Share
Explore BrainMass

Geometry and Topology

Linear function applications

Library Assignment Part 1: What is the formula for the volume of a rectangular solid? Find an object in your residence that has the shape of a rectangular solid. Measure and record the length, width, and height of your object in either centimeters (to the nearest 10th of a centimeter) or inches (to the nearest quarter of an inc

Polygons : Angles Encountered as One Walks Around a Polygon

Draw three different nonconvex polygons. When you walk around a polygon, at each vertex you need to turn either right (clockwise) or left (counterclockwise). A turn to the left is measured by a positive number of degrees and a turn to the right by a negative number of degrees. Find the sum of the measures of the turn angles of t

Characteristic function proof

Let A be a subset of R^n. Show that the characteristic function Xa is continuous on the interior of A and on the interior of its complement A' but is discontinuous on the boundary ∂A = A (bar)∩A' (bar)

Mean, Median, Mode, Tables, Pictographs and Bar Graphs

Find the median of each set of numbers. 14. 1, 4, 9, 15, 25, 36 Find the mode of each set of numbers. 18. 41, 43, 56, 67, 69, 72 20. 9, 8, 10, 9, 9, 10, 8 Solve the following applications. 24. Statistics. A salesperson drove 238, 159, 87, 163, and 198 miles (mi) on a 5-day trip. What was the mean number of mil

Vectors

Consider a regular tetrahedron with vertices: (0,0,0) , (k,k,0) , (k,0,k) , and (0,k,k) a) sketch the graph of the tetrahedron b) find the length of each edge c) find the angle between any two edges d) Find the angle between the line segments from the centroid ( k/2, k/2, k/2) to two vertices.

Orthogonal planes.

Given two planes with equations x + 2y + z = 1 and x - 2y + 3z = 3, (a) Show that the planes are orthogonal. (b) Find the plane that is orthogonal to the given ones and passes through the point (1;-1; 2).

Coordinate Geometry ...

(1) Show that the points A(4, 1), B(2, -3), C(0, 3) cannot form an equilateral triangle. (2) Draw the graph of the straight line 3x ?4y = 12 (3) Find the equation of a line parallel to the x- axis and passing through the point (5, 7).

Radians, Circles, and Angular Velocity

1. Find the area of a sector having a central angle of 60° in a circle of radius 8 inches. 2. Find the perimeter and area of a circular sector whose angle is 3.5 radians if the circumference of the circle is 58 ft. 3. A point on the wheel of radius 10 feet moves with a linear velocity of 40 feet per second. Find the angul

smallest possible value of an angle

T(A) is defined for A by T(A)= 3cos(A - 60) + 2 cos(A + 60) I have established that T(A) can be written SQRT(7)sin(A + 70.9), now need to find the smallest possible value of A such that T(A) + 1 = 0.

Functional Analysis: Topological Space Proof

Just a note on notation: X*_w* is X* (set of all linear functionals) with a weak-* topology (the weakest topology in which all functionals are continuous) This posting is for #1 See attached. Let Y be a topological space...

GCF and area

How do you feel about mathematics now that you have completed MAT 115? Describe some coping mechanisms you developed in MAT 115 that you can use for your next math course. Example: Find the GCF of 24 and 18 Example: Calculate the area of a circle that has a radius of 8 cm (use 3.14 for pi). Example: Calculate the area o

Golden ratio

The shape for a rectangle was one which the ratio of the length to the width was 8 to 5, the golden ratio. If the the length of a rectangular painting is 2ft longer than its width, then for what dimensions would the length and width have the golden ratio.

