A boy is launching a toy rocket he got for his birthday from the top of an 80 ft building. The function representing the height is f(0) = -16x? +64x + 80 where x represents time in seconds.
How many seconds did it take the rocket to reach it's maximum height?
A
144 sec
B)
2 sec
Eliminate
1.5 sec
D)
128 sec

2 seconds, assuming the "?" in the equation is supposed to be ^2 (the exponent of 2):  f(h) = -16x^2 +64x + 80

Step-by-step explanation:

You can either graph the functuion or take the first derivative to find the maximum height.  The first derivative will give us the slope for a values of x.  The slope at the top height of the rocket is zero, since it has stopped and is starting it's way back down.

First Derivative:

f(x) = -16x^2 +64x + 80

f'(x) = -32x + 64

Set this equal to zero and solve for x

0 = -32x + 64

x = 2 seconds.

Use 2 seconds in the original equation to find the height at 2 seconds.

f(2) = -16x^2 +64x + 80

f(2) = -16(2)^2 +64*(2) + 80

f(2) = 144 feet

Graph:

A graph is attached.  You can locate the maximum at (2,144)

12

step-by-step explanation:

a triangle's   full angle is 180 degrees so 180 - 156 = 24. 24/2=12

step-by-step explanation:

one of the most important purposes of surface treatment is to alter surface properties according to the requirement of specific applications. for example, hydrophobic coating has been utilized on windshield and eyeglasses. gold atom monolayer on substrate has become a popular surface bioconjugation strategy.