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# Geometry and Topology

### 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 Dimensions of a Page with Margins

A rectangular page is to contain 30 square inches of print. The margins are 1 inch from each side. Find the dimensions of the page such that the least amount of paper is used.

### Find the Perimeter of an Octagon within a Circle

A regular octagon is inscribed in a circle of radius 15.8 cm. Find the perimeter of the octagon.

### 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

### Real world geometry

Assume were 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 t

### 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?

### Find the volume of a solid of revolution using cylindrical shells.

Using the method of cylindrical shells, find the volume of the solid generated when the region bounded by the curves y=x^2, x=1, x=3, and y=0 is revolved about the y-axis.

### Circle Theorem Mapped

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

### Finding the Volume of a Solid of Revolution - Disk or Washer

Find the volume of the solid obtained by rotating the region bounded by the given curves about the specified line. y=sec(x), y=1, x=-1, x=1; about the x-axis

### Functional Analysis: Weak Closures

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

### Canonical Imbedding of the Normed Linear Space

Topology Suppose that Ε is a normed linear space. Let j: Ε→ Ε** be the canonical imbedding and let x** be a linear functional on Ε*. Then x*

### 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 curves 2. Show that the given vector is orthogonal to the line passing through the given points. 1. Find the point of intersection of each line with each of the coordinate planes 2. Tell whether the two line

### Transformation of Half Plane to Interior of a Circle

2. Show that when c1<0 the image of the half plane x<c1 under the transformation w = 1/z is the interior of a circle. What is the image when c1=0?

### Coordinate Geometry: Find the diameter of the largest circular pond that could fit in a triangular garden.

Find the diameter of the largest circular pond that could fit in a triangular garden with vertices at (18,54), (-27,36), and (27,-18), where a unit reprsents 1m.

### Coordinates and Geometry : Shape of Quadrilateral

Determine algebraically what type of quadrilateral ABCD is given that the vertices p(-8, 4), q(3,7),r(6,-4),s(-5,-7).

### The Geometry of a Cycloid

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.

### Maclaurin Series : Circles

4. Let C denote the circle |z|=1, taken counterclockwise, and following the steps below to show that: {see attachment for steps and equation} Please specify the terms that you use if necessary and clearly explain each step of your solution.

### Finding the Area of a Trapezoid Using Two Methods

A.) Determine the area of the trapezoid shown by finding the area of the three parts indicated and finding the sum of the three areas. 10 in ____________ / . . . sqrt 45 in / . . . /__ ._____

### Set Up Integral for Volume; Revolve Bounded Region

1. Draw a representative strip and set up an integral for the volume of the solid formed by revolving the given region: a) about the x-axis b) about the y-axis *Set up the integral only; DO NOT EVALUATE I. The region bounded by the curves {see attachment for curves and diagram} 2. Find the volume by: a) disk/washer meth

### What is the volume of the truncated solid if each base is 36 and each lateral edge is 12 sq.rt. 21.

A truncated pyramid is what is left when a plane parallel to the base cuts off the top. If a regular hexagon pyramid is truncated half way from the base to the top, what is the volume of the truncated solid if each base edge is 36 and each lateral edge is 12 sq.rt. 21?

### Volume of large sphere given surface areas and sum of volumes

The areas of two spheres are 49 pi and 81 pi. The sum of their volumes is 11,792. What is the volume of the large sphere?

### Find the Volume of a Cylinder Given Its Height and Surface Area

A cylinder is 10 inches high and has a total area of 150 pie. What is it's volume?

### 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.

### Find the volume of cylinder with hemisphere sitting on top.

A cylinder of radius 9 has a hemisphere sitting on top. The total height of this solid is 30. How do I find the volume of this solid?

### Find Distance Travelled Given Radius and Revolutions of a Wheel

The radius of a wheel is 35 inchs. How far will the wheel travel in 15 revolutions?

### Area of Hexagon Given Apothem

Find the area of a regular hexagon which has an apothem of 2 square root 3.

### Find the area of a sector given radius and angle.

What is the area of a segment of a circle of radius 23 if it's central angle is 53 degrees? (nearest hundreth)

### Find the Idea of a Polygon

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.