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Geometry and Topology

Angle between these two planes

What is the angle between these two planes: x + 2y - z = 13 & -2x - 4y + 2z = -13? What is the second derivative of f(x, y) = 3x2y + 4y3 first with respect to y and then with respect to x?

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

Dimensions of the Prism

A rect. prism has a length of (l), a width of (w), and a height of 1. Volume of the rect prism is 24cm3. Use your knowledge of volume and surface area to derive a function F(W) that represents the surface area of the rect. prism in terms of its width. Next, graph it on calculator. Lastly, find the dimensions of the prism t

Determining Radius and Volume of Sphere

8. An ice cube that measures 2.5 centimeters on each side contains how many cubic centimeters of ice? Include correct units with your solution. 9. How many cubic inches of air can a fully inflated basketball hold if its radius is 5.2 inches? Give solution accurate to the nearest hundredth. Include correct units with your sol

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

Congruency in Triangles: Example Questions

Given: A square CDEF such that point C is on the bottom right corner, point D is on the top right corner, E is on the top left corner, and F is on the bottom left corner. A line is then drawn from point E to a new point B on the line segment FC, where point B is about 1/3 distance between F and C and closer to point F than

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.

mean value theorem .

If f: [0, 1] -> R is differentiable on R and f' is continuous on [0, 1] with f(0)=0 and f'(x) > 0 for all x in [0, 1], prove that there exists c > 0 so that f(x) > cx for all x in (0, 1]

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

Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s) = s3 - 13s2 + 54s - 72. a) Find V(10). b) If the new width is s - 6 centimeters, then what are the new length and height? c) Find the volume when s = 10 by multiplying the length, width, and height.

Decreasing cube. Each of the three dimensions of a cube with sides of length s centimeters is decreased by a whole number of centimeters. The new volume in cubic centimeters is given by V(s) = s3 - 13s2 + 54s - 72. a) Find V(10). b) If the new width is s - 6 centimeters, then what are the new length and height? c) Find t

Convert from Standard English Measure to Metrics

Ability to use a ruler and convert from Standard English measure to Metrics. Students will then apply their knowledge of the geometric measurements of area and volume through real world problems. a. Choose a room in your house. Measure the length, the width and the height. Make sure you use feet and inches. Most roo

Clock Angles

At midnight the minute hand of the clock lies directly over the hour hand. At what time does this next occur? Give your answer correct to the nearest second.

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