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John and Jane are analyzing promises from political candidates about reducing the cost of attending university. Their daughter, Jane Jr., plans to attend the University of Southern Ontario (USO) for four years, starting one year from now. Tuition at USO is currently $6000 per year, paid at the beginning of each year. Tuition is expected to rise by $400 each year. Use an annual interest rate of 5%.
(a) The Red Party promises to freeze tuition, so that it will stay at $6000 for each of the four years that Jane Jr. attends USO. What is the value today of the Red Party's plan?
(b) The Yellow Party promises to give scholarships of $1000 per year, awarded at the beginning of each school year. What is the value today of Jane Jr.'s scholarship?
(c) The Blue Party promises to give Jane Jr. a tax credit after she graduates. At the end of the first year after she graduates, and continuing each year afterwards, her income taxes will be reduced by $200. What is the value today of the Blue Party's tax credit? Assume she lives forever.
Select and discuss two examples of real life objects that incorporate the parabolic shape. Explain why the parabolic shape was used for the objects.
Suppose the position of a particle after t seconds is given by the following vector equation - evaluate each of the following vectors:
The report costs Paula $ 15 to produce, but Paula is able to sell reports for $ 350 each. Of course, any reports not sold by the end of the week have no value. How many reports should Paula produce each week?
A mini license plate for a toy car must consist of a letter followed by two numbers. Each letter must be a C, A or R. Each number must be a 3 or 7. Repetition of digits is permitted.
Suppose that a body moves in a straight line through a resisting medium with resistance proportional to the square of it's speed v with initial speed v_0 and initial position x_0.
Biased Bernoulli Process, Suppose that two teams that meet in the world series are closely matched: the better team wins a given game with a probability of .55
A stone thrown upward from the top of a 80 ft cliff at 118 ft/sec eventually falls to the beach below. (For this problem take the acceleration due to gravity to be -32 ft/sec; take upwards to be a positive direction.)
find that the sample mean and sample standard deviation
Two point charges q1 and q2 separated by a distance of 3m experience a mutual force of 16x10^-15N. Calculate the magnitude of charge when q1=q2=q. What will be magnitude of force if separation between the charges is changed to 6m?
Explain the five-steps for solving rational equations. Can any of these steps be eliminated? Can the order of these steps be changed? Would you add any steps to make it easier, or to make it easier to understand?
Rational root theorem and synthetic division - Use the rational roots theorem and synthetic division to find the years the country " broke even" (dept = surplus = 0) from 1990 to 2000.
Consider the curve 5x3+8xy+5y2 = 45. Use implicit differentiation to calculate the derivative dy/dx. Hence determine the point/s which has/have a horizontal tangent.
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