<span>Length = 1200, width = 600
First, let's create an equation for the area based upon the length. Since we have a total of 2400 feet of fence and only need to fence three sides of the region, we can define the width based upon the length as:
W = (2400 - L)/2
And area is:
A = LW
Substitute the equation for width, giving:
A = LW
A = L(2400 - L)/2
And expand:
A = (2400L - L^2)/2
A = 1200L - (1/2)L^2
Now the easiest way of solving for the maximum area is to calculate the first derivative of the expression above, and solve for where it's value is 0. But since this is supposedly a high school problem, and the expression we have is a simple quadratic equation, we can solve it without using any calculus. Let's first use the quadratic formula with A=-1/2, B=1200, and C=0 and get the 2 roots which are 0 and 2400. Then we'll pick a point midway between those two which is (0 + 2400)/2 = 1200. And that should be your answer. But let's verify that by using the value (1200+e) and expand the equation to see what happens:
A = 1200L - (1/2)L^2
A = 1200(1200+e) - (1/2)(1200+e)^2
A = 1440000+1200e - (1/2)(1440000 + 2400e + e^2)
A = 1440000+1200e - (720000 + 1200e + (1/2)e^2)
A = 1440000+1200e - 720000 - 1200e - (1/2)e^2
A = 720000 - (1/2)e^2
And notice that the only e terms is -(1/2)e^2. ANY non-zero value of e will cause this term to be non-zero and negative meaning that the total area will be reduced. Therefore the value of 1200 for the length is the best possible length that will get the maximum possible area.</span>
Answer:
Ax+BY=z First subtract Ax from both sides to get By=z-Ax. Then divide by B from both side to get y=(z-Ax)/B
Step-by-step explanation:
Answer:234
Step-by-step explanation:
XY>=90
9x>=90
x>=10
possible solutions include 134131413 4234234232 342342423 2342423423 342423432 42342423 23423424 23424242234 244324242424234 2342 and 497553452353570542389579523954875923759237529
Step-by-step explanation:
A rectangle: P=2l+2w or P=2(l+w) (same formula written differently)
50=2x17+2w
50=34+2w
2w=50-34
2w=16
w=16÷2=8
Since it says twice as wide then we will multiply w with 2
2xW
2x8=16 which is the width of the 2nd rectangle
Hope this helps :)
Answer: D
Step-by-step explanation:
