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Question: The documentation for the Java programming language recommends that when a boolean "equals method" is defined for an object, it should be an equivalence relation. That is, if r is defined by xry 4 x.equals(y) for all objects in the class, then r should be an equivalence relation. In a graphics application, a programmer creates an object called a point, consisting of two coordinates in the plane. The programmer defines an equals method as follows: If p and q are any two points in the plane, then where c is a small positive number that depends on the resolution of the computer display. Is the programmer's equals method an equivalence relation? Justify your answer.
When she is 30, Sue starts making annual deposits of $2150 into a bond fund that pays 5 percent annual interest compounded continuously.
Compare the advantages and disadvantages of substitution and elimination methods with the matrix method to solve systems of linear equations and the relationship these have with matrix method solving.
Without the contribution, the Wealthys taxable income for 2012 would be $2 million. What impact would the contribution have on the Wealthys 2012 tax bill?
a carpenter is building a rectangular room with a fixed perimeter of 104 ft. what dimensions would yield the maximum area? what is the maximum area?
Estimate the instantaneous rate of change of the function f(x) = x ln x at x = 1 and at x = 2. What do these values suggest about the concavity of the graph.
FINANCIAL PLANNING Joe plans to deposit $200 at the end of each month into a bank account for a period of 2 yr, after which he plans to deposit $300.
To win the jackpot of the Massachusetts lottery game in bygone days, you had to correctly pick the six numbers selected from the numbers 1 through 36. What was the probability of winning the Massachusetts lottery? (round to seven decimal places)
If we add 20 kJ of energy to 2 kg of liquid water originally at 20 C, 100kPa, a) How hot does it get if it is heated at constant pressure? b) How fast does it move if it is pushed by a constant horizontal force?
What are the dimensions of this rectangle?
Jamal currently earns $20,000 a year in gross wages. On January 1, he is due to receive a 2% COLA.
Let R be the elliptical region in the first quadrant bounded by x^2/3^2 +y^2/2^2 =1. Use the change of variables, x =3u , y =2v , to evaluate the area of R .
Reflect on your work or your life. Discuss a time where you used discrete probabilities to help solve a problem. How did this type of thinking help you in that process?
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