Aball is thrown straight up from the top of a building that is 400 ft high with an initial velocity of 64 ft/s. the height of the object can be modeled by the equation s(t) = -16t2 + 64t + 400. determine the time(s) the ball is higher than the building. write your answer in interval notation. then in two or more complete sentence, explain your solution method.

The time(s) the ball is higher than the building: Interval (0,4)

Step-by-step explanation:

s(t)=-16t^2+64t+400

Determine the time(s) the ball is higher than the building:

s(t)>400

-16t^2+64t+400>400

Subtracting 400 both sides on the inequality:

-16t^2+64t+400-400>400-400

-16t^2+64t>0

Multiplying the inequality by -1:

(-1)(-16t^2+64t>0)

16t^2-64t<0

Fatorizing: Comon factor 16t:

16t(16t^2/16t-64t/16t)<0

16t(t-4)<0

t is greater than zero:

t>0→t-4<0→t-4+4<0+4→t<4

Then t>0 ant t<4:

Solution = (0, Infinite) ∩ (-Infinite, 4)

Solution = (0,4)

the answer is; biodiversity resulting from few ancestors

adaptive radiation occurs when a population is subjected to a large natural environment with spatial ecological variations. the parts of the population in the different ecologies begin to adapt to their local environments. due to non-random mating across the large populations, this causes the different populations from the large population to speciate within their local environments. they, therefore, diverge to different species sharing a common ancestor.  

whole numbers.

step-by-step explanation:

we are given the average monthly rainfall (in millimeters) model r(m) for the years 1900-2009 as a function of the month number m.

as we can see m is taken for the number of months for years 1900-2009.

we know that number of months can't be a negative number or decimal number or a fraction.

so, the number of months could be only positive whole numbers.

therefore, whole numbers is more appropriate for the domain of r.