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Geometry and Topology

Volume of a Solid Inside a Sphere

Use cylindrical coordinates to find the volume of the solid The solid that is bounded above and below by the sphere x^2+y^2+z^2=9 and inside the cylinder x^2+y^2=4 Write the limits of integration dz r dr dθ.

Geometry and Set Notation

1. Determine the following and show your work A'∪B' 2. Write a statement that makes the following set true A = {q, r, s, t, u} 3. Can the word "RATES" be played from the letters A, E, O, N, R, S, T as the first move in a Scrabble game? Explain your answer. 4. Express the following in roster form: Set M is the set of na

surface area of the cylinder

Build a three dimensional shape and prepare a set of questions to be presented to the class for problem solving. Questions should encourage students to cover the concepts of perimeter, volume, surface area, number of vertices, faces, and edges associated with the three-dimensional shape.

Rational Expressions and Simplifying Fractions

Week Four Assignment - Ch. 5 Cumulative Test Problems 5.1 22) 34) 46) 5.2 20) 36) 46) 5.3 28) 34) 42) 5.4 56) 60) 70) 5.5 32) 52) 70) 5.6 20) Science and medicine. A small business jet took 1 h

Area of Circle

A radio station sends out waves in all directions from a tower at the center of the circle of broadcast range. If the broadcast range has a diameter of 196 miles, determine how large an area is reached. If the broadcast range increases to a diameter of 210 miles, what is the area reached? If the broadcast range decr

What is the formula for the volume of a rectangular solid?

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 inch). Compute the volume of yo

What is the formula for the volume of a rectangular solid?

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 inch). Compute the volume of yo

Volumes, Perimeter and Areas

1 Find the perimeter and area of a right triangle if the shortest side is 2.5 m. and the longest side is 6.5 m. Include correct units with each part of your solution. 2. How many cubic centimeters can a cigar box hold if its dimensions are 3 centimeters by 16 centimeters by 12 centimeters? Include correct units with your so

Polar and Rectangular Coordinates: Example Problems

For the given curves, write equations in both rectangular and polar form. Please show which formulas/properties are used and explain steps taken. 1. The horizontal line through (1,3) 2. The circle with center (3,4) and radius 5 3. The circle with center (5,-2) that passes through point (1,1)

Measurement: Perimeter

Why do we measure perimeter in ft, area in ft^2 (or feet squared), and volume in ft^3 (or feet cubed)? What does each mean within the strand of measurement? Why do you think so many students label their measurements with the incorrect exponent?

Lagrange multipliers hemispherical top

A hot water tank is a vertical cylinder surmounted by a hemispherical top of the same diameter . The tank is designed to hold 750m^3 of liquid. Determine using Lagrange multipliers the total height and the diameter of the tank if surface heat loss is to be a minimum.

Geometry - Find the area of a trapezoid

Find the area of a trapezoid with a height of 4 m and bases of 15 m and 12 m. a. 108 square meters b. 720 square meters c. 27 square meters d. 31 square meters e. 54 square meters

Solving a Mathematical Modelling Problem

Suppose that the lift force F (M L T-2) on a missile depends on characteristic length scales D (L) and r (L) of the missile. Additionally, F may depend on the air density ρ (M L-3), the viscosity µ (M L-1 T-1) and missile velocity v (L T-1) . a) Develop a model for the lift force F. b) Find two other possibili

Topology- Compactness Continuous Function

Topology- Compactness Please do the problem #1. My textbook is Topology by James R. Munkres. The following are the contents covered in class so far. Do not use any knowledge exceeding them. (If you have more questions about my posting, communicate through the Message Center.) Sep-08-09 Session 1 Metric spaces and continuous

x-intercept and the y-intercept

1. The area of a trapezoid is given by A=1/2h (a+b) where h is the height of the trapezoid, and a and b are the lengths of the upper and the lower base, respectively. Solve for a. 2. The length of a rectangle is four times its width. If the area of the rectangle is 196m (m has a 2nd power) , find its perimeter.

Graphing Functions and Finding Tangents of a Curve

The curve C has equation: y = x^3 - 2x^2 - x + 9, x>0 The point P has coordinates (2,7). (a) Show that P lies on C. (b) Find the equation of the tangent to C at P, giving your answer in the form of y = mx+c, where m and c are constants. The point Q also lies on C. Given that the tangent to C at Q is perpendicular to

Maximize volume of a pyramid cut from piece of paper.

