We are standing on the top of a 1024 foot tall building and launch a small object upward. The object's vertical altitude, measured in feet, after t seconds is h(t)=−16t2+192t+1024. What is the highest altitude that the object reaches?

The highest altitude of that object is 1,600 feet.

Step-by-step explanation:

Given that,

where h(t) is the height of the object after t seconds.

Differentiating with respect to t

h'(t)= -32t+192

Again differentiating with respect to t

h''(t)= -32

To find the maximum or minimum value, first we set h'(t)=0.Then we get a equation of t and solve it. Assume  t=a is the solution of the equation .

Now check h''(t) at t=a, if h''(a)<0 then the function h(t) has a maximum value at t=a

If h''(a)>0 then the function h(t) has a minimum value at t=a.

Now,

-32t+192=0

⇒32t=192

⇒t= 6

h''(6) = -32<0, So the object reaches at its highest altitude after 6  seconds.

Now plunging t=6 in the given function

h(6)= -16 (6)²+192×6 +1024

     =1600 feet

The highest altitude of that object is 1,600 feet.

i need a picture

step-by-step explanation:

the final amount you will pay is $68.04.

the tip is determined by the pre-tax amount, so we calculate the tip based on the original bill, not after we've added sales tax.

to find the tip:

we can divide 54.00 by 100 to get 1% of 54. then we multiply that by 18.

54 / 100 = .54

.54 x 18 = 9.72

tip = 9.72$

to find the tax:

we can divide 54.00 by 100 to get 1% of 54. then we can multiply that by 8 to get 8%.

54 / 100 = .54

.54 x 8 = 4.32

tax= 4.32

now we can add the tip and tax to the bill to get our total.

54 + 9.72 + 4.32 = 68.04

total: $68.04

step-by-step explanation: