A stone is thrown vertically upward at a velocity of 10 feet per second from a bridge that is 60 feet above the level of the water. The height h (in feet) of the stone at time t (in seconds) after it is thrown is given by h = -16t2 + 10 + 60.

(a) Find the time when the stone is again 60 feet above the water. sec

(b) Find the time when the stone strikes the water. (Round your answer to two decimal places.) sec

(c) Does the stone reach a height of 90 feet? O Yes O No​

9514 1404 393

  (a) 0.625 seconds (rounds to 0.63)

  (b) 2.27 seconds

  (c) No

Step-by-step explanation:

(a) We want to find t such that h = 60

  60 = -16t^2 +10t +60

  0 = t(-16t +10) . . . . . . . . . subtract 60, factor

  t = 0  or  t = 10/16 = 5/8 = 0.625

The stone is again 60 feet above the water after 0.625 seconds.

__

(b) We want to find t such that h = 0

  0 = -16t^2 +10t +60

  16t^2 -10t = 60

  16(t^2 -5/8t +25/256) = 60 +25/16 . . . . complete the square

  (t -5/16)^2 = 61.5625/16 = 3.84765625 . . . . simplify a bit

  t = 5/16 +√3.84765625 ≈ 2.274 . . . . square root, add 5/16

The stone strikes the water at about 2.27 seconds.

__

(c) The equation above tells us the peak height of the stone is about 61.56 feet. It does not reach a height of 90 feet.

d. 9

step-by-step explanation:

54/12 = 4.5

sf = 4.5

so x = 2 · 4.5 = 9

choice b is correct

step-by-step explanation:

we have been given the following system of inequalities;

we are required to graph the solution to the system of inequalities. using a graphing tool, the graph of the system is as shown in the attachment. the continuous line represents the graph of while the dotted line represents .