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Consider two systems of springs, one in which a mass m is attached two the end of two springs which are placed one at the end of the other.
If n >= 1, the number of strings using the digits 0,1, and 2 with no two consecutive places holding the same digit, is 3x2^n-1.
A bacteria culture starts with 760 bacteria and grows at a rate proportional to its size. After 2 hours there will be 1520 bacteria.
You are in a driving conttest and you are expected to maintain an average speed of 60mph for two miles.
What types of Error correction codes are used in wireless systems? What is the difference between them? Which has the highest gain?
A traffic engineer wants to know whether measurements of traffic flow entering and leaving a road network are sufficient to predict
Let a and b be integers. A common multiple of a and b is an integer n for which amn and b|n. We call an integer m the least common multiple.
Properties of condition numbers : Orthogonal Matrices and Eigenvalues
Find all solutions of each of the following congruences.Provide complete and step by step solution for the question.
A boat travels 30 miles upstream against the current in the same amount of time it takes to travel 42 miles downstream with the current.
When they try to divide it they have two pieces of candy left over. One of the children leaves, taking the 26 pieces of candy she collected with her.
In a certain triangle the measure of one angle is double the measure of a second angle but is 10 degrees less than the measure of the third angle.
Lydia takes ten minutes more to complete an illustration than Tom. The total time taken by both of them is six hours.
Translate the following into algebraic expressions. Clearly identify the variables, coefficients, and constants:
The value of the second prize is five-sixths the value of the first prize, and the value of the third prize is fourth-fifths that of the second prize.
The space occupied by character 2 takes 5 units more than character 1, character 3 takes 7 units less than the character 2.
Lisa is coloring her creation. The blue color used is 50% of the green color used, yellow is 5% of the blue color used, and brown is 7% of the amount.
Use induction to show that the number of nodes in a binary tree is equal to one more than the sum of the degrees of the nodes in a binary tree.
The sum of 2 nonnegative numbers is 20. Find the numbers if the product of one number and the square root of the other is to be as large as possible.
Linear programming proof.One can convert the problem to an equivalent one with equality constraints
Linear Algebra : Modules, Linear Operators, Characteristic and Minimal Polynomials, Generators, Abelian Groups and Annihilators
Prove that for all odd integers n, (1^n)+(2^n)+(3^n)...+(n^n) is a proper multiple of 1+2+3+...n
If a,b,c are odd integers, show that all real roots of ax^2+bx+c=0 are irrational numbers.
If x were replaced with its opposite in each of the terms of the given polynomial, will it result in the opposite of the polynomial?
How many rectangles (of all sizes) are there in this grid? Can you generalize your results to an n by n grid? Can you generalize further?