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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.
Why is it important that I explain to them so that they will understand that measurement has some common skills and tools necessary?
The total surface area of a square based open-top rectangular box is 12 cm2. Find the dimensions of the box of maximum volume.
A box is made from a sheet of metal that is 8 meters by 10 meters, by removing a square from each corner of the sheet and folding up the sides.
If slate costs five times as much (per unit area) as glass, find the dimensions of the aquarium that minimize the cost of the materials.
The growth in the population of a certain rodent at a dump site fits the exponential function A(t)=336e0.031t, where t is the number of years since 1963.
Suppose that you have 600 feet of fencing which you plan to use to fence in a rectangular area of land.
Find the plane that is orthogonal to the given ones and passes through the point (1;-1; 2).
I am to draw any thee non collinear points. I am to construct a circle containing them on its circumference. Can you construct a different one?