SOLUTION: A water balloon is thrown upward from a height of 5 feet with an initial velocity of 35 feet per second.The quadratic equation function h(t)=-16t^2+35t+5 represents the height of t

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Question 1197205: A water balloon is thrown upward from a height of 5 feet with an initial velocity of 35 feet per second.The quadratic equation 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.

Please also show me how you got the answer I need both things.
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

t = number of seconds
h(t) = height of the water balloon

Let's determine what time value(s) apply when the height is 10 feet.

Replace h(t) with 10 and get everything to one side
h(t) = -16t^2+35t+5
10 = -16t^2+35t+5
0 = -16t^2+35t+5-10
0 = -16t^2+35t-5
-16t^2+35t-5 = 0

Consider the general form at^2+bt+c = 0
We have these coefficients
a = -16
b = 35
c = -5
in which we plug into the quadratic formula
t+=+%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29

t+=+%28-35%2B-sqrt%28%2835%29%5E2-4%28-16%29%28-5%29%29%29%2F%282%28-16%29%29

t+=+%28-35%2B-sqrt%28905%29%29%2F%28-32%29

t+=+%28-35%2B-++30.083218%29%2F%28-32%29

t+=+%28-35%2B30.083218%29%2F%28-32%29 or t+=+%28-35-30.083218%29%2F%28-32%29

t+=+%28-4.916782%29%2F%28-32%29 or t+=+%28-65.083216%29%2F%28-32%29

t+=+0.153649 or t+=+2.033851
The decimal values are approximate.

The water balloon reaches a height of 10 feet at approximately 0.153649 seconds. This is when the balloon is going upward.

It comes back down to get back to 10 feet at around 2.033851 seconds

The balloon is more than 10 feet off the ground for the interval 0.153649 < t < 2.033851
Basically anything between 0.153649 seconds and 2.033851 seconds, excluding each endpoint.

You can use graphing technology like Desmos or GeoGebra to visually confirm the answers.
Be sure to use x in place of t, and use y in place of h(t)

Round each approximate decimal value according to the instructions your teacher provides.