Kevin has a spinner that has 10 equal sections and 2 sections of each color—red, blue, green, yellow, and purple. Kevin spins th
2 answers:
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This one is quite the deal, but we can begin by distributing the negative on the denominator and getting rid of the parenthesis:
See how the denominator now is more a simplification of like terms, with this I mean that you operate the numbers with an "i" together and the ones that do not have an "i" together as well. Namely, the 7 and the -4, the -2i with the -9i.
Therefore having the result:
Now, the
This means that we get the result 7i for the numerator.
In order to rationalize this fraction even further, we have to remember an identity from the previous algebra classes, namely:
The difference of squares allows us to remove the imaginary part of this fraction, leaving us with a real number, hopefully, on the denominator.
See, all I did there was multiply both numerator and denominator with (3+11i) so I could complete the difference of squares.
See how
I'll let you take it from here, all you have to do is simplify it further.
The simplification is quite straightforward, the numerator distributed the 7i. Namely the product
You should know from your classes that i^2 = -1, thefore the numerator simplifies to
You can do it as a curious thing, but simplifying yields the result:
Answer:
Step-by-step explanation:
Comment
There are a number of ways of doing this problem. I don't know which method you are intended to use. One sure way in this case is graphing the equation, I have done this for you. See below. The maximum volume occurs where x = 2
The graph shows that there is a peak at x = 2. That is where the maximum volume is,
Answer
x = 2
