When you have the power multiplied to another power you have to multiply
so
(a^3)^3 - (b^3)^3 = a^9 - b^9
A is correct.
B is incorrect because when you multiply the exponents you get a^18 - b^18
C is incorrect because when you distribute the 2 you get a^6 - b^6
D is correct too
Volume of the pyramid:
Perimeter of the cross-section:
Area of the cross-section:
First derivative test:
Then the height of the cross-section/pyramid is
The volume of the pyramid that maximizes the cross-sectional area 
is
Answer:
-51 6/10 or -51 60/100
Step-by-step explanation:
I believe it to be 1 over 3 as 1 as the numerator and 3 as the denominator
There are two of them.
I don't know a mechanical way to 'solve' for them.
One can be found by trial and error:
x=0 . . . . . 2^0 = 1 . . . . . 4(0) = 0 . . . . . no, that doesn't work
x=1 . . . . . 2^1 = 2 . . . . . 4(1) = 4 . . . . . no, that doesn't work
x=2 . . . . . 2^2 = 4 . . . . . 4(2) = 8 . . . . . no, that doesn't work
x=3 . . . . . 2^3 = 8 . . . . . 4(3) = 12 . . . . no, that doesn't work
<em>x=4</em> . . . . . 2^4 = <em><u>16</u></em> . . . . 4(4) = <em><u>16</u></em> . . . . Yes ! That works ! yay !
For the other one, I constructed tables of values for 2^x and (4x)
in a spread sheet, then graphed them, and looked for the point
where the graphs of the two expressions cross.
The point is near, but not exactly, <em>x = 0.30990693...
</em>If there's a way to find an analytical expression for the value, it must involve
some esoteric kind of math operations that I didn't learn in high school or
engineering school, and which has thus far eluded me during my lengthy
residency in the college of hard knocks.<em> </em> If anybody out there has it, I'm
waiting with all ears.<em>
</em>
