Height h (in feet) above ground of a seat on a Ferris wheel at time t (in seconds) is modeled by. H(t)= 51 + 45sin ( (pi/12)t - pi/2) (A) find the period of the model. (B) what does the period tell you about the ride? What does the amplitude tell you about the ride?

A. 48 s

B. i. The period tells me that it takes the ride less than one minute to complete the ride.

ii. this tells me that the maximum height of the ride above the ground is 51 + 45 = 96 feet.

Step-by-step explanation:

A. Find the period of the model

Since H(t)= 51 + 45sin ( (π/12)t - π/2), let be period of the motion be T. The first maximum value of sin ( (π/12)t - π/2) = 1 is obtained when t = T/4.

Substituting T/4 into sin ( (π/12)t - π/2) = 1, we have

sin ( (π/12)t - π/2) = 1

sin ( (π/12)T/4 - π/2) = 1  

(π/12)T/4 - π/2 = sin⁻¹(1)

πT/48 - π/2 = π/2

collecting like terms,

(πT/48 = π/2 + π/2

πT/48 = π

dividing through by π, we have

T/48 = π/π

T/48 = 1

cross-multiplying, we have

T = 48 s

So, the period is T = 48 s

B.

i. What does the period tell you about the ride?

The period tells me that it takes the ride less than one minute to complete the ride.

ii. What does the amplitude tell you about the ride?

Since the amplitude is the coefficient of sin ( (π/12)t - π/2) which is 45 feet, this tells me that the maximum height of the ride above the ground is 51 + 45 = 96 feet.

answer: a video game has three difficulty levels: easy, medium, and expert. the game's scoring works in such a way that a player has to score a fixed number of points to advance to the next level, and then the scoring starts over. the total score needed to clear all three difficulty levels is 7,500. two times the number of points needed to clear the easy level is 500 more than the number of points needed to clear the medium level. twice the number of points needed to clear the medium difficulty level is 1,500 more than the number of points needed to clear the expert level. if x, y, and z represent the easy, medium, and expert levels, respectively, and a is the coefficient matrix of the system of equations modeling this situation, identify the inverse matrix, a-1, and the solution matrix, x, of the system of equations.

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