Im on some homework and came across this problem.
A contractor is to fence off a rectangular field along a straight river, the side along the river requiring no fence
a) What is the least amount of fencing needed to fence off 30,000m^2
I'm assuming im supposed to use 2X + Y = 30,000m^ for perimiter. However i know that i cant have two variables in the function. What'd be the function from here?
and b) What is the greatest area the contractor can fence off using 500m of fencing.
This is trying to find the maxima for area... and the formula would be (x^2)(y) for Volume yes? how do you get the function from here? Im pretty sure I can finish it after i get the function though
And theres another problem..
dont remember how its worded but it wants the minimum of the sum of two positive numbers, where the first is ^3 and the second is ^2. Also, they, without the ^, = 4
X^3 + (-x+4)^2 -> X^3 + X^2 -8X +16
F'= 3x^2 + 2x -8
and after using -b plus/minus (Radical b^2 (-4)(a)c) divided by 2a
the x's are .. 1.33333333333etc and .. -2 i think
and the 1.3333333333333 comes to be the min because after plugging it into f" = 6x +2 it is a Positive concave,
so 1.3333333333 being x, i'd put it into f' to find the y, which comes to be.. around 9.45 or something similar,
and putting that into the origional equation, (1.33333333^3) + (9.45^2) = around 95 or a high number like that
HOWEVER this MUST be wrong because 9.45 + 1.3333 does NOT = 4
Where did i mess up on this one?
thanks for your help!