Answer:
Step-by-step explanation:
a. Table.
To fill out the table, use the expression and substitute the values of t to get a value of h and write in the table. Do it in the following fashion:
1. For t= 7:
[tex]h=1457-16(7)^{2}\\\\h= 673[/tex]
2. For t= 8:
[tex]h=1457-16(8)^{2}\\\\h=433[/tex]
3. For t= 9:
[tex]h=1457-16(9)^{2}\\\\h=161[/tex]
4. For t= 10:
[tex]h=1457-16(10)^{2}\\\\h=-143[/tex]
5. For t= 11:
[tex]h=1457-16(11)^{2}\\\\h=-479[/tex]
After you fill out the table, it should look like attached image 1 (check below).
b. Time if landing.
Knowing that the function gives us the dictance between the penny and the ground, when the penny lands its distance from the ground will be 0. To get the time of landing, subsitute the value of h by 0 and solve the equation for t. Do it like this:
[tex]1457-16t^{2}=0\\ \\-16t^{2}=-1457\\ \\t^{2}=\frac{-1457}{-16} \\ \\t=\sqrt{\frac{-1457}{-16}} \\ \\t=9.54seconds[/tex]
c. Verify the answer graphically.
To verify graphically, graph the function around the origin of the cartesian plane and see in what value of x the function touches the y axis (check attached image 2 below).
