Free brainlst! please help

if a projectile is fired straight upward from the ground with an initial speed of 32 feet per second, then its height h in feet after t seconds is given by the function h(t)= -16t^2 + 160t. Find the maximum height of the projectile?

400 ft

Step-by-step explanation:

h(t)= -16t^2 + 160t

The vertex is found at

h = -b/2a  where b is the coefficient of t and a is the coefficient of t^2

   = -160/(2*-16)

   -160/-32

  5

The time where the maximum occurs is at t=5

To find the maximum substitute into the function

h(5) = -16 (5)^2 +160*5

       = -16*25 +800

       =-400+800

       = 400

The maximum height is 400 ft

what are the statments

step-by-step explanation:

region b will make the inequalities y < 2x + 1 and y > -x - 2 true ⇒ answer a

step-by-step explanation:

* lets study the graph and the inequality to solve the question

- the inequality y > -x - 2

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = -2 that means the line intersect the y-axis at point (0 , -2)

∵ the sign of the inequality is >

∴ we shad the part over the line

  region a and b

- the inequality y < 2x + 1

∵ the form of the inequality is y > mx + c , m is the slope of the line

  and c is the y-intercept (the line intersect y-axis at point (0 , c)

∴ c = 1 that means the line intersect the y-axis at point (0 , 1)

∵ the sign of the inequality is <

∴ we shad the part under the line

  region b and c

∵ the common region between the two lines is region b

∴ region b will make the inequalities y < 2x + 1 and y > -x - 2 true