Vertex Figures and Tessellations

Another definition of a regular tessellation is one whose vertex figures are identical regular polygons. A vertex figure is made by connecting the midpoints of all the edges which touch a given vertex. (1) Sketch the vertex figures for the regular semiregular tessellation of the plane and verify the definition. (2) The

Proofs - Give an indirect proof of the theorem

Give an indirect proof of the theorem. 1. If two lines are parallel to a third line then they are parallel to each other 2. Solve the equation S=(n-2) 180 degrees for n when S is a given value. Find the number of sides of the polygon ( if possible) if the given value corresponds to the number of degrees in the sum of the in

Constructing a polygon

To construct a regular 5-gon , first draw a circle with the center O. Then proceed to find on the circle the vertices V1, V2, V3 and V5 of the Regular pentagon as follows: ___

Word Problems - volume of solid

Directions. 1.Find the volume of the solid generated by revolving the region about the y-axis. The region enclosed by the triangle with vertices (1,0), (1,2),(3,2) 2.Find the volume of the solid generated by revolving the region bounded by the given lines and curves about the x-axis. y=2/x (this is 2 over x, couldn

Circle construction

I am to draw any thee non collinear points. I am to construct a circle containing them on its circumference. Can you construct a different one? How many different circles are thee through the three points? Can you construct a circle through three collinear points.

Basic Math Geometry: Circumference, Perimeter and Area

Exercises 4, 10, 20. 4. Find the circumference of each figure. Use 3.14 for [ ] and round your answer to one decimal place. In a circle for 3.75 ft 10. Find the perimeter of the curves is semicircles. Round answer to one decimal place 10 inches. 20. Find the area figure of 5 inches and 7 inches.

A rectangular storage container with an open top is to have a volume of 10m3. The length of its base its twice the width. Material for the base costs of $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container.

A rectangular storage container with an open top is to have a volume of 10m3. The length of its base its twice the width. Material for the base costs of $10 per square meter. Material for the sides costs $6 per square meter. Find the cost of materials for the cheapest such container.

Golden ratio

The ancient Greeks thought that the most pleasing shape for a rectangle was one for which the ratio of the length to the width was 8 to 5, the golden ratio. If the length of a rectangular painting is 2 ft longer than its width, then for what dimensions would the length and width have the golden ratio?

Poincare's model of Lobachevskian geometry

Poincare's model of Lobachevskian geometry was to say that points of the plane are represented by points in the interior of a circle and lines by both the diameters of the circle and the arcs of circles orthogonal to it. Draw a diagram(s) to illustrate his model and explain his theory.

Need to know the differences between regular Tic Tac Toe and cylindrical

A careful player can always guarantee at least a draw at regular tic tac toe. (a) Is this also true with cylindrical tic-tac-toe? Explain. (b) In cylindrical tic-tac-toe, can two players co-operate to play a draw? Explain. I know this must be simple but I can find nothing on it anywhere.

Functions and Coordinate Geometry

Functions and Coordinate Geometry - (1) Find an equation of the line having the given slope and containing the given point m= , (6,-8) (2) Write an equation of the line containing the given point and parallel to the given line. Express your answer in the form y=mx+b (7,8); x+7y=5 ... ... (6) The table lists data regard

A=(LP)/2-L^2, gives the area of a rectangle of perimeter P and length L.

A=(LP)/2-L^2, gives the area of a rectangle of perimeter P and length L. Suppose that you have 600 feet of fencing which you plan to use to fence in a rectangular area of land. Choose any two lengths for a rectangle and find the corresponding area for each using the given equation. Include units and show all calculations. Which

Relationship between volume and cone angle

Please help with the attached problem. Shown at the right is a cone with a slant height of 10 cm. Let's explore the relationship between the volume and the angle at the top of the cone....

Solve equilibrium of price, estimate population, and dimension of rectangular

Need assistance in solving the attached problems. My answers are falling short of the choices given in the problem. Please explain the steps to get answers. Thank you. 1. Find the equilibrium price. Suppose the price p of bolts is related to the quantity q that is demanded by: P=520-5q^2 where q is measured in hundred

Minimizing cost of materials to build an aquarium

The base of an aquarium with given volume V is made of slate and the sides are made of glass. If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials.

Maximizing the Volume of a Box

A box is made from a sheet of metal that is 8 meters by 10 meters, by removing a square from each corner of the sheet and folding up the sides. Find the width of the square to removed in order to have a box of maximum volume.