A stone is launched vertically upward from a cliff 192 ft above the ground at a speed of 16 ft/s. Its height above the ground t seconds after the launch is given by s = -16t² + 16t + 192 for 0≤t≤4. When does the stone reach its maximum height?

0.5 sec

Step-by-step explanation:

s(t) = -16t² + 16t + 192

Lets differentiate the equation first w.r.t 't', we will have:

s'(t)=-32t + 16

In order to find critical points, equating s'(t) to zero, and determine values where s'(t) is undefined

Therefore, s'(t)=0

-32t + 16= 0     (solving for t)

-32t = -16

t= 16/32

t= 0.5s

Now, we will evaluate 's' at endpoints and critical points.

->s(0)= -16(0)² + 16(0) + 192

s(0)= 192

->s(0.5)= -16(0.5)² + 16(0.5) + 192

s(0.5)= 196

->s(4)= -16(4)² + 16(4) + 192

s(4)= 0

Thus, s(0.5)= 196 is the largest function from above i.e the absolute max. value of s on [0,4]

the stone reach its maximum height i.e 196 ft at 0.5sec

answer: the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

step-by-step explanation:

the given rate of interest i= 85%

in calculating the monthly payment for a loan with an interest rate compounded monthly, the value of the interest rate per period we use in the formula must be in decimal form.

to convert it in decimal, we divide it by 100, we get

hence, the value should be used for i in the formula of calculation the monthly payment , the interest rate per period is 0.85.

the answer is su.k.my? ? co.kc