of the weight and time will be a sine wave.

y = A sin(bt)

where A = amplitude of the wave

b = time period for a complete oscillation

Since b =

It has been given in the question, Time period t = 3 sec.

b =

Amplitude A = 2 in.

Now we plug in the values of amplitude and time period in the standard equation.

y =

y =

Option C. is the answer.

$464

Step-by-step explanation:

Christine worked 52 hours last week.

If her regular hourly rate is $8 per hour and she is paid 1.5 times her hourly rate for every hour beyond 40 hours.

Fixed rate hours = 40 hours

Fixed hourly rate = $8 per hour

Total earn in 40 hours = 8 × 40

                                   = $320

Number of extra hours = 52 - 40

                                    = 12 hours

Extra hours rate = 1.5 × 8

                          = $12 per hour

Total earn in 12 hours = 12 × 12

                                   = $144

Total earn in 52 hours = $320 + $144

                                   = $464

Hence, Christine weekly paycheck is $464