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Discrete Mathematics
Show that the number of distinct sequences of positive integers which add up to n is exactly 2n. Note that we do not place any restrictions on