An object is propelled upward from the top of a 300 foot building. the path that the object takes as it falls to the ground can be modeled by h = 16t^2 + 80t + 300 where t is the time (in seconds) and h is the corresponding height (in feet) of the object. how long does it take the object to hit the ground?

As per the statement:

The path that the object takes as it falls to the ground can be modeled by

where h is the height of the objects and t is the time (in seconds)

At t = 0 , h = 300 ft

When the objects hit the ground, h = 0

then;

For a quadratic equation:         ......[1]

the solution for the equation is given by:

On comparing the given equation with [1] we have;

a = -16 ,b = 80 and c = 300

then;

Simplify:

sec and sec

Time can't be in negative;

therefore, the time it took the object to hit the ground is 7.5 sec

{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1

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step-by-step explanation: