The function h(t) = -16^2 + 120t + 300 gives the height in feet of a projectile fired from the top of a building after t seconds. When will the object reach a height of 350ft?

Answer 1

If -16^2 + 120t + 300

mean

h(t) = -16 t² + 120 t + 300

then

-16 t² + 120 t + 300 = 350

subtract 350 to both sides

-16 t² + 120 t + 300 - 350 = 0

-16 t² + 120 t - 50 = 0

Multiply both sides by - 1

16 t² - 120 t + 50 = 0

Solve with the quadratic formula:

t1/2 = [ - b ± √ ( b² - 4 ∙ a ∙ c ) ] / 2 ∙ a

In this case a = 16 , b = - 120 , c = 50

t1/2 = { - ( - 120 ) ± √ [ ( - 120 )² - 4 ∙ 16 ∙ 50 ] } / 2 ∙ 16

t1/2 = [ 120 ± √ ( 14 400‬ - 3 200 ] / 32

t1/2 = ( 120 ± √11 200 ) / 32

t1/2 = [ ( 120 ± √ ( 1 600 ∙ 7 ) ] / 32

t1/2 = ( 120 ± √ 1 600 ∙ √7 ) / 32

t1/2 = ( 120 ± 40 ∙ √7 ) / 32

t1/2 = 40 ∙ ( 3 ± √7 ) / 32

t1/2 = 8 ∙ 5 ∙ ( 3 ± √7 ) / 8 ∙ 4

t1/2 = 5 / 4 ∙ ( 3 ± √7 )

t1 = 5 / 4 ∙ ( 3 - √7 ) = 5 / 4 ( 3 - 2.645751311 ) =

5 / 4 ∙ 0.354248689 = 0.44281086125 sec

t2 = 5 / 4 ∙ ( 3 + √7 ) = 5 / 4 ( 3 + 2.645751311 ) =

5 / 4 ∙ 5.645751311 = 7.05718913875 sec

Answer 2

if two piece of siopao cost 120 how many pieces of siopao can you buywith 300