Atoy cannon ball is launched from a cannon on top of a platform. the equation h(t) = -5t^2 + 20t + 4 gives the height h, in meters, of the ball t seconds after it is launched.

a. what equation can be used to tell whether the ball reaches a height of 12 m ?
b. does the ball reach a height of 12m? (yes or no)

A)  =0

B)t= 0.45 seconds or t= 3.5 seconds

If time is greater than 0.45 seconds then ball will reach height 12m and higher.

Step-by-step explanation:

Given Equation:

h(t)= ------------------------------(Equation 1)

a) Equation to tell if ball reaches height of 12m . for that :

h= 12m

put in Equation 1.

12 =

or =12

or -12 = 0

=0

or  = 0 -----------------------------------(Equation 2)

This Equation tells if ball reaches height of 12m

b) Does ball reaches height of 12m :

For that, the value of time can be found out from the equation above,

 = 0

It can be solved using the quadratic formula:

t= 0.45 seconds or t= 3.5 seconds

If time is greater than 0.45 seconds then ball will reach height 12m and higher.

The maximum height reached is greater than 12m, hence the ball reach a height of 12m

The height of the toy cannon all launched is expressed as

h is the height reached by the ball

t is the time taken by the ball to reach its maximum height

A) In order to determine whether the ball reached the height of 12m, we will have to substitute h = 12 into the formula as shown:

Hence the equation that can be used to tell whether the ball reaches a height of 12 is

B) At the maximum height

dh/dt = 0

-10t + 20 = 0

-10t = -20

t = 20/10

t = 2

Get the maximum height reached

h(2) = -5(2)^2 + 20t + 4

h(2) = -5(4) + 20t + 4

h(2) = -20 + 20(2) + 4

h(2) = -20+40+4

h(2) = 24 m

Since the maximum height reached is greater than 12m, hence the ball reach a height of 12m

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452,489 to the nearest thousand is 452,000