Abuoy floating in the ocean is bobbing in simple harmonic motion with period 5 seconds and amplitude 4ft. its displacement d from sea level at time =t0 seconds is −4ft, 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.

Step-by-step explanation:

We are given that

Period =5 s

Amplitude=4 ft

Displacement d from sea level at time

We have to find the modelling equation displacement d as a function of time.

We know that

The general equation of sinusoidal function is given by

B=

When t=0, y=d=-4 ft, D=0

Substitute the values then we get

We know that Cos(-x)=Cos x

 ()

Substitute the values then, we get

b. x- 48 =120

step-by-step explanation:

b. 6

step-by-step explanation:

we are given the table representing an exponential function.

we can see from the table that, as x is increasing, the value of y is increasing in the power of 6.

i.e. the following relation is obtained,

x = 1, y = 6

x = 2, y = 36 =

x = 3, y = 216 =

x = 4, y = 1296 =

x = 5, y = 7776 =

so, the geometric series obtained is .

thus, the common ratio is given by = = 6.

hence, the common ratio is 6.