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Geometry and Topology

Derive an mathematical equation for a beehive puzzle

In Fig.1 a beehive is enclosed in a bee cage. The bees can fly with a speed C. Each bee is flying non-stop from the hive to the wall of the cage and then back. Each time one returns to the hive, it is counted as one hit. There are hundreds and hundreds of bees in the cage and they fly out from the beehive in all directions. In s

5 Topology Questions (Including: de Morgan's Laws)

1. Prove the following de Morgan's laws: (a) ... (b) ... 2. Let A be a set. For each p E A, let Gp be a subset of A such that p C Gp C A. Then show that A = Up E A Gp. 3. Let f : X ---> Y be a function and A, B C Y. Then show that (a)... 4. Let f : X ?> Y be a function and A C X, B C V. Then show that (a) A C f-1 o f(A).

Circles and Coordinates : Distance from the Center

I have solved this question and I would like to know if I am correct. " A pizza shop delivers to all customers within a circle determined by the equation X squared + Y squared = 400, If the pizza shop is at coordinates (0,0), would they delvier to someone who lives at coordinates (16,-11) x + y = 20 Therefore the radius of t

Find the Variables and Internal Dimensions For a Studio and Patio

I am building a rectangular studio on south side of house, so that the north side of the studio will be a portion of the currrent south side of the house. The studio walls are 2 feet thick, and the studio's inside south wall is twice as long as its inside west wall. Also, I am building a semicircular patio around the st

Area of circle

An Indian sand painter begins his picture with a circle of dark sand. He then inscribes a square with a side length of 1 foot inside the circle. What is the area of the circle?

Circles

Secants QM and RM intersect the circle at S and T as shown, a) IF RV=12,VS=4,and TV=8 find VQ. OK so i figured it follows this theorem : If 2 secant segments are drawn to a circle from the same external point, then the products of the length of each secant and the length of its external segment are equal.... So i mapped

Functional Analysis

1) Let E be an infinite dimensional normed space, and let S =... Find the weak closure of S. Please see attached for full question.

Parametric Equations; Orthogonal Vector; Point of Intersection

Please assist me with the attached problems, including: 1. Find the parametric equations for each of the given curvbes 2. Show that the given vector is orthogonal to the line plassing through the given points. ----- 1. Find the point of intersection of each line with each of the coordinate planes 2. Tell whether t

Cycloid Geometry

The circle has a radius of 8. As the circle rolls along the line, the point P (a pencil point) draws a curve. a) Draw the curve for three complete revolutions of the circle. b) Find the area between the curve (one loop) and the line. c) Find the length of the curve - all three loops.

Volume of Cone from Circle with Missing Sector

A circle has a radius of 5. A sector of that circle has a central angle of 120 degrees. This sector is cut out and the two radii folded together thus forming a cone. Find the volume of that cone.

Volume of Box Containing Spheres

240 spheres, each of radius 2, are placed in a box in 5 layers. There are 6 rows with 8 spheres in each row at each layer. The outside spheres are each tangent to the box and the spheres are tangent to those spheres next to them. Find the volume of the box which is between the spheres.

Area Bounded by Chord and Arc

In a circle, the arc of a chord is 2 pie square root 2. The radius of that circle is 3 square root 2. Find the area bounded by that chord and that arc.

Volume and Density

A hollow steel shaft 12 feet long has an outside diameter of 16in. the inside diameter is 9 inches. What is the weight of this shaft if the steel weighs 0.29 lbs per cubic inch?