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

if gloria has "carry over" minutes, (that is, any minutes paid for but not used in a month can be applied to her payment for minutes in the next month,) her total usage for the three months is: total minutes = 320 + 243 + 489 = 1052 minutes number of 200 minute blocks = 1052/200 = 5 r52 (that is 5 with a remainder of 52) rounding up the number of 200 minute blocks gives her usage for the three months as 6 blocks. the cost for six blocks is 6 x $25 = $150 she also has 200 - 52 or 148 carry over minutes if gloria pays each month and unused minutes are lost, applying the rounding up procedure to each month gives: first month usage of 320 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 second month usage of 243 minutes rounds up to 2 blocks of 200 minutes for a payment of 2 x $25 = $50 third month usage of 489 minutes rounds up to 3 blocks of 200 minutes for a payment of 3 x $25 = $75 total payments for the three months are $50 + $50 + $75 = $175 get the plan with carry over minutes!

income. 10x+1300

expenses 3x+(1800+1500)

expenses 3x+3300

to break even:

income = expense,

10x + 1300 = 3x + 3300,

solve for x.

step-by-step explanation:

mark brainliest