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James wanted a photo frame 3 in. longer than it was wide. The frame he chose extended 1.5 in. beyond the picture on each side.
If 2400 square centimeters of material is available to make a box with a square base and an open top, find the largest possible volume of the box.
If V is the volume of a cube with edge length x and the cube expands as time passes, find dV/dt in terms of dx/dt.
(Extreme Value Theorem) prove if f:K->R is continuous on a compact set K subset or equal to R, then f attains a maximum and minimum value.
A closed rectangular box with volume 576 in^3 is to be made so its top (and bottom) is a rectangle whose length is twice its width.
The metal used to make the top and bottom of a cylindrical can costs 4 cents/in^2, while the metal used for the sides costs 2 cents/in^2.
The area of a circle which is inscribed in a square is 169pi. What is the area of the square?
Find a point x ? [0, 1) and a neighborhood N of x in [0, 1) such that f (N) is not a neighborhood of f (x) in C. Deduce that f is not a homeomorphism.
Let X be a topological space and let Y be a subset of X. Check that the so-called subspace topology is indeed a topology on Y.
Suppose (X,T) is a topological space. Let Y be non-empty subset of X. The the set J={intersection(Y,U) : U is in T} is called the subspace toplogy on Y.
Use an n-tuple integral to find the volume enclosed by a hypersphere of radius r in n-dimensional space Rn.
Let X:={a,b,c} be a set of three elements. A certain topology of X contains (among others) the sets {a}, {b}, and {c}. List all open sets in the topology T.
A cube has a sphere inscribed inside of it. It has another sphere circumscribed on the outside ot if (it being the cube).
Suppose that is a normed linear space. Let j: e? e·· be the canonical imbedding and let x·· be a linear functional on e· .
An Indian sand painter begins his picture with a circle of dark sand. He then inscribes a square with a side length of 1 foot inside the circle.
A regular octagon is inscribed in a circle of radius 15.8 cm. Find the perimeter of the octagon.
Find the volume of the following region in space: The first octant region bounded by the coordinate planes and the surfaces y=1-x2, z=1-x2.
A homemade loaf of bread turns out to be a perfect cube. Five slices of bread, each 0.6 in. thick, are cut from one end of the loaf.
A cube has a surface area of 54 square inches. If the length of each side is tripled, the what will the volume of the cube be?
Show that the tangents at P and Q to ellipse (ii) are at right angles to one another. Please show this using parametric equations.
While traveling across flat land, you notice a mountain directly in front of you. The angle of elevation to the peak is 2.5 degrees.
Prove that if A is a family of functions in C_0 such that A is uniformly bounded and equicontinuous, then every sequence of functions.
If two lines are parallel then they do not intersect. If 2 lines do intersect then they are not parallel .
If the volume of the balloon was 100cm^3 when the process of inflation began what will the volume be after t seconds of inflation.
A Car leaves Oak Corner at 11:33 a.m traveling south at 70km/h. at the same time, another car is 65 km west of Oak Corner traveling east at 90km/h.