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Geometry and Topology

Using Differentials to Estimate

1. In the manufacturing process, ball bearings must be made with radius of 0.5mm, with a maximum error in the radius of +/- 0.016 mm. Estimate the maximum error in the volume of the ball bearing. Solution: The formula for the volumen of the sphere is _____. If an error deltaR is made in measuring the radius of the sphere

Calculating the amount of material for finishing a basement

Question 11A Guest needs material to finish a room in a basement. The room is square and one wall measures 15'. The height of the room is 8'. There is one door that measures 3' wide and 7' high, and two windows that measure 3' wide and 4' high. The Guest is covering the walls with 1x6 carsiding (we will say that it covers 5"

Inductive Reasoning to Predict Numbers

Glenda Everson Math 1002 Practice Problems 1. Use inductive reasoning to predict the next three numbers in the pattern (or sequence). 4, −20, 100, −500, . . . Step 1: Form a Hypothesis: Step 2: Make observations related to the hypothesis: Step 3: Come to a conclusion: 2. Flying West New York City is on easter

real dimensions shapes

Math Assignment Directions: If you are using Microsoft® Word 2007 and plan to insert equations into this document using Equation Editor, go to the Insert tab, click Object, and select Equation Editor 3.0. Equation Editor allows you to easily insert equations into this document. 1. A cylindrical hockey puck is 1 in. high a

PQR and ABA Angle Geometry

1. Use the following figure to find out the following. [Please refer to the attachment for the figure and questions] 2. Angle PQR and Angle ABC are complementary angles and Angle PQR is eight times as large as Angle ABC. Determine the measure of each angle. Please show all work step by step. 3. A recreation room has the f

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

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

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

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

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


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.

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

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

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: ___

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.

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

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

Understanding the geometric principles

How would you incorporate the use of standard units, the use of tools to measure, the importance of precision and accuracy, estimation and the use of manipulatives and other visual aides to a group of third graders to make them understand the common concept behind measurements regardless of what is being measured? Why is it impo

Simple equations in one variable.

1.) t+4=-9 2.)98=7z 3.)37=y/5+14 4.)2/7x-4/3=-3/2 5.)8(x-8)-5x= -37 6.)u+3>19 7.)-4x-17 is less than or equal to 19 8.)word problem a local hamburger shop sold 577 hamburgers and cheeseburgers on Tuesday. they sold 73 fewer cheeseburgers than many hamburgers did they sell? 9.)a=1/2h

Geometry : Area and Distance

Area For locations between 20degrees and 60degrees north latitude a solar collector panel should be mounted so its angle with the horizontal is 20 greater than the local latitude. Consequently, the solar panel mounted on the roof of Solar Energy, Inc., in Atlanta (latitude 34degrees) forms a 54degree angle with the horizontal.

Point and Segment, Volume and Dimensions

Please see attachment for full problem description. 1. (4 pts) Use the figure below to find the following: Hint: Your answers will be points or segments from this figure. See attachment 2. Lines A and B are parallel and are cut by the transversal shown. Determine the measures of angles 1 throu