A ball is thrown straight up into the air. The table shows the data collected over t seconds, where h(t) is the height of the ba
1 answer:
You might be interested in
Answer: The required result is 15.
Step-by-step explanation: We are given to evaluate the following :
"6 choose 4".
Since we are to choose 4 from 6, so we have to use the combination of 6 different things chosen 4 at a time.
We know that
the formula for the combination of n different things chosen r at a time is given by
For the given situation, n = 6 and r = 4.
Therefore, we get
Thus, the required result is 15.
Answer:
1. 6 feet
2. 6.25 feet
3. 1 feet
4. 6 feet
Step-by-step explanation:
The equation is :
1. The diving board is where Kendra dives off. Here, the horizontal distance, x from the diving board is 0.
So, substituting x = 0 in the equation, we get
So, the diving board is 6 feet above the surface of the water.
2. From the equation, we known that it is a parabola and the vertex is minimum.
It is the minimum height which represents the depth Kendra dives into the water.
So the coordinate of the vertex is =
Here, a and b are the coefficients of linear term and the quadratic terms in the equation. Therefore,
a = 1 and b = -7
∴ x coordinate =
Now substituting to find f(x),
= -6.25
Therefore, the diver dives 6.25 feet below the water surface.
3. The horizontal distance from the board the diver enters into the water.
This is the y-intercept and it is the value of x when h(x)=0.
∴
Factorizing, we get
∴
So there are two solutions that are the two x intercepts of the function. Here at x = 1 shows the horizontal distance from the board from where Kendra dives into the water.
4. We know that the equation given has x intercepts. These two x intercepts are the points where the parabola crosses the x-axis, which is the height
. The height is the water surface level.
The first x intercept represents the points where Kendra dives into the water.
And the second x intercept is the point where Kendra comes out of the water surface. This this is for
.
Thus Kendra dives out of the water surface at 6 feet from the board.