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.

answer:  

step-by-step explanation:

here x represents the height of the pole,

and, the height of the shadow of the pole is 12 feet.

also, the angle of elevation from the top of the pole is 40°,

therefore,

by the low of sine,

which is the required equation for finding the value of x,

a) y = -3x +2

b) y = 1/2x -6

these 2 can be combined into one equation.

-3x +2 = .5x -6

8 = 3.5x

x = 8 / 3.5 = 2.2857142857

y = -3 * (8 / 3.5) +2

y = (-24 / 3.5) + 2

y = -4.8571428571

step-by-step explanation: