In this problem we have a pumpkin is launched from the top of a 20 foot tall platform at an initial velocity of 84 feet per second. So the height, h, of the pumpkin at time t seconds after the launch can be modeled by the equation:
So this is the equation of a parabola. The maximum of this parabola occurs at its vertex. So let's find this vertex:
Finally, the maximum occurs at time 2.625 seconds when the height is 130.25m
We will work on adding two fractions correctly with different denominators. The two denominators must be equated first.
In order to add these fractions, we need finding the common denominator by multiplying both denominators together.
Both denominators, 16 and 2, are multiplied by one another. What about numerators? Pay attention to the treatment of each fraction.
Let's take a break here to think.
Alternatively, develop a sharper method as below.
Note how this is performed. Absolutely indeed, cross-multiplication!
The numerator and denominator are divided by two to make it a simple fraction. After that, we simplify again into mixed fractions.
Gently let's take a break once more to think strategically.
Observing the steps above, we still find a large number when there is a direct multiplication of the two denominators. Are there more highly recommended steps? Of course there is!
The denominators 2 and 16 have LCM = 16. So, we convert the given fractions into equivalent fractions with denominator 16.
Do not forget simplifying again into mixed fractions.
<u>Note:</u>
In the form of fractions, the steps that must be considered are
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