A rollercoaster ride reaches a height of 80 feet before it sharply drops. The height above the ground of the rollercoaster car during the drop is modeled by the function, h(t)=10t2−40t+80 , where t is measured in seconds since the car started its decline. The model is accurate for 0≤t≤4 . On this portion of the ride, how long does the car take to reach a minimum height from the ground before rising again?

Therefore the car takes 2 s to reach a minimum height from the ground before rising again.

Step-by-step explanation:

Given that a roller coaster ride reach a height of 80 feet.

The height above the ground of the roller coaster is modeled by the function

h(t)=10t²-40t+80

where t is measured in second.

h(t)=10t²-40t+80

Differentiating with respect to t

h'(t)= 10(2t)-40

⇒h'(t)=20t-40

To find the minimum height we set h'(t)=0

∴20t-40=0

⇒20t =40

⇒t=2

The height of the roller coaster minimum when t=2 s.

The minimum height of of the roller coaster is

h(2)= 10(2)²-40.2+80

     =40-80+80

     =40 feet.

Therefore the car takes 2 s to reach a minimum height from the ground before rising again.

-3

step-by-step explanation:

a drawing really does here:

so i draw the horizontal line y=2 and the vertical line x=-2 at this intersection i put b (this is where my right angle is going to be).   so point b is at (-2,2).   point a is 5 units long and is also on y=2 so this point has to be (3,2) or (-7,2) -doesn't matter i will go with (3,2).

now we know c is at (-2,y) we don't know the y yet bet we know that c is on x=-2.

we have the area of the triangle is .5bh=12.5

we know the base length is 5 (ab)

we have the height is (2-y) if you look at your

plug in

.5(5)(2-y)=12.5

solve for y to get the y-coordinate for c

2.5(2-y)=12.5

divide both sides by 2.5 giving:

2-y=5

now subtract 2 on both sides

-y=3

y=-3

nswer: a   y-axis

step-by-step explanation: