Find the lowest common multiple (LCM) of 30 and 42
2 answers:
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9514 1404 393
Answer:
time to max height: 2.5 seconds
max height: 104 ft
range of function: [4, 104]
Step-by-step explanation:
The equation for ballistic motion is ...
h(t) = -16t^2 +v0·t +h0 . . . . where v0 is the initial upward speed and h0 is the initial height
For the given parameters, the height function is ...
h(t) = -16t^2 +80t +4
The time for maximum height is ...
-b/(2a) = -80/(2(-16)) = 2.5 . . . seconds
The maximum height is ...
h(2.5) = (-16·2.5 +80)(2.5) +4 = 104 . . . feet
The range of the function is from the minimum height (at launch) to the maximum height:
4 ft ≤ h(t) ≤ 104 ft.
Assuming you know the quadratic formula:
You can fill in a, b and c in this and get:
Now, let's create a shorthand to make the writing easier:
But since one root is three times the other root (but we don't know which one), we also know that:
or
If you solve this, you get:
or
However, since q is a square root, it must be postive.
So we know that:
From this you find that
So p = 3/2
The roots are x=1/2 and x=3/2.