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.
Vowels include AEIOU, so in the first box there is 2 vowel out of the 5 letters so 2/5 probability for the first box. Box 2 includes 2,4,6,8 as the even numbers out of the 9 numbers so 4/9
If you were solving the probability for each box individually that would be your answer
However if you are doing statistics and need to do it in a certain order you multiply the fractions
2/5 x 4/9 = 8/45
(.17777)
This leaves you with a 17% (8/45) chance of picking a vowel then an even number.
(-4)+10=6 if you add (-4) to 10
it is like subtracting 4 from 10
witch equals six
Answer:
A.
Step-by-step explanation:
The volume of the pyramid on the left is greater by 2 inches cubed.
hope this helps! :3
3x9x10^1
27x10^1
27x100
2700
