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The rope forms an angle of 33degrees with the horizontal. how much work is done pulling the box 22 feet along the ramp.
If a window entails a seamless glass area formed by a rectangle capped by semi-circle, if the semi-circle's diagonal and the rectangle's width coincide.
Let the function f(z) = u(x,y) + iv(x,y) be analytic in a domain D, and consider the families of level curves u(x,y) = c1 and v(x,y) = c2.
A section of road follows a circular arc with a central angle of 23.8. The radius of the inside of the curve is 281.0 m, and the road is 15.4 m wide.
Annual demand for a popular sandal is 500 pairs, and John Dirk, the owner of Shoe Shine, has been in the habit of ordering 100 pairs at a time.
The Italian General's Pizza Parlour is a small restaurant catering to patrons with a taste for European pizza. One of its specialties is Italian Prize pizza.
X is given the usual topology and Y is given the Sogenfrey topology. X is given the Sogenfrey topology and Y is given the usual topology.
The foundation will be 6 inches thick. How much cement, in cubic feet, will be required to lay the foundation?
Your city must have at least six parallel streets, five pairs of streets that meet at right angles and at least three transversals.
Let X be given the co-finite topology. Suppose that X is a infinite set. Is X Hausdorff? Should compact subsets of X be closed?
Let Fr(A) denote the frontier set of A and Cl(A) denote the closure of A, where A is a subset of R^n. Solve the following problems.
The definitions of surface (in terms of gluing panels) and what it means for two surfaces to be topologically equivalent.
Let X be a topological space with at least two points and the indiscreet topology. Why is this not a topology that comes from a metric on X?
In my latest battle with squirrels, I have strategically hung my bird feeder so that a squirrel cannot steal my birdseed.
Use the Chain Rule to compute (g o f)' at (1,0,1). Provide complete and step by step solution for the question.
In which points(a , b) ? R2 does f have a local inverse i.e., for which points (a, b) does there exist a neighbourhood U of (a, b) such that f is injective on U
The medial triangle of a triangle ABC is the triangle whose vertices are located at the midpoints of the sides AB, AC, and BC of triangle ABC.
If the consecutive midpoints of the sides of a parallelogram are joined in order, then the quadrilateral formed from the midpoints is a parallelogram.
It is important to know how to use dynamic, interactive software programs such as The Geometer's Sketchpad, Cabri Geometry.
Explain the importance of Euclid's parallel postulate and how this was important to the development of hyperbolic and spherical geometries.
Describe the historical development of statistics and probability. Please include some reference to non-Western mathematics history.
Steve is buying a farm and needs to determine the height of a silo on the farm. Steve, who is 6' tall, notices that when his shadow is 9' long.
Use the method of Lagrange multipliers to find the minima and maxima of f on the boundary of S given by x^2 + 4y^2 =1.
Prove that the metric space X is not isometric to any subset of En for any n. Can you realise X as a subset of a sphere S2 of appropriate radius.
Write an equation for the parabola that has vertex (1,2) and its axis is parallel to the x-axis, passes through the point (13,4)