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:
4 km/h
Step-by-step explanation:
We are told that Dina and Masha started out on a 10 km bike path at the same time.
Dina's biking speed is 5 km/h.
Let us find taken by Dina to cover 10 kn distance.
Therefore, Dina took 2 hours to complete 10 km.
Since both started at the same time, therefore, Masha also took 2 hours to complete 2 km less than Dina.
Let us find distance covered by Masha.
Now let us find Masha's biking speed.
Therefore, Masha's biking speed is 4 km per hour.
Answer:
I also need help with this one. I don't know what it is. I don't fully understand the two column proof. I might figure it out and edit this answer or put it in comments.
Step-by-step explanation:
You would want to divide 30 by 2/3 so you would do 30/1 times 3/2. This method is known as keep change flip or kcf (Kentucky Chicken Fried is what some people say) your final answer should come out to 90/2 which simplified is 45. Hope this helped
Answer:
2
Step-by-step explanation:
12x+6=20-10 (subtract 6 to -10)
12x=20x+-16 (subtract 20)
-8=-16 (divide -16 by -8)
x=2
