Aball is thrown into the air with an upward velocity of 36 ft/s. its height h in feet after t seconds is given by the function h = −16t2 + 36t + 5. 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?

25.25 m

Step-by-step explanation:

The path of the ball is modeled by a quadratic. Depending on which way it is facing, a quadratic always has a either a minimum value or a maximum value. Always. Each quadratic can have either one or the other, never both. The first step in finding this minimum or maximum value is first finding the x value that gives out this minimum/maximum value when substituted into the function. There are many ways of doing this, one of them being:

x =

After finding this x, substitute this into the initial function and you have your minimum/maximum value.

So for this question h =

so t = =

Again this is not the maximum value of the function but it is the input value that gives out the maximum height. We find this by plugging in the calculated t.

maximum height =

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2