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1) The astronomer Giovanni Cassini (1625-1712) studied the family of curves with polar equations
r4 - 2c2r2 cos 2θ + c4 - a4 = 0
where a and c are positive real numbers. These curves are called the ovals of Cassini even though they are oval shaped only for certain values of a and c. (Cassini thought that these curves might represent planetary orbits better than Kepler's ellipses).
(a) Investigate the variety of shapes that these curves may have by considering different values for a and c.
(b) Determine how a and c are related to each other when the curve splits into two parts.
Important information about Find the probabilities, Suppose a family plans 6 children, and the probability that a particular child is a girl is ½.
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where is its height above the ground and is the horizontal distance traveled in meters. Calculate the distance traveled by the prey from the time it is dropped until the time it hits the ground.
Probability: Mary is taking two courses, photography and economics. Student records indicate that the probability of passing photography is 0.75, that of failing economics is 0.65, and that of passing at least on of the two courses is 0.85.
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The probability that a house in an urban area will be burglarized is 5%. If 50 houses are randomly selected, what is the probability that one of the houses will be burglarized?
evaluate the derivative of the given function by using the definition of derivative.find the derivative of the
question1athe connected planar graph g has degree sequenceg1 g2 g3 g4 g5 g6and the connected planar graph h has degree
Set up a hypothesis test to try to prove that the mean number of hours studied at your school is different from the 14.6-hour-per-week benchmark reported by BusinessWeek.
A rectangular package with a square base to be sent by a postal service can have a maximum combined length and girth (perimeter of a cross section) of 108 inches. Find the dimensions of the package of maximum volume that can be sent.
What is the shortest length of fence that the rancher can use? Note: The answer to this problem requires that you enter the correct units.
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