Answer:
The pebble will hit the ground 8.29 second after it is thrown.
Step-by-step explanation:
Given that,
The height of the pebble after t seconds is given by the equation
h= -16t²+24 t+900.
When the pebble hit the ground, the height of the pebble will be zero.
So putting h=0 in the given equation.
0 = -16t²+24 t+900
⇒-4(4t²-6t-225)=0
⇒4t²-6t-225=0
Applying quadratic formula
, here a=4, b= -6 and c= -225.

⇒ t = 8.29, -6.79
Since time can not negative.
∴t=8.29 seconds.
The pebble will hit the ground 8.29 second after it is thrown.
Answer:
1) 
2) 
Step-by-step explanation:
Assuming that our function is
for the first case and
for the second case.
Part 1
We can rewrite the expression like this:

And we can reorder the terms like this:

Now if we apply integral in both sides we got:

And after do the integrals we got:

Now we can use the initial condition 

And the final solution would be:

Part 2
We can rewrite the expression like this:

And we can reorder the terms like this:

Now if we apply integral in both sides we got:

And after do the integrals we got:

Now we can use the initial condition 

And the final solution would be:
