Let x and y be the dimensions of the rectangle. If the perimeter is 40, we have
We can expression one variable in terms of the others as
Since the area is the product of the dimensions, we have
This is a parabola facing down, so it's vertex is the maximum:
So, the maximum is
And since we know that , we have
as well.
This is actually a well known theorem: out of all the rectangles with given perimeter, the one with the greatest area is the square.
Answer:
The standard form of a circle is (x-h)^2 + (y-k)^2 = r^2 with (h,k) being the center of the circle and r being the radius. In this case the circle's equation in standard form is (x-2)^2 + (y+3)^2 = 18. Knowing this it's easy to see that the center of the circle (h,k) is (2,-3). Finally the radius is or in simplified terms, 3
Step-by-step explanation:
Let x <u>represent</u> the <u>number of cups</u> of Superfiber Will ate this week and let y represent the number cups of Fiber Oats he ate this week.
1. If in Superfiber cereal, there are 5 grams of fiber in one cup, then in x cups there are grams of fiber.
2. If in Fiber Oats cereal, there are 4 grams of fiber in one cup, then in y cups there are grams of fiber.
3. The total amount of fiber Will ate is grams.
4. This week Will ate at least 30 grams of fiber. Then
Answer: correct choice is A.