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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.
We say e is a Lebesgue number of a covering of a metric space X if the following condition holds: any subset of X of diameter < e is contained in some set.
Unfortunetly, the vertex of the angle is in the middle of a lake. How can we locate the fence line using straight edge and compass?
Find the function V that represents the volume of the box in terms of x. Show and explain the answer, and also graph this function.
A stone is thrown into a lake, and t seconds after the splash the diameter of the circle of ripples is t meters.
Prove that a set A, a subset of the real numbers, is compact if and only if every sequence {an} where an is in A for all n, has a convergent subsequence.
The region in the first quadrant that is bounded above by the curve y=1/vx, on the left by the line x=1/4, and below by the line y=1.
When Maria was considering buying the peanut butter cookie plant, one of her options was to convert it to make more lemon crème cookies.
Between (0,0) and (0,2), the triangular region between those points on the y-axis and the straight line x=3y/2 using the formula V=?p[R(y)]²dy
Suppose the volume of a cylinder (think about the volume of a can) is given by V = pr2h where r is the radius of the cylinder and h is the height.
The pasture must contain 180,000 square meters. What dimensions would require the least amount of fencing if no fencing is needed along the river?
Exactly how many minutes is it before eight o'clock, if 40 minutes ago, it was three times as many minutes past four o'clock?
Water is being pumped into the pool at 1/4 cubic meter per minute, and there is 1 meter of water at the deep end.