Aflying objects height in the sky can be represented by the equation d=30+vt+4t^2 where d is the height in feet , v is the velocity in feet per second, and t is the time in seconds. how long has the flying object been traveling if it has velocity of 8 feet per second and has risen to a height of 126 feet? a: 4 seconds b: 6 seconds c: 8 seconds d: 16 seconds

4 s  

Step-by-step explanation:

d = 30 + vt + 4t²

v = 8 ft/s; d = 126 ft

             126 = 30 + 8t + 4t²     Subtract 126 from each side

4t² + 8t - 96 = 0                        Divide each side by 4

 t² + 2t – 16 = 0                        Factor the equation

(t + 6)(t – 4) = 0

t + 6 =  0     t – 4 = 0

     t = -6           t = 4

We reject the negative time, so t = 4.

The object has been travelling for 4 s.

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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