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Geometry and Topology

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

Area, Perimeter and Polar Equation of an Ellipse

Consider the formed by the parametric equations: x=5cosθ+3; y=4sinθ a) estimate the perimeter of the ellipse. b) estimate the area enclosed by the ellipse. c) find a polar equation for the ellipse.

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 law of cosines

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

Linear Equation Questions

Linear Equation Questions. See attached file for full problem description. Let S be the subspace.... Explain why this linear equation represents a subspace and find a basis for it. Clearly explain why this subspace is a plane. Find two orthogonal vectors in the plane. Make the set you found orthonormal. Explain why your

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

Volume and Surface Area

For problem A, find the area of the triangle. For problem B, find the volume of the cylinder and volume of cylinder if applicable. See attached file for full problem description.

Height, Volume and Diameter

Two similar cones have surface areas of 225 cm^2 and 441 cm^2. 32. If the height of the larger cone is 12 cm, find the height of the smaller cone. 33. If the volume of the smaller cone is 250 cm^3, find the volume of the larger cone. 34. A leg bone of a horse has a cross-sectional area of 19.6 cm^2. What is the diameter of th

The Symmetric Difference Of Two Sets

A ring of sets is a non-empty class A of sets such that if A and B are in A, then A difference B and A intersection B are also in A. Show that A must also contain the AUB. Please see attachment for correct format and symbols which may not show up correctly here.

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

Finding the volume of a solid of revolution.

The region is rotated around the x-axis find the volume bounded by y= sq rt. (cosh2x) y=0 x=0 x=1 keywords: integration, integrates, integrals, integrating, double, triple, multiple

Biography of Don Aldson

I have been searching the internet for a biography for Don Aldson. I see a lot on him with regards to what theroms and other scientific things he has done, but I just do not see any information on his life. 1. I need a picture of him 2. Birth Place (and Country) 3. Educational Background 4. Why the person you choose studi

Geometry

Let C(0, A) be the circle with center 0 and radius OA. Carefully define: a. a diameter of the circle. b. a chord of the circle. C. a line tangent to the circle. d. a secant line to the circle. e. concentric circles. {DIAGRAM} Please see the attached file for the fully formatted problems.

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.

Compact Sets and Compact Exhaustions

Definition: Let omega be a domain in C. Then e compact exhaustion {Ek} of omega is 1. Ek are all compact, Ek is contained in Ek+1 for all k 2. Union of Ek=omega 3. Any compact set K contained in omega is contained in some Ek Problem. Find an example of Ek's satisfying 1 and 2 but not 3 for omega=unit disk

Geometry : Volume and Surface Area

4. A sphere has an area of 324 pi. What is the volume? 5. The lateral area of a cone is 80 pi. The slant height is 10. Find the volume. 6. A cylinder and a cone have the same height. The radius of the cylinder is 12. What is the radius of the cone if their volumes are equal?

Ratio of Surface Area to Volume

#8 How do I find the dimensions of a cube with a volume of 1000 cubic centimeters. What is the ratio of Surface Area to Volume. #9 Find the ratio of surface area to volume for a cube with volume of 64 cubic inches #10 What is the surface area of cube in exercise.

Equation of a Tangent Plane

1) Find the equation of the tangent plane to the graph of the function f(x, y) = (x3 + siny) / (y^2+1) at the point (2, 0, 8). 2) Let g(x, y, z) = x2 - y3 + z4. Let L be the level surface of g containing the point P(3, 2, 1). Find the equation of the tangent plane to the surface L at the point P.

Geometry

Would like more details and explanations as to how the attached graph is solved. Create a graph with four odd vertices. See attached file for full problem description.

Geometry Proofs

Formalizing Proofs. See attached files for full problem description.