What is Index Law 1? please give a definition
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Multiply both numerator and denominator of by the complex conjugate of the denominator, -2+9i.
Multiplication can be transformed into difference of squares using the rule: .
By definition, i² is -1. Calculate the denominator.
Multiply complex numbers 5-3i and -2+9i in the same way as you multiply binomials.
Do the multiplications in .
Combine the real and imaginary parts in -10+45i+6i+27.
Do the additions in .
Divide 17+51i by 85 to get .
The real part of is
.
Check the picture below.
as you can see, the graph of the volume function comes from below goes up up up, reaches a U-turn then goes down down, U-turns again then back up to infinity.
the maximum is reached at the close up you see in the picture on the right-side.
Why we don't use a higher value from the graph since it's going to infinity?
well, "x" is constrained by the lengths of the box, specifically by the length of the smaller side, namely 5 - 2x, so whatever "x" is, it can't never zero out the smaller side, and that'd happen when x = 2.5, how so? well 5 - 2(2.5) = 0, so "x" whatever value is may be, must be less than 2.5, but more than 0, and within those constraints the maximum you see in the picture is obtained.
