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Geometry and Topology

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 : 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

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.

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.

Finding the distance between two fire towers

A ranger in fire tower A spots a fire at a direction of 295 degrees. A ranger in fire tower B, located 45 miles at a direction of 45 degrees from tower A, spots the same fire at direction of 255 degrees. How far from tower A is the fire? From tower B? I need these example explained to me so that I might better understand the

Six Geometry Word Problems

The finished product should be one combined document for the entire group, showing all calculations and graphical representations used. 1. Find the length L from point A to the top of the pole. 2. Lookout station A is 15 km west of station B. The bearing from A to a fire directly south of B is S 37°50' E. How far is the

What is the volume of the solid revolution?

The region in the first quadrant bounded by the graphs of y = x and y = x^2/2 is rotated around the line y=x. Find (a) the centroid of the region and (b) the volume of the solid of revolution.

Cylindrial shells problem

Using the method of cylindrical shells to find the volume of the solid rotated about the line x=(-1) given the conditions: y=x^3 -x^2;y=0;x=0.

Find the angle subtended of a guy wire strung from the top of a pole and the ground.

A guy wire (a type of support used for example, on radio antennas) is attached to the top of a 50 foot pole and stretched to a point that is d feet from the bottom of the pole. Express the angle of inclination as a function of d.

Geometry - Calculating the Maximum Area a goat can graze

If a goat is tied on a 50 foot lead to a corner on the outside of a rectangular barn and the barn is 20 feet by 20 feet and the goat can not get into the barn nor is the barn a grazing area, what is the maximum grazing area and show how the maximum grazing area was determined. A man has a barn that is 20 feet by 10 feet, he t

Compute the total mass of a wire bent in a quarter circle

See attached file for full problem description. Compute the total mass of a wire bent in a quarter circle with parametric equations: x = 7 cost, y = 7 sint, where 0 < t < pi/2 and density function rho(x,y) = x^2 + y^2

Circles and Cross Ratios

A) Let z1 and z2 be two points on a circle C. Let z3 and z4 be symmetric with respect to the circle. Show that the cross ratio (z1,z2,z3,z4) has absolute value 1. b)Let ad-bc=1, c not zero and consider T(z)=(az+b)/(cz+d). Show that it increases lengths and areas inside the circle|cz+d|=1 and decreases lengths and areas outsid

Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters , then what are the lengths of the sides?

Rectangular stage. One side of a rectangular stage is 2 meters longer than the other. If the diagonal is 10 meters , then what are the lengths of the sides?

Volume of a Solid of Revolution

Volume of a solid generated by the rotating the region formed by the graphs - y= x^2 , y =2, x = 0

Projective Geometry Points and Planes

Projective Geometry Problem 1 i. Prove that a set of four points in a projective plane P (i.e. dim P = 2) form a projective frame if and only if no three of the points are collinear, i.e. no three lie on the same projective line. ii. Find a necessary and sufficient condition for five points to form a projective frame in a t

Applications of div, grad, curl: Verification of the divergence theorem on two given surfaces

Verify the divergence theorem (&#8747;&#8747; (F.n) ds = &#8747;&#8747;&#8747; (grad.F) dV) for the following two cases: a. F = er r + ez z and r = i x + j y where s is the surface of the quarter cylinder of radius R and height h shown in the diagram below. b. F = er r^2 and r = i x + j y + k z where s is the surface of th

Determining Number of Calories

(See attached file for full problem description) The number of calories K needed each day by a moderately active man who weighs w kilograms, is h centimeters tall, and is a years old can be estimated by the formula K = 19.18w + 7h - 9.52a + 92.4 A) Marv is moderately active, weighs 97 kg, is 185 cm tall, and is 55 yr

Errors in Measuring Volume of Small Balls in Large Container

Consider an experimental procedure to measure the average volume of M&M Peanut candies. One hundred piece of the candy are poured into a graduated cylinder with a 30 diameter. The cylinder is then filled with 1 mm diameter beads and shaken so that the beads and candies pack as tightly as possible. Finally, the candies are remove

Weightage Method

Four cities plan to build a new airport to serve all four communities. City B (population 180,000) is 4 miles north and 3 miles west of city A (population 75,000). City C (population 240,000) is 6 miles east and 12 miles south of city A. City D (population 105,000) is 15 miles due south of city A. Find the best location for the

Euclidean Geometry Construction

Given a line l and a point P not on l, I contructed a line that contains P and meets l at a 45 degree angle using a compass. Now I need to construct a line that contains P and meets l at 30 angle and prove it. I attached what I have so far.

Tychonoff and Hausdorff Spaces

Let X and Y connected, locally path connected and Hausdorff. let X be compact. Let f: X ---> Y be a local homeomorphism. Prove that f is a surjective covering with finite fibers. Prove: a) Any subspace of a weak Hausdorff space is weak Hausdorff. b)Any open subset U of a compactly generated space X is compactly generated

Real Analysis : Open and closed discrete spaces

Show that every subset of a discrete space is both open and closed.

Maximum Volume of an Open-Top Box

An open-top box is to be constructed from a 6 by 8 foot rectangular cardboard by cutting out equal squares at each corner and the folding up the flaps. Let x denote the length of each side of the square to be cut out. 1. Find the function V that represents the volume of the box in terms of x. 2. Graph this function and sh

Geometry: Finding the angles of Polygons

Please help with the following problems on geometry and topology. Provide step by step calculations. See the attached files for diagrams to go along with the questions. Find the value of x and any unknown angles. Find the measure of one angle in the polygon. Round to nearest tenth if needed. 4. Regular 30-gon 5. Regular

Descriptions and Drawings of Regular and Non Regular Polygons

(a) Draw polygons with sides n = 4, 5, 6, 7, 8, 9, 10 for the following three cases. 1- non regular polygon 2- regular polygon 3- a shape that is not a polygon (b) Name the following polygons Number of sides name of polygon ------------------ -------------------- 4 5 6 7 8 9 10

Epsilon-Delta Definition of Continuity

Proof that f is continuous for each x in D in accordance with the epsilon-delta defitinition of continuity(can use the defintion involving f(x+h) (2 problems) f(x)=x/(x+1), D={x in R:x>-1} (can restrict |h|<(x+1)/2 f(x)=1/sqrt(x-4), D={x in R:x>4} (can restrict |h|<(x-4)/2

How do you calculate the volume of the cylinder?

The volume of a cylinder (think about the volume of a can) is given by V = pi*r2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters. Write h as a function of r. b) What is the measurement of the height if the radius of the cylinder is 3 centimete

Value of x, volume of a cylinder

1) Using the graph, what is the value of x that will produce the maximum volume? 2) The volume of a cylinder (think about the volume of a can) is given by V = &#960;r2h where r is the radius of the cylinder and h is the height of the cylinder. Suppose the volume of the can is 121 cubic centimeters. Write h as a function