Jan and Mickey Haggerty graduated from college several years ago. Each majored in biology, and they were fortunate to receive good job offers at graduation; their combined income last year was over $100,000. The Haggertys enjoy a high level of curren...

Integrate {cos(x)cos(3x)cos(5x),x}

Please see the attached file for the fully formatted problems.
1: Use the Euclidean Algorithm to find the Highest Common Factor of 1176 and
1960.
2: Use the rules of natural deduction to prove ((A --> (B -->C)) -->((A B)--> C)).
[12 marks]
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Extend e^(x) into a power series at center x=1

A manufacturer of refrigerators must ship at least 100 refrigerators to its two West Coast warehouses. Each warehouse holds a maximum of 100 refrigerators. Warehouse A holds 25 refrigerators already, and warehouse B has 20 on hand. It costs $12 to...

1. Consider the sequence of triangles Ti, i >= 2: T2 is simply a triangle sitting upright, on its base. T3 is T2, except that an additional straight line is drawn from the upper vertex, down to somewhere on the base. For each Ti+1, one more line is a...

6. A string that contains only 0s 1s and 2s is called a ternary string
a) find a recurrence relation for the number of ternary strings that contain two consecutive 0s
b) what are the initial conditions
c) how many ternary strings of length six ...

11) Use generating functions to determine the number of different ways 12 identical action figures can be given to five children so that each child receives at most three action figures.
12) Use generating functions to find the number of ways to ...

A new set of automatic sliding doors at the entrance to a supermarket is being designed. The doors will consist of a pair of 100cm wide glass panels which are programmed to slide open in opposite directions when a sensor is triggered. The panels are ...

The sequence of value given by the iterative formula is
X n+1=2/9-lnXn with initial value X=1,converges to alpha.
1) State an equation satisfied by alpha, and hence show that alpha is the x coordinate of a point on the curve where y=3.
...