Factor out the common term; 3
(3(x + 1))^2 = 36
Use the Multiplication Distributive Property; (xy)^a = x^ay^a
3^2(x + 1)^2 = 36
Simplify 3^2 to 9
9(x + 1)^2 = 36
Divide both sides by 9
(x + 1)^2 = 36/9
Simplify 36/9 to 4
(x + 1)^2 = 4
Take the square root of both sides
x + 1 = √4
Since 2 * 2 = 4, the square root of 2 is 2
x + 1 = 2
Break down the problem into these 2 equations
x + 1 = 2
x + 1 = -2
Solve the first equation; x + 1 = 2
x = 1
Solve the second equation; x + 1 = -2
x = -3
Collect all solutions;
<u>x = 1, -3</u>
h(t) is the height of the diver in feet above the water
Now it asks about the time at which diver reaches the water
When diver reaches the water , the height of diver from water should be zero
So we plug h(t) =0
So

divide whole equation by -16

we can now factor the quadratic equation
So we get
(t+4)(t-3) =0
plug each factor equal to zero and solve for t
t+4 =0 and t-3 =0
So t=-4 and t=3
Now time cannot be negative , So t=3
So time = 3 seconds
It takes 3 seconds for the diver to reach the water
Answer:


or

Step-by-step explanation:
We are going to see if the exponential curve is of the form:
, (
).
If you are given the
intercept, then
is easy to find.
It is just the
coordinate of the
intercept is your value for
.
(Why? The
intercept happens when
. Replacing
with 0 gives
. This says when
.)
So
.
So our function so far looks like this:

Now to find
we need another point. We have two more points. So we will find
using one of them and verify for our resulting equation works for the other.
Let's do this.
We are given
is a point on our curve.
So when
,
.


Divide both sides by 8:

Reduce the fraction:

So the equation if it works out for the other point given is:

Let's try it. So the last point given that we need to satisfy is
.
This says when
,
.
Let's replace
with 2 and see what we get for
:






So we are good. We have found an equation satisfying all 3 points given.
The equation is
.
Answer: its correct
Step-by-step explanation: and its correct cuase its the answer you choose