Area of Triangles: Moving Partitions

Please see the attached file for the fully formatted problems.

Creating models for incidence axioms.

Construct a model in which axioms I-1, I-2, I-4, and I-5 are valid but I-3 is not. Axioms: I-1 Each 2 distinct points determine a line I-2 Three non-collinear points determine a plane I-3 If 2 points lie in a plane, then any line determined by those 2 points lies in that plane. I-4 If 2 points meet their intersection is a l ...continues

Metric space and triangle inequality.

Prove that in a metric space, if C lies between A and B and O is any other point, then OC<=OA + OB. (Hint make 3 applications of the triangle inequality) Triangle inequality: For triangle ABC AB+BC=>AC

Trigonometric Identity

Verify the following identity: (sin(x) + cos(x))^2 = 1 + sin(2x)

Trigonometric Identity

Verify the following identity: sec(x)-cos(x) = tan(x)sin(x)

Inequality

Suppose that there are three points A,B and C on a line where C is between A and B. o is any other point not on the line. Prove that OA+OB>OC

Prove that adjacent angles around a point and covering an entire plane add up to 360.

Prove (using angle,ray,line,plane axioms)That the sum of the measures of any set of adjacent angles about a point, whose sides and interiors cover the entire plane is 360.

Finding the area between two circles inner-tangential to a parabola.

Imagine a valley y=x^2. A circle with radius = 5 is inside it. Another circle, with radius = 4 is above the previous circle, (and inclined to right side) (PLEASE SEE THE ATTACHMENT zip file) Find the area between y=x^2 and the 2 circles (Not allowed to use computer.)

Trigonometric Points in terms of Radians : Transformations

In terms of radians and X, what would be the specifications of the anlges for trigonometric points which result from the following transformations of the trigonometric point P(X)? (Work these out on a diagram of the unit circle) 1) A reflection y = x followed by a rotation through pi 2) A reflection in y = -x 3) A refle ...continues

Trigonometric Points in Terms of Radians

Complete the attached table using exact notation. For the column p(X) this is the co-ordinates that are needed for that particular point. X Co-ordinates of X Cos X Sin X Tan X Cot X Sec X Cosec X 11 pi / 8 11 pi / 4 pi / 8 pi / 12 -7 pi / 12 5 pi / 8