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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 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?

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

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

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.

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

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 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.