During a soccer game, a goalie kicks a ball upward from the ground. the equation h(t)=−16t2+42t represents the height of the ball above the ground in feet as a function of time in seconds. when the ball begins moving downward toward the ground, a player from the other team intercepts the ball with his chest at a height of 5 feet above the ground. how long after the goalie kicks the ball does the player intercept the ball?

Step-by-step explanation:

The height of the ball after t seconds is represented by,

Putting h(t) = 5, we get

At the ball was moving upward, since .

It will be downward at

The player intercept the ball after 2.5 seconds of the kick.

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation:

what is the model?

step-by-step explanation: