A ball is thrown into the air with an upward velocity of 48 ft/s. Its height h in feet after
t seconds is given by the function h = -16t2 + 48t + 8. In how many seconds does the ball
reach its maximum height? Round to the nearest hundredth if necessary. What is the ball’s maximum height?

Step-by-step explanation:

The equation used to represent the height of the ball, h in feet after t seconds is expressed as

h = -16t² + 48t + 8

The equation is a quadratic equation. The plot of this equation on a graph would form a parabola whose vertex would be equal to the maximum height travelled by the ball.

The vertex of the parabola is calculated as follows,

Vertex = -b/2a

From the equation,

a = -16

b = 48

Therefore,

Vertex = - 48/2 × - 16 = 48/32 = 1.5 seconds

So the ball will attain maximum height in 1.5 seconds.

To determine the maximum height, we would substitute t = 1.5 into the given equation. It becomes

h = -16(1.5)² + 48(1.5) + 8

h = - 36 + 72 + 8 = 44 feet

pentagon

step-by-step explanation:

the coordinates   a(5, -2), b(3,-1),c(-4,-4) d(-3,8) and e(-1,4) forms the vertices of the polygon when they are connected in order.

in order to classify that which polygon is it with the given coordinates, first count the number of vertices and then count the number of sides it can make with these vertices.

since, the given coordinates have five vertices, therefore, it will make five sides. moreover, pentagon is regular in nature therefore it will be convex.

now, a polygon with five sides is known as pentagon, therefore, the given polygon is the pentagon.

8/k

step-by-step explanation: