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A guy wire (a type of support used for example, on radio antennas) is attached to the top of a 50 foot pole and stretched to a point that is d feet.
The region in the first quadrant bounded by the graphs of y = x and y = x^2/2 is rotated around the line y=x.
A ranger in fire tower B, located 45 miles at a direction of 45 degrees from tower A, spots the same fire at direction of 255 degrees.
Find the volume of the solid generated by the revolving R around the y-axis by the methods of cylindrical shells.
Determine the equilibrium position of a cylinder of radius 3 inches, height 20 inches, and weight 5pi lb that is floating with its axis vertical.
If she uses 60 yards of fencing to enclose an area of 352 square yards, then what are the dimensions marked L and W?
If " S " is the set of all "x" such that 0=x=1, what points, if any, are points of accumulation of both "S" and C(S)?
You are part of a panel of parents, teachers, and administrators working to revise the geometry curriculum for the local high school.
Driving down a mountain, Tom finds that he has descended 1800 ft in elevation by the time he is 3.25 mi horizontally away from the top of the mountain.
Prove the main property of the first set mapping: A1 ? A2 ? f(A1) ? f(A2)
Let X be a non-empty set. The identity mapping ix on X is the mapping of X onto itself defined by ix(x) = x for every x.
Two mappings f: X?Y and g: X?Y are said to be equal ( and we write this f = g ) if f(x)= g(x) for every x in X. Let f , g and h be any three mappings.
Consider an arbitrary mapping f: X?Y. Suppose that f is a one-to-one onto. Prove the main property of the second set mapping: f-1 (Y) = X
If 1 gallon of paint covers 300 ft2, how many gallons are needed to paint the surface if it requires three coats? Round up to the nearest gallon.
Let X and Y be non-empty sets and f a mapping of X into Y. Show that f is onto ? there exists a mapping h of Y into X such that fh = iY .
If there exists a mapping g with this property, then there is only one such mapping. Why?
Let X and Y be non-empty sets. If A1 and A2 are subsets of X , and B1 and B2 subsets of Y.
Let X and Y be non-empty sets. If A1 and A2 are subsets of X and B1 and B2 subsets of Y, show that (A1 x B1) U (A2 x B2) = (A1 U A2) x (B1 U B2).
Let f: X?Y be an arbitrary mapping. Define a relation in X as follows: x1 x2 means that f(x1) = f(x2).
In the set R of all real numbers, let x˜y means that x - y is an integer. Show that this is an equivalence relation and describe the equivalence sets.
Decide which ones of the three properties of reflexivity, symmetry, and transitivity are true for each of the following relations.
The length of a rectangle is 3 cm more than 5 times its width. If the area of the rectangle is 76 cm2, find the dimensions of the rectangle.
For locations between 20° and 60° north latitude a solar collector panel should be mounted so its angle with the horizontal is 20 greater.
Carpeting will cost $8.00 a square yard. How many square yards of carpet will be needed and how much will it cost?
The importance of geometry's role in the math curriculum is debated in many high schools and colleges.