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What is a fair price for the competition?A community 5K run will award $50 to the winner. 55 people enter the race
Problems on central force (a) Suppose that the force on a particle of unit mass is
Construct a model of incidence geometry that has neither the elliptic hyperbolic nor Euclidean parallel properties.
Find the length or width of similar triangles or rectangles.A drawing on a transparency is6.5 inches wide and 3 inches long.
Calculate the area of a playground.A playground is 37 ft by 52 ft and surrounded by chain-link fencing. Calculate the area of given playground.
Unit Conversions: Inches to Feet.Maria is using a cylindrical oxygen tank while scubadiving. It holds 80 cubic inches of air.
Steps on Calculating the Angle of a Triangle.In a triangle ABC, the measure of angle B is 5 times the measure of angle A, and the measure of angle c is 3 degre
Undefined terms, basic definitions of geometry, postulates, theorems, corollaries and problems based on the theorems.
Chart movement using latitude and longitude.To chart the movement of a polar bear, scientists attached a radio transmitter to its neck.
Identifying types of conics. For each of the equations identify the type of conic it is and list the major features associated with this type of conic
For each of the 5 regular polyhedra, enumerate the number of vertices (v), edges (e), and faces (f), and then evaluate the quantity v - e + f.
Subset Game involving Intervals and Subintervals.In the following infinite game, Alice and John take turns moving.
Path connected problems.Show that, for n>1 , the sphere Sn is path connected.
Nullhomotopic Mappings and Contractible Spaces. A space X is contractible if and only if every map f:X to Y (Y is arbitrary) is nullhomotopic.
Write down the Taylor polynomial Pn,0 (x) of 1n(x+1),x>-1. Use Taylor's theorem to
Compact metric space and contraction maps.What property regarding fixed points and contraction maps can be deduced from this result ?
Protective Planes Spaces.Show that the projective space with a disk removed (more precisely, the image of a disk on S2 under the natural projection pi
Truth table statement and argument. Write the statements in symbolic form
Set builder notation.Are the two sets below equal, equivalent, neither or both? Explain your answer.
Determine the following and explain your answer-Symbolic form
Mathematical reasoning.The Pythagorean Theorem for right triangles states that if a and b are the lengths of the legs
Give a counterexample to show that the converse (if limn?8 an = 0 then limn?8 1/an = 8) is false.
Continuous problems 1. Use the definition of ƒ(x) ?8 as x ?8 to show that ƒ(x) = x + 2 ?8 as x?8
Uses of the Pythagorean Theorem.Geometry is a very broad field of mathematics composed of a wide range of tools
Gaussian Elimination with Partial Pivoting.Solve the following system using Gaussian elimination with partial pivoting: