A water balloon is thrown upward from a height of 5 feet with an initial velocity of 35 feet per second. The quadratic function h(t)=-16t^2+35t+5 represents the height of the balloon, h, in feet t seconds after it is thrown. Determine when the balloon is more than 10 feet above the ground. Round your answer to the nearest thousandth.

t>2.034s and t>0.154s

Step-by-step explanation:

Given the quadratic function h(t)=-16t^2+35t+5 which represents the height of the balloon, h, in feet t seconds after it is thrown.

To determine when the balloon is more than 10feet above the ground, we will substitute h = 10 into the expression to have;

h(t)=-16t^2+35t+5

-16t^2+35t+5>10

-16t^2+35t+5-10>0

16t^2-35t+5>0

Find t;

t > 35±√35²-4(16)(5)/2(16)

t>35±√1225-320/32

t>35±√905/32

t>35±30.08/32

t > 35+30.08/32 and t > 35-30.08/32

t>65.08/32 and t>4.92/32

t>2.034s and t>0.154s

Hence the balloon is more than 10feet above the ground at when t>2.034s and t>0.154s

1k

step-by-step explanation:

-6k+7k

(-6+7)k

1k