I'm awarding 20 points for an answer! A ball is thrown into the air with an initial upward velocity of 48 ft/s. It height h in feet after t seconds is given by the function h (t)=-16t^2+48t+4.

In how many seconds will the ball reach its maximum height?

Step-by-step explanation:

h(t)=-16t^2+48t+4

dh/dt=-32t+48

d2h/dt2=-32

Since acceleration is always negative when the velocity, dh/dt=0, it will occur at the maximum height.

dh/dt=0 when

-32t+48=0

-32t=-48

t=1.5 seconds

Without calculus, the vertex of a parabola will be at -b/(2a) of the quadratic equation. In this case

-48/(2(-16))

-48/-32

1.5 seconds

option 2 is correct.

step-by-step explanation:

we are given two inequality equation

x+y> 5 and -3x+2y< -2

first we draw the graph of both function using t-table method

equation: x+y> 5

for x=0, y=5

for x=-5, y=0

table:

x   :   0     5

y   :   5     0

test point (0,0) , 0> 5

false

equation: -3x+2y< -2

for x=0, y=-1

for x=2, y=4

table:

x   :   0     2

y   : -1       4

test point (0,0) , 0< -2

true

now we draw the graph. see the attachment for graph.

common region would be solution set.

option 2 is correct.

21

step-by-step explanation: