Question 117153This question is from textbook Algebra 2
: I have to simplify each expression. # 11 is: (2+3i)(8-5i).
And # 14 is: Physics
For a model rocket, the altitude h, in meters, as a function of time t, in seconds, is given by h=68t-8t(squared). Find the maximum height of the rocket. How long does it take to reach the maximum height?
This question is from textbook Algebra 2
Answer by wgunther(43)   (Show Source):
You can put this solution on YOUR website! 2(8-5i)+3i(8-5i)=16-10i+24i+15=31+14i
So, the maximum height is when h is at it's maximum in h=68t-8t^2. There's a lot of ways to find this out.
One could, for example, take the first derivative, which would be 68-16t which is 0 when t=17/4, so the maximum is 68(17/4)-8(17/4)=255.
Another way would be to take advantage of the symmetry of quadratics, and say that the two zeros of 68t-8t^2 are 0 and 17/2, so the maximum occurs halfway in between them, or at 17/4.
Another way is the generalization you may have learned that the vertex is at the x value -b/2a, which is this case is -68/-16=17/4. Lots of ways.
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