On your family trip, you used 14 gallons of gas.
1 answer:
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Question:
A fastball is hit straight up over home plate. The ball's height, h (in feet), from the ground is modeled by h(t)=-16t^2+80t+5, where t is measured in seconds. Write an equation to determine how long it will take for the ball to reach the ground.
Answer:
Step-by-step explanation:
Given
Required
Find t when the ball hits the ground
This implies that h(t) = 0
So, we have:
Reorder
Using quadratic formula, we have:
Where
So, we have:
This gives:
or
or
or
But time can not be negative.
So, we have:
<em>Hence, time to hit the ground is 5.0625 seconds</em>
We analyze the chart and observe that the linear function is 
, since this relation holds for all values in the table. Drawing this line over the quadratic function shows that they intersect twice, at both the positive and negative x-coordinates.
This is by far the easiest way to solve this problem, but if you're interested in learning how to do it algebraically, read on! To prove this more rigorously, we can find that the equation of the parabola is
Substituting in , we find that the intersection points occur where 
, or 
or 
This equation doesn't factor nicely, so we use the quadratic formula to learn that
Hence, the x-coordinates of the intersection points are 
, which is positive, and 
, which is negative. This proves that there are intersection points on both ends of the axis.
This is by far the easiest way to solve this problem, but if you're interested in learning how to do it algebraically, read on! To prove this more rigorously, we can find that the equation of the parabola is
This equation doesn't factor nicely, so we use the quadratic formula to learn that
- Three time the quotient of a number and 2 increased by 5 is at most -12.