(Problem) A pyramid consists of 4 isosceles triangles around a square base. If this is to be cut and folded out of a single square piece of paper, Maximize the volume. h=height of pyramid x=one side of base square P=length(or width) of paper I know... V=x^2(h/3) h=sqrt((x/2)^2+something^2) h=sqrt((P/2)^2+somethi

Angles/segments on dotted paper

On a sheet of dot paper or on a geoboard like the one shown, create the following: 1. Right angle 2. Acute angle 3. Obtuse angle 4. Adjacent angles 5. Parallel segments 6. Intersecting segments

Validity of the arguments by using Euler Circles

Truth tables are related to Euler circles. Arguments in the form of Euler circles can be translated into statements using the basic connectives and the negation as follows: Let p be "The object belongs to set A." Let q be "the object belongs to set B." All A is B is equivalent to p -> q No A is B is equivalent to p -> ~q

Finding the Focus of a Parabolic Dish

A satellite dish, is the shape of a parabola. Signals coming from a satellite strike the surface of the dish and are reflected to the focus where the receiver is located. The satellite dish has a diameter of 12 ft and a depth of 2 ft. If the diameter of the dish is halved how far from the base of the dish should the receiver

Quaternion group presentation

Show that the quaternion group Q_2 = {+1, -1, +i, -i, +j, -j, +k, -k} has presentation <a,b|a^4 =1, a^2 = b^2, ab = ba^3> I need a rigorous proof with explanations so that I can study and understand please. I have an exam on Thursday.

Calculating Perimeters and Areas

1. An ecology center wants to set up an experimental garden using 300m of fencing to enclose a rectangular area of 5000 . Find the dimensions of the garden. 2. A landscape architect has included a rectangular flown bed measuring 9ft by 5ft in her plans for a new building. She wants to use two colors of flowers in the bed, on

Open Sets, Connectivity and Continuous Functions

3. a) Let M be a connected topological space and let f : M ---> R be continuous. Pick m1,m2 2 M and suppose that f(m1) < f(m2). Let x 2 R be such that f(m1) < x < f(m2). Show that there is m M with f(m) = x. (Hint: Use a connectedness argument.) b) Give R1 the usual product topology as the product of infinite copies of the rea

Three-Dimensional Topological Group

Please help with the following problem. Let M = SL(2) be the set of 2 × 2 matrices with unit determinant. Show that, when regarded as a subset of R4 under ( a b ) ( c d ) <--> (a, b, c, d) Exists R4 and equipped with subspace topology, SL(2) becomes a 3-dimensional topological group. That is, show that (i) SL(2) is a g

Geometry - Converses

4. State the converse of each of the following statements: (a) If lines l and m are parallel, then a transversal to lines l and m cuts out congruent alternate interior angles. (b) If the sum of the degree measures of the interior angles on one side of transversal r is less than 180°, then lines l and m meet on that side of tr

Volume of a Conical Slice

20. R is a slice of thickness k perpendicular to the axis of a right circular cone having maximum radius b and minimum radius a. Show that its volume is V(R) = pi/3(a^2 + ab + b^2)k. Explain how Exercise 18 and 19 are essentially special cases of this. 18. C is a cone of height h and base radius a. Show V(C) = pi/3*a^2*h.

Lines and Intersections

Incidence Geometry: Give proofs for the following: i.For every line there is at least one point not lying on it. ii.For every point, there is at least one line not passing through it iii.For every point P, there exist at least two distinct lines through P.

Length of a rectangle is 4 centimeters more than its width

The length of a rectangle is 4 centimeters more than its width. If the width is increased by 2 centimeters and the length is increased by 3 centimeters, a new rectangle is formed having an area of 44 square centimeters more than the area of the original , rectangle. Find: 1. The dimensions of. The, new rectangle 2. The perim

Order of operations, Area and Volume of figures

I need to know what steps are taken to come to the answer to these two problems. (8-6)^5 - 28 Evaluate. 72 ÷ 8 - 9 ÷ 3 What and how do I find the area of this figure? What and how do I find the volume of the solid shown? How do I show the answer in simplest form for the next three problems?

Geometry of Circumference and Sphere

The equatorial radius of the earth is approximately 3960 mL. Suppose that a wire is wrapped tightly around the earth at the equator. Approximately how much must this wire be lengthened if it is to be strung all the way around the earth on poles 10 ft above ground?