Determine whether the relationship is an inverse variation or not. Explain.
1 answer:
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General Idea:
If we have a quadratic function of the form f(x)=ax^{2} +bx+c , then the function will attain its maximum value only if a < 0 & its maximum value will be at x=-\frac{b}{2a} .
Applying the concept:
The height h is modeled by h = −16t^2 + vt + c, where v is the initial velocity, and c is the beginning height of the firecracker above the ground. The firecracker is placed on the roof of a building of height 15 feet and is fired at an initial velocity of 100 feet per second. Substituting 15 for c and 100 for v, we get the function as .
Comparing the function f(x)=ax^{2} +bx+c with the given function , we get
,
and
.
The maximum height of the soccer ball will occur at t=\frac{-b}{2a}=\frac{-100}{2(-16)} = \frac{-100}{-32}=3.125 seconds
The maximum height is found by substituting in the function as below:
Conclusion:
<u>Yes !</u> The firecracker reaches a height of 100 feet before it bursts.
Notice that the height of the pine cone when it hits the ground is zero. So, to find the tame it takes for the pine cone to hit the ground, we just need to replace the height, 
, with 0 in the function, and solve for time 
:
Since time cannot be negative, the solution is
seconds.
Since 1.5 second is significantly less than 2 seconds, we can conclude that <span>2 seconds is not a reasonable answer to this model.</span>
Since time cannot be negative, the solution is
Since 1.5 second is significantly less than 2 seconds, we can conclude that <span>2 seconds is not a reasonable answer to this model.</span>