Answer:
A. The football does not reach a height of 15ft
Step-by-step explanation:
Given
![h(t) = -16t^2 + 30t](https://tex.z-dn.net/?f=h%28t%29%20%3D%20-16t%5E2%20%2B%2030t)
Required
Determine which of the options is true
The option illustrates the height reached by the ball.
To solve this, we make use of maximum of a function
For a function f(x)
Such that:
:
![f(\frac{-b}{2a}) = maximum/minimum](https://tex.z-dn.net/?f=f%28%5Cfrac%7B-b%7D%7B2a%7D%29%20%3D%20maximum%2Fminimum)
i.e we first solve for ![\frac{-b}{2a}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%7D%7B2a%7D)
Then substitute
for x in ![f(x) = ax^2 + bx + c](https://tex.z-dn.net/?f=f%28x%29%20%3D%20ax%5E2%20%2B%20bx%20%2B%20c)
In our case:
First we need to solve
Then substitute
for t in ![h(t) = -16t^2 + 30t](https://tex.z-dn.net/?f=h%28t%29%20%3D%20-16t%5E2%20%2B%2030t)
By comparison:
![b = 30](https://tex.z-dn.net/?f=b%20%3D%2030)
![c = -16](https://tex.z-dn.net/?f=c%20%3D%20-16)
![\frac{-b}{2a} = \frac{-30}{2 * -16}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%7D%7B2a%7D%20%3D%20%5Cfrac%7B-30%7D%7B2%20%2A%20-16%7D)
![\frac{-b}{2a} = \frac{-30}{-32}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%7D%7B2a%7D%20%3D%20%5Cfrac%7B-30%7D%7B-32%7D)
![\frac{-b}{2a} = \frac{30}{32}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%7D%7B2a%7D%20%3D%20%5Cfrac%7B30%7D%7B32%7D)
![\frac{-b}{2a} = \frac{15}{16}](https://tex.z-dn.net/?f=%5Cfrac%7B-b%7D%7B2a%7D%20%3D%20%5Cfrac%7B15%7D%7B16%7D)
Substitute
for t in ![h(t) = -16t^2 + 30t](https://tex.z-dn.net/?f=h%28t%29%20%3D%20-16t%5E2%20%2B%2030t)
![h(\frac{15}{16}) = -16(\frac{15}{16})^2 + 30(\frac{15}{16})](https://tex.z-dn.net/?f=h%28%5Cfrac%7B15%7D%7B16%7D%29%20%3D%20-16%28%5Cfrac%7B15%7D%7B16%7D%29%5E2%20%2B%2030%28%5Cfrac%7B15%7D%7B16%7D%29)
![h(\frac{15}{16}) = -16(\frac{225}{256}) + \frac{450}{16}](https://tex.z-dn.net/?f=h%28%5Cfrac%7B15%7D%7B16%7D%29%20%3D%20-16%28%5Cfrac%7B225%7D%7B256%7D%29%20%2B%20%5Cfrac%7B450%7D%7B16%7D)
![h(\frac{15}{16}) = -(\frac{225}{16}) + \frac{450}{16}](https://tex.z-dn.net/?f=h%28%5Cfrac%7B15%7D%7B16%7D%29%20%3D%20-%28%5Cfrac%7B225%7D%7B16%7D%29%20%2B%20%5Cfrac%7B450%7D%7B16%7D)
![h(\frac{15}{16}) = \frac{-225 + 450}{16}](https://tex.z-dn.net/?f=h%28%5Cfrac%7B15%7D%7B16%7D%29%20%3D%20%5Cfrac%7B-225%20%2B%20450%7D%7B16%7D)
![h(\frac{15}{16}) = \frac{225}{16}](https://tex.z-dn.net/?f=h%28%5Cfrac%7B15%7D%7B16%7D%29%20%3D%20%5Cfrac%7B225%7D%7B16%7D)
![h(\frac{15}{16}) = 14.0625](https://tex.z-dn.net/?f=h%28%5Cfrac%7B15%7D%7B16%7D%29%20%3D%2014.0625)
This implies that the maximum height reached is 14.0625ft.
So, the option that answers the question is A because ![14.0625 < 15](https://tex.z-dn.net/?f=14.0625%20%3C%2015)
What are the answer choices
7.32
10 = 73.2
100 = 732
1000 = 7320
0.006
10 = 0.06
100 = 0.6
1000 = 6
The decimal place moves to the right depending on how many zeros the number has.
For example, if you had 0.6 multiplied by 100, you would move 2 decimal places to the right because 100 has two zeros.
Answer:
1/6*6
Step-by-step explanation:
Answer:
3.25
Step-by-step explanation:
The slope formula is slope = y2 - y1 / x2 - x1 and the variables are found by assigning them with their corresponding values. Here, x1 = -9, x2 = -13, y1 = 18, and y2 = 5. Next, substitute these values in and get 5 - 18 / -13 - (-9). This can fully simplify to 13 / 4 or 3.25.