12. An object is fired from the top of a 200 ft. tower with an initial velocity of 80 ft/sec. and is modeled by the equation h(t) = -16t^2+80t + 200.

a) How long after firing does it reach its maximum height?

b) What is the maximum height?

a) The object reaches its maximum height at t=2.5 seconds

b) The maximum height is 300 m

Step-by-step explanation:

Maximum Value of a Function

First derivative criteria:

If f(t) is a real continuous function of t and the first derivative of f called f'(t) exists, then solving the equation:

f'(t)=0

Gives the critical points of f, some of which could be maximum or minimum.

Second derivative criteria:

If t=t1 is a critical point of f(t) and the second derivative of f:

f''(t1) is positive, then t1 is a minimum of f

f''(t1) is negative, then t1 is a maximum of f.

f''(t1)=0, no conclusion can be drawn.

The height of the object is modeled by the function:

a)

To find the maximum height, we use the above criteria.

Find the first derivative:

h'(t) = -32t+80

Equate h'(t)=0

-32t+80=0

Solve:

t=2.5 seconds

Find the second derivative:

h''(t)=-32

Since the second derivative is negative, the critical point is a maximum.

The object reaches its maximum height at t=2.5 seconds

b) Evaluate h(2.5)

h(2.5)=300 m

The maximum height is 300 m

what is the information provided?

step-by-step explanation:

second option

step-by-step explanation:

the measures of a triangle equal 180. use that to find x.

2x+3x+4x=180

9x=180

9x/9=180/9

x=20

now you know x, you know angle a is 40°, angle b is 60°, angle c is 80°.

because angle a is 40°, the first option doesn't work.

because angle b is 60°, the second option does work.

when you add angle a and b, you get 100°. complementary means it equals 90°, so the third option doesn't work.

when you add angle a and c, you get 120°, which is not 100.