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Geometry and Topology

Writing Equations from Word Problems

The length of a rectangle is 3 cm more than 5 times its width. If the area of the rectangle is 76 cm2, find the dimensions of the rectangle to the nearest thousandth.

Reflexivity, symmetry, and transitivity

Topology Sets and Functions (XLVIII) Functions Decide which ones of the three properties of reflexivity, symmetry, and transitivity are true for each of the following relations in

18 basic math problems

10. In the number 456,719 A) What digit tells the number of thousands? B) What digit tells the number of tens? 12. In the number 324,678,903 A) What digit tells the number of millions? B) What digit tells the number of thousands? 32. Business and finance. Inci had to write a check for $2,565. There is a space on

Difference of the product of sets

Topology Sets and Functions (XLII) Functions Let X and Y be non-empty sets. If A_1 and A_2 are subsets of X, and B_1 and B_2 subsets of Y. Show that

Topology and mapping functions

Topology Sets and Functions (XXXIV) Functions Let X be a non-empty set. The identity mapping ix on X is the mapping of X onto itself defined by ix(x) = x

Topology and functions

Topology Sets and Functions (XXXIII) Functions Two mappings f : X --> [Y and g : X --> Y are said to be equal ( and we write this f = g ) if f(x) = g(x) for every x in X.

The First Second Mapping

Topology Sets and Functions (XXX) Functions Consider an arbitrary mapping f : X -->Y. Prove the main property of the second set mapping:

Proving the Main Property of a Second Set Mapping

Consider an arbitrary mapping f : X → Y. Suppose that f is a one-to-one onto. Prove the main property of the second set mapping: B1 is a subset of B2 implies f^(-1)(B1) is a subset of f^(-1)(B2). See the attached file for format

Main property of the first Set Mapping

Consider an arbitrary mapping f : X -> Y. Prove the main property of the first set mapping: f(intersection_i A_i) = intersection_i f(A_i) Please see attachment if the symbols are compromised.

Perimeter of a Rectangle

3. A rectangle is a parallelogram with four right angles. A rectangle has a width of 15 feet and a diagonal of a length 22 feet; how long is the rectangle? What is the perimeter of the rectangle? Round to the nearest foot. See attached file for full problem description.

Main property of the first set mapping

Consider an arbitrary mapping f : X --> Y. Prove the main property of the first set mapping: A_1 is a subset of A_2 implies that f(A_1) is a subset of f(A_2). The attached file contains the symbol version of the above statement for clarity.

Prove a First Set Mapping

Consider an arbitrary mapping f : X -->Y. Prove the main property of the first set mapping: f(X) is a subset of Y. See attachment for fully-formatted version of the question, should your display not include the symbols.

Basic Graphing

46. Technology. Driving down a mountain, Tom finds that he has descended 1800 ft in elevation by the time he is 3.25 mi horizontally away from the top of the mountain. Find the slope of his descent to the nearest hundredth. Section 7.2 pp. 626-627 16,20,28 16. Find the slope of any line perpendic

Real Life Applications of Geometry

You are part of a panel of parents, teachers, and administrators working to revise the geometry curriculum for the local high school. On tonight's agenda, you will be brainstorming creative ways to teach surface area and volume. The teachers are especially interested in methods which will help the students connect geometry to li

Application of laws of cosine and sin rule

At 1:00pm Jill left home traveling 45mph on a bearing of N 40 degrees W. At 1:30pm John left traveling 50mph on a bearing of S 75 degrees W. A) Illustrate the positions of Jill and John at 3:00pm. (I calculated that Jill would be 90 miles away and John would be 75 miles away) B) Find the measure of the angle between their

Find the set of points of convergence of a given filter on an infinite set X with the cofinite topology. Prove that a space is compact if and only if every open cover has an irreducible subcover.

1. Let X be an infinite set, let T be the cofinite topology on X, and let F be the filter generated by the filter base consisting of all the cofinite subsets of X. To which points of X does F converge? 2. Let X be a space. A cover of X is called irreducible if it has no proper subcover. (a) Prove that X is compact if and o

Sets and Sequences

2.) If " S " is the set of all "x" such that 0≤x≤1, what points, if any, are points of accumulation of both "S" and C(S)? 3.) Prove that any finite set is closed. 5.) Prove that, if "S" is open, each of its points is a point of accumulation of "S". 1.) Suppose "S" is a set having the number "M" as its least up

Radical Equations and Basic Geometry

Please see the attached file for the fully formatted problems. Section 9.5 Solve each of the equations. Be sure to check your solutions. Exercise 8 Exercise 14 Exercise 30 Section 9.6 Exercise 15 Geometry. A homeowner wishes to insulate her attic with fiberglass insulation to conserve energy. The insulati

Geometry Problems

Please explain in full detail the steps to these problems. Do not do #25 instead explain the following: 18. What is the area of a square if the length of a diagonal is 4 sq. rt. 2? 22. The floor of a room is 120 feet by 96 feet. The ceiling is 9 feet above the floor. Everything is to be painted except the floor. (Don't worr

Length and width of a rectangle.

An architect has designed a motel pool within a rectangular area that is fenced on three sides. If she uses 60 yards of fencing to enclose an area of 352 square yards, then what are the dimensions marked L and W? Assume L is greater than W.