Respuesta :
Answer:
Since h(max) is less than 30 ft, it will never reach a height of 30ft
The maximum height it can reach is 11.25ft.
Step-by-step explanation:
Given;
The height equation of the rock;
h = -16t^2 +20t +5
To determine whether it would reach 30 ft, we need to find its maximum height. Which is at;
dh/dt = 0
dh/dt = -32t +20 = 0
At Maximum height.
t = 20/32
We then substitute into the height equation.
h(max) = -16(20/32)^2 + 20(20/32) +5
h(max) = 11.25 ft
Since h(max) is less than 30 ft, it will never reach a height of 30ft
The maximum height it can reach is 11.25ft.
Answer:
There are no real solution to the equation [tex]h = -16t^2 +20t +5[/tex] when h = 35 ft.
Step-by-step explanation:
Here we have the equation for the height of the rock in ft given as
[tex]h = -16t^2 +20t +5[/tex]
For the rock to reach 30 ft we must have
[tex]30 = -16t^2 +20t +5[/tex]
That is [tex]0 = -16t^2 +20t +5 - 30 = -16t^2 +20t -25[/tex]
[tex]0 = -16t^2 +20t -25[/tex] or
[tex]16t^2 -20t +25 = 0[/tex]
From which it is observed that since the root of the equation is given by the quadratic formula
b² should be greater than 4·a·c however
(-20)²[tex]\ngeqslant[/tex] (4×16×25)
Hence the equation has only imaginary roots.
