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.
Answer:
784.3
Step-by-step explanation:
3.14(15.8)^2 = 784.3
hope this helped :>
Answer:
y^2*y^3
Step-by-step explanation:
Use the power of 5
16, think of 4 plus 4 plus 4 plus 4.
Complete Question
Veronikas four test scores are 59, 80, 95, 88 and 93 if the outlier of 59 is removed what is the mean absolute deviation of the remaining four test scores?
Answer:
5
Step-by-step explanation:
We have the four test scores
80, 95, 88 and 93
Step 1
We find the mean of the 4 test scores
= 80 + 95 + 88 + 93/4
= 356 / 4
89
Step 2
The formula for Mean Absolute Deviation =
Summation( x - Mean)/n
Hence,
|(80 - 89 )+( 95 - 89) + (88 - 89) + (93 - 89)|/5
= 9 + 6 +1 + 4/4
= 20/4
= 5
