Proposition 2.30. suppose x and y are topological spaces, and f : x → y is any map. (a) f is continuous if and only if f (a c f(a) for all asx. (b) f is closed if and only if f (a) 2 f(a) for all a cx. (c) f is continuous if and only if f -(int b) ) for all b cy. (d) f is open if and only if f-'(int b) 2 int f-'(b) for all b c y.

Drag and drop the answers into the boxes to complete this informal argument explaining how to derive the formula for the volume of a cone. since the volume of a cone is part of the volume of a cylinder with the same base and height, find the volume of a cylinder first. the base of a cylinder is a circle. the area of the base of a cylinder is , where r represents the radius. the volume of a cylinder can be described as slices of the base stacked upon each other. so, the volume of the cylinder can be found by multiplying the area of the circle by the height h of the cylinder. the volume of a cone is of the volume of a cylinder. therefore, the formula for the volume of a cone is 1/3 1/2 1/3πr^2h 1/2πr^2h πr^2h πr^2

Look at the following graph of the given equation. determine whether the equation is a function. explain why or why not.

Which of the following is the result of expanding