Let's try to tease out a function for the area of our hypothetical rectangle:
We know that the area of a rectangle is Base x Height, and the base will be the length of the x-axis portion of the rectangle. Looking at a graph of y=27 - x^2 will help with intuition on this.
The length of the base will be 2x, since it will be the distance from the (0,0) axis in the positive direction and in the negative direction.
So our rectangle will have an area of 2x, multiplied by the height.
What is the height? The height will be our y value.
Therefore,
A = 2x * y, where x is x-value of the positive vertex.
We already know what y is as a function of x:
y= 27 - x^2
That means our equation for the area of the rectangle is:
A = 2x (27 - x^2) Distribute the terms....
A = 54x - 2x^3
This is essentially a calculus optimization problem. We want to find the Maximum for A, so let's find where the derivative of A is equal to zero.
First, we find the derivative:
A = 54x - 2x^3
A' = 54 - 6x^2
Set A' equal to zero to find the maximum value for A
0 = 54 - 6x^2
6x^2 = 54
x^2 = 9
x = 3
We got our x-value! Now let's find the y value at that point:
y= 27 - x^2
y = 27 - 9
y = 18
The height our rectangle will be 18, and our base will be 2*x = 2*3 = 6
Area = base x height = 18 * 6 = 108
The answer is B) 108.
To find the difference between these numbers you need to subtract 8.3 - 3.9
and that equals 4.4<span />
Answer:
Step-by-step explanation:
Independent variable is 5 means x = 5
solve for f(x) when x = 5
f(5) = -2(5) +1
f(5) = -10 + 1
f(5) = -9
Solution (5,-9)
Answer
B. (5,-9)
Answer:
x = 10
Step-by-step explanation:
X = 10 because if you look at the 28 and 14, 14 is half of 28 so the ratio is 1:2 which would also work for the 20 so the answer is 10
