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Integrate the concepts from different units in the Advanced Functions course to design a rollercoaster. Your coaster must meet the following conditions.
• The first part of the ride is modelled by a polynomial function. It includes a steep hill that starts at the origin, where the cars obtain their initial energy.
• The second part of the ride is modelled by a sinusoidal function with at least two cycles.
• The third part of the ride is modelled by a rational function that brings the cars back close to the ground.
• The rates of change where one part of the ride meets another part of the ride must not differ by more than 10%.
a) Determine an equation for each part of the ride.
b) Graph all three equations and show how they join each other.
c) Show that the rates of change at the points at which the models join each other do not differ by more than 10%.
Find the number of hours that represent the 40 percentile.
Solve equations and systems of equations in two variables, formulate real-world problems in terms of linear equations and solve these systems by several commonly applied methods.
Suppose 2 cards are drawn without replacement from an ordinary deck of 52. Find the probabilities of the following results.
Prove the parallelogram equality that is, the sum of the squares of the diagonals of a parallelogram equals the sum of the squares of its sides.
Prepare a research paper on two independent variables
State the null & alternative hypotheses
The asterisk implies a conditional usually indicated by an arrow. The & sign indicates "and". In Aristotelian logic (X)(FX*GX) logically implies (EX)(FX & GX). Is this true in predicate logic? If not, why not?
Assume that the spinner cannot land on a line. Determine the probability that the spinner lands on (a) red, (b) green, (c) yellow, (d) green. The spinner is divided into 8 halves. There are (a) red = 4, (b) green = 1, (c) yellow = 1, and (d) blue = ..
the salaries of a group of 60 workers in one year had a mean of $34,100 and a standard deviation of $7,200. At the end of the year each worker recieved a bonus $2,500 what are the mean and standard deviation of the salaries after the bonus is incl..
Determine the expected payoff of the game
A hat contains n coins, f of which are fair and b of which are biased to land on heads with a probability of 2/3. A coin is drawn from the hat and tossed twice.
A tent for a family of 6 is on sale for $109.99. Find the volume of space inside the tent (w= 8ft, l=12ft, h=6ft) for the family to sleep.
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