If an object is propelled upward from a height of s feet at an initial velocity of v feet per second, then its height h after t seconds is given by the equation h=-16t^2 +vt+ s , where h is in feet. if the object is propelled from a height of 8 feet with an initial velocity of 64 feet per seconds , it's height h is given by the equation h=-16t^2+64t+8 after how many seconds is the height 68 feet? the time is .

At 1.5 seconds and 2.5 seconds

Step-by-step explanation:

Because this is parabolic motion, the object will reach the height of 68 feet when it's going up AND when it's coming down.  In order to find out those times, you set the h on the left side of the equation equal to 68, because h stands for height.

Set that equal to 0 and factor to solve for t:

Using the quadratic formula, we get t = 1.5 and t = 2.5

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.

because linear equations are a lot simpler than quadratics equations, and linear equations formula is a lot easier to memorize. that's why i think they're harder.