Afountain launches a stream of water directly out of a pool at a vertical speed of 48 feet per second. the water shoots up and then falls back into the pool. the height, h, of the water at time t, in seconds, is given by the equation h = –16t 2 + 48t. the greatest height of the water above the pool is

36 feet.

Step-by-step explanation:

h = -16t² + 48t .......... (1)

The above equation relates the height h, in feet of the water at time t, in seconds.

Now, condition for greatest height is ......... (2)

So, differentiating equation (1) with respect to t we get, -32t + 48 = 0 {From condition (2).

⇒ t = 1.5 seconds

So, the greatest height is = -16 (1.5)² + 48 (1.5) = 36 feet. (Answer)

i'm going to search it

step-by-step explanation:

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!