Alain throws a stone off a bridge into a river below. The stone's height (in meters above the water), x seconds after Alain threw it, is modeled by: h(x)=−5x^2+10x+15 How many seconds after being thrown will the stone hit the water?

3 seconds

Step-by-step explanation:

The stone hits the water when h(x)=0

h(x)=0

-5x^2+10x+15=0

x^2-2x-3=0

(x+1)(x-3)=0

x+1=0 OR x-3=0

x=-1 OR x=3

We found that h(x)=0 for x=−1 or x=3. Since x=−1 doesn't make sense in our context, the only reasonable answer is x=3.

In conclusion, the stone will hit the water after 3 seconds.

9514 1404 393

  obtuse

Step-by-step explanation:

Using the idea of a "form factor", we find ...

  f = a² + b² - c²

  f = 25² +30² -50² = 625 +900 -2500 = -975

The form factor is negative, so the triangle is obtuse.

_____

Additional comment

The form factor, as defined above, classifies the triangle according to its sign:

  f > 0 . . . acute

  f = 0 . . . right

  f < 0 . . . obtuse

The largest angle in the triangle can be found from ...

  cos(C) = f/(2ab)

Here, it is C = arccos(-975/1500) ≈ 130.5416°