The function y = –16t2 + 486 models the height y in feet of a stone t seconds after it is dropped from the edge of a vertical cliff. how long will it take the stone to hit the ground? round to the nearest hundredth of a second. question 7 options: 0.25 seconds 5.51 seconds 11.02 seconds 7.79 seconds

5.51 seconds

y = 0 when the stone hits the ground. At that point, t can be found from ...

... 0 = -16t^2 +486

... 0 = t^2 -30.375 . . . . divide by -16

... 30.375 = t^2 . . . . . . add the opposite of the constant

Take the square root to get ...

... √30.375 = t ≈ 5.51 . . . . seconds

1/5x+9 2/5y+7

step-by-step explanation:

the direct variation says that:

then the equation is of the form is given by:

            where k is the constant variation.

from the given table:

consider any value of x and m(x)=y

x = 2 and m(x)=y = 3

substitute these value in [1]; we have;

divide both sides by 2 we get;

⇒

check:

put x = -1 and m(x) = -1.5

substitute in the equation:

-1.5 = -1.5                   true

therefore, the function m(x) represents a direct variation

graph of this function as shown below: