Answer:
The school where the donut and coffee day will take place.
The number of boxes of donuts the PTO bought.
The number of cups of coffee the PTO bought.
A rectangle that is 10 wide and 10 high and 8 units long would have 800 cubic units
Partitioning means to find the dividing point between two points.
This is done by prorating the difference in x- and y-coordinates, and adding to the first.
We will take the first point (from A to B) as A(16,8).
The difference is B-A, i.e.
(1,3)-(16,8) = (-15,-5)
2/5 of the difference is (2/5)*(-15,-5) = (-6,-2)
Add the difference to the first coordinates (point A) gives
Point of division = (16,8)+(-6,-2) = (16-6, 8-2) = (10,6)
Because the angels are equivalent, you can set the expressions equal to each other and solve. You will find that x = 54.
Work shown in image - let me know if I made any errors or if you have any additional questions.
Area = π r²
area of the required sector = (80/360) π * 15²
≈ 157.08