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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' .
Draw three different nonconvex polygons. When you walk around a polygon, at each vertex you need to turn either right (clockwise) or left (counterclockwise).
The equatorial radius of the earth is approximately 3960 mL. Suppose that a wire is wrapped tightly around the earth at the equator.
If the width is increased by 2 centimeters and the length is increased by 3 centimeters, a new rectangle.
R is a slice of thickness k perpendicular to the axis of a right circular cone having maximum radius b and minimum radius.
Let M = SL(2) be the set of 2 × 2 matrices with unit determinant. Show that, when regarded as a subset .
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).
Build a three dimensional shape and prepare a set of questions to be presented to the class for problem solving.
Arguments in the form of Euler circles can be translated into statements using the basic connectives and the negation.
Find the area of a trapezoid with a height of 4 m and bases of 15 m and 12 m.
Write equations in both rectangular and polar form. Please show which formulas/properties are used and explain steps taken.
In an 8 inch square cake pan and a 9 inch square cake pan, what is the difference in volume each pan will hold? Assume each pan is 3 inches high.
A radio station sends out waves in all directions from a tower at the center of the circle of broadcast range.
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.
Let (X, d) be a metric space, and f : X ? X a continuous map. Prove that the function g : X ? R defined by g(x) = d(x, f(x)) is a continuous function.
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?
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.
Find two other possibilities to represent the standardized lift force F in terms of non-dimensional products. (Buckingham's Theorem).
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.
Signals coming from a satellite strike the surface of the dish and are reflected to the focus where the receiver is located.
An ecology center wants to set up an experimental garden using 300m of fencing to enclose a rectangular area of 5000.
Axis horizontal, parabola passing through: (1, 1), (1, -3), and (-2, 0). Latus rectum joining the points (2, 5) and (2, -3) & opening to the left.
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.
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.
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 corn