49.15 is the smallest f can be while 49.24 is the largest it can be. Well technically we could have something like 49.2499 or 49.24999 and so on. We slowly approach 49.25 but never actually get there
So the variable f is between 49.15 and 49.25 inclusive of the first value but excluding the second value. We can write it as
For similar reasoning,
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If we wanted to subtract those variables and get the smallest result possible, then we need to pick values that are closest together. It might help to set up a number line.
This means we'd go for f = 49.15 and g = 7.85
The lower bound for f-g is f-g = 49.15-7.85 = 41.3
In contrast, the upper bound is when the two variables are spaced as far apart as possible. The upper bound is f-g = 49.25 - 7.75 = 41.5
Then use your z table (should be on your formula sheet if not look one up) to find your proportion (in this problem it would be .2119) and convert it to a percent.
1. The function H= -16T^2+80T+5 is a parabola of the form , so to find the maximum height of the ball, we are going to find the y-coordinate of the vertex of the parabola. To find the y-coordinate of the vertex we are going to evaluate the function at the point . From our function we can infer that and , so the point \frac{-b}{2a} [/tex]will be . Lets evaluate the function at that point:
We can conclude that the ball reaches a maximum height of 105 feet.
2. Since we now know that the maximum height the ball reaches is 105 feet, we are going to replace with 105 in our function, then we are going to solve for to find how long the ball takes to reach its maximum height:
We can conclude that the ball reaches its maximum height in 2.5 seconds.
3. Just like before, we are going to replace with 5 in our original function, then we are going to solve for to find how long will take for the ball to be caught 5 feet off the ground:
We can conclude that it takes 5 seconds for the ball to be caught 5 feet off the ground.