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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
Find the approximate value of the volume of the right circular cone with a circular base shown below. Approximate your solution to the nearest hundredth.
Find the dimensions of the prism to the nearest tenth of a centimeter that will minimize the quantity of material needed to manufacture the can.
Calculate the volume for each of the boxes. Which has the greatest volume? Which has the smallest volume?
Transform the equation to standard form and find the center and radius of the circle.
A 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'.
In Rn with the usual topology, let A be the set of points x = (x1 , x2 .....xn) such that x12 + x22 + .....+xn2 = 1.
Denote by Intx(A) the interior of A in the topological space X and by Inty(A) the interior of A in the topological space Y.
The intersection of two open sets is compact iff it is empty. Can the intersection of an infinite collection of open sets be a non-empty compact set?
Every discrete space is first-countable; it is moreover second-countable if and only if it is countable.
Y = R, T is the discrete topology, A is the set consisting of all the numbers that do not have 5, 3, or 2 in any of their decimal expansions.
Find the interior, the closure, the accumulation points, the isolated points and the boundary points of the set A = { x = (x_1, x_2 ...) e l^2 : -1
Let p be an odd prime, and n = 2p. Show that a(n-1) is congruent to a (mod n) for any integer a.