A passenger on a stranded lifeboat shoots two distress flares into the air. The first flare travels a maximum height 196 feet and lands in the water after 7 seconds. The height (feet) of the second flare above the water is given by f(t) = -16t(t-8), where t is time (seconds) since the flare was shot. Which flare travels higher? Which remains in the air longer?

The second flare travels higher, 256 feet, and remains in the air longer, 8 seconds, than the first flare

Step-by-step explanation:

The given parameters are;

The height of the first flare = 196 feet

The duration the first flare spends in the air = 7 seconds

The function representing the height of the second flair is f(t) = -16t(t - 8)

Where;

t = The time since the passenger shot the second flare

The time the flair stays i the air is given by the time it takes for the height, f(t),  to be 0 as follows;

f(t) = 0 = -16t(t - 8)

-16t(t - 8) = 0

t = 0, or t = 8

The time the second flare stays in the air = 8 seconds

The maximum height reached by the second flair is given by the finding the maximum point of the curve of the function as follows;

d(f(t))/dt = 0 = d(-16t(t - 8))/dt = -32t + 128 at the maximum point (the coefficient of t² is negative in the quadratic equation)

-32t + 128 = 0

128 = 32t

32t = 128

t = 128/32 = 4

t = 4 at maximum height and f(4) = -16 × 4 × (4 - 8) = 256 feet

The maximum height reached by the second flare f(4) = -16 × 4 × (4 - 8) = 256 feet.

Therefore, the second flare travels higher, 256 feet, and remains in the air longer, 8 seconds, than the first flare, with maximum height of 196 feet, and time in the air of 7 seconds.

a. turk and mcalister

b. howard, mission, and market

c. yes. since streets end some do not cross yet are not parallel to others. example: mcalister and 5th

step-by-step explanation:

parallel lines are lines which do not intersect ever and look a lot like railroad tracks. turk, mcalister and golden gate are examples of these.

intersect are streets which cross each other and a car on one can reach the other. howard, mission, and market intersect with 6th.

skew lines are lines which neither intersect nor are parallel. these lines exist here because some streets end and never intersect another like mcalister and 5th.

hope it you

step-by-step explanation:

sin(7pi/6 - pi/3)  

= sin(7pi/6 - 2pi/6)  

= sin(5pi/6)  

= sin(pi - pi/6)  

= sin(pi/6)  

= 1/2  

sin 7pi/6 - sin pi/3  

= sin (pi + pi/6) - sin pi/3  

= -sin pi/6 - sin pi/3  

= -1/2 - sqrt(3)/2  

= -(1+sqrt(3))2