I just recieved a worksheet to do for homework and was stuck on two of the problems. Could anyone please explain them to me?

1. In the coordinate plane, what is the distance between the point with the coordinates 3,5 and the point with the coordinates -5,20?

2. A section is cut out of a circular piece of paper having radius four inches. The edges are then glued together forming a right circular cone. What is the circumference of the base of the cone? Express your answer in terms of pi.

For your first problem. It helps me to draw a picture.. Using the x y on a graph you can put 2 points.. one at 3,5 and a 2nd at -5,20.
The question is how long is the line that joins those 2 points? Looking at the x's the distance in only the x direction is 8 units.
+3 to -5. In the y direction only there's a differenct of 15 units. You now have a right triangle and can use the pythagorian theorm.
D^2 = 8^2 + 15^2

your second problem you can also use the pythagorean theorm to solve. First what is a 'right' circular cone? One that has a 90 degree apex. The length of each side is from the center down to the rim... exactly equal to the radius of the circle we started with.
The base of the cone is a diameter that is equal to the 3rd side of the triangle formed by the sides and the bottom.

We have 2 sides of R.
R^2 + R^2 = base ^2.
4^2 +4^2 = base ^2
16 +16 = base^2
32=base^2
The base diameter = the square root of 32
We're supposed to reduce the number inside the radical so it's 4*sqrt(2).

The formula for Circumference is Pi*D.
We now know D and can report the answer in terms of pi.