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# Geometry and Topology

### 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

### 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

### Geometry Word Problems

The first problem is an attachment. The second problem as follows: 10. The shortest sides of two similar polygons are 5 and 12. How long is the shortest side of a third similar polygon whose area equals the sum of the areas of the others. 18. The radius of a wheel is 35 inches. How far will the wheel travel in 15 revolu

### Creative ways to teach surface area and volume.

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

### 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 Features

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 Final Exam Problems

Please see the attached file for the fully formatted problems. keywords: collinearity, bisectors, angles, congruences, syllogism, perpendicular, congruent, triangles, Law of, tests, parallelorams, rhombus, circles, pyramids, squares, rectangles

### Geometry Final Exam Problems

Please see the attached file for the fully formatted problems. keywords: collinearity, bisectors, angles, congruences, syllogism, perpendicular, congruent, triangles, Law of, tests, parallelorams, rhombus, circles, pyramids, squares, rectangles

### 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.

### Equilibrium Position of a Foating Cylinder

Determine the equilibrium position of a cylinder of radius 3 inches, height 20 inches, and weight 5pi lb that is floating with its axis vertical in a deep pool of water of weight density 62.5 lb/ft^2. keywords: buoyant force

### Geometry

Need help understanding Geometry principles when solving the attached problems.

### Geometry : Angles, Lengths, Areas, Volumes And Graphs

1. DEF and GHI are complementary angles and GHI is eight times as large as DEF. Determine the measure of each angle. 2. If line p and q are parallel, find the measure of angle 2. 3. Using ABC, find the following: a) The length of side AC b) The perimeter of ABC c) The area of ABC 4. A diagonal wa

### Equation of a Plane and Describe and Sketch the Surface

51. Find an equation of the plane with x-intercept a, y-intercept b, and z-intercept c. Describe and sketch the surface. 4. z = 4 - x^2 8. x^2 ? y^2 = 1

### Geometry Word Problems, Angles, Lengths, Areas, Volumes and Graphs

Please see the attachment for the proper formatting and related diagrams. 1. DEF and GHI are complementary angles and GHI is eight times as large as &#61648;DEF. Determine the measure of each angle. 2. If line p and q are parallel, find the measure of angle 2 3. (Using ABC, find the following: a) The length of s

### Volume of a Solid of Revolution : Method of Cylindrical Shells

R is bounded below by the x-axis and above by the curve y=2cosx, 0 <= x <= Pi/2. Find the volume of the solid generated by the revolving R around the y-axis by the methods of cylindrical shells.

### Latin Squares

1) Show that for n less than or equal to 4, any Latin square of order n can be obtained from the multiplication table of a group by permuting rows, columns, and symbols. Show that this is not true for n=5 2) If n is an order for which mutually orthogonal Latin squares exist, does every Latin square of order n have an orthogo

### Angle of Elevation and Rate

See attached file for full problem description.

### dimensions of the trapezoid of greatest area with longer base

Find the dimensions of the trapezoid of greatest area with longer base on the x axis and its other two vertices above the x axis and on the graph of 4y = 16 - x^2. keywords: trapezium, trapezoids

### Sets and Functions : The Symmetric Difference of Two Sets

The symmetric difference of two sets A and B, denoted by A &#916; B, is defined by A &#916; B = ( A - B ) U ( B - A ); it is thus the union of their differences in opposite orders. Show that A &#916; ( B &#916; C ) = ( A &#916; B ) &#916; C.

### Irreducible Algebraic Sets and Prime Ideals

For any ideal J in k[x1,...,xn], show that the algebraic set Z(J) is irreducible iff J is a prime ideal.

### Affine Algebraic Sets and Topologies

1. Show that affine algebraic sets satisfy the axioms for the closed sets of a topology, i.e. show that the intersection of an arbitrary collection of algebraic sets is algebraic and the union of two algebraic sets is algebraic.

### dimensions of rectangle that has an area equal to its perimeter

Find the dimensions of a rectangle that has an area equal to its perimeter.

### Geometry: Traingle Proofs (7 Problems)

Please see the attached files for the fully formatted problems.