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Prove that any amount of postage greater than or equal to 12 cents can be built using only 4-cent and 5-cent stamps.
Write the Lagrangian for a one-dimensional particle moving along the x-axis and subject to a force F=-kx (with k possitive).
Student tickets were $8.50 and non-students were $13.25. If the total revenue for the game was $75,925, then how many tickets of each type were sold?
Solve each system by the substitution method. Indicate whether each system is independent, dependent or inconsistent.
Assume k>0 is fixed. Explain why, for large x, the relative growth rate of the function g(x) = e^kx is larger than the relative growth rate of f(x).
Solve each compound inequality. State the solution set using interval notation and graph it. x 3
Your company produces a product in a market that has grown by 10% per year for the past 15 years.
Jenny purchased a prepaid phone card for $20. The long distance calls cost 10 cents a minute using this card.
Derive the formula for the entropy of an ideal monoatomic gas using the microcanonical ensemble. This formula is known as the Sackur-Tetrode equation.
Now, develop a projection for the amount of the prize for the winner for the year 2004 using the relationship between the prize and the purse winnings.
What are the steps you use to change a measurement in degrees Celsius to degrees Fahrenheit?
How do you solve the inequality (x + 1)(x - 6) < 0, and express the solution using interval notation.
Simplify the following. Make sure to show all the steps involved. Expression: (3t^2 - 8t +3) + (-5t^2 + 4) - (t^2 + 5t - 3)
Prove that if R is commutative ring and N=(a1,a2,..am) where each ai is a nilpotent element, then N is a nilpotent ideal, i.e N^n=0 for some positive integer n.
Simplify each expression assume the variables represent any real #s and use absolute value as necessary.
For the exponential function ex and logarithmic function log x, graphically show the effect if x is doubled.
Solve each equation by using the quadratic formula. Find b^2-4ac and the number of real solutions to each equation.
Using the transfer function obtained in part (a) above, derive an expression for the phase angle of the output voltage.
Let x be a nilpotent element of the commutative ring R i.e. x^m for some positive integer m Prove that x is either zero or a zero divisor.
Tom took 16 hours to drive the 1,000 highway miles from Chicago to Boston.
The hickory company manufactures wooden desks. Management schedules overtime every weekend to reduce the backlog on the most popular models.
Refer to the graph given below and identify the graph that represents the corresponding function. Justify your answer.
What is the rebound ratio of the megaball. (hint:rebound ratio=rebound height/starting height).
Let R be a ring with 1 and let M be a left R-module. Let N be a submodule of M. Prove that if both M/N and N are finitely generated then so is M.
Systems of inequalities in two variables, graph the system of inequalities. Find the coordinates of any vertices formed.