<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:
The answer is
<h2>
</h2>
Step-by-step explanation:
The slope of the line passing through two points can be found by using the formula
<h3>
</h3>
where
(x1 , y1) and (x2 , y2) are the points
From the question
The points are (-2,5) and (3/2, 2)
The slope is
<h3>
</h3>
We have the final answer as
<h3>
</h3>
Hope this helps you
The formula is
A=p e^rt
A future value?
P present value 500
E constant
R interest 0.011
T time 15 years
A=500×e^(0.011×15)
A=589.7
Answer:
-11
Step-by-step explanation:
To find the y-intercept, simply look at the constant at the end of this equation. Let's look at the linear function equation. The equation is y=mx+b. In this case, the constant is b. The constant always is the non-x term, so for the question, the y-intercept would be -11.
