Solve the absolute value inequality
1 answer:
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Answer:
4.50 s
Step-by-step explanation:
The motion of the ball is represented by the following equation:
(1)
where
h(t) is the elevation at time t
2 ft is the initial elevation at t = 0
+70 ft/s is the initial vertical velocity
is the acceleration due to gravity
The green is located at an elevation of -7 feet, so the ball lands on the green when
h(t) = -7
Substituting into (1)
And re-arranging we get
This is a second-order equation in the form
which has solutions
(2)
Here we have:
a = 16
b = -70
c = -9
Substituting into (2) we find the solutions:
The two solutions are:
t = 4.50 s
t = -0.125 s
The second solution is negative, and since negative time has no physical meaning, the only correct solution is
t = 4.50 s
The equation will be of the form:
where A is the amount after t hours, and r is the decay constant.
To find the value of r, we plug the given values into the equation, giving:
Rearranging and taking natural logs of both sides, we get:
The required model is:
where A is the amount after t hours, and r is the decay constant.
To find the value of r, we plug the given values into the equation, giving:
Rearranging and taking natural logs of both sides, we get:
The required model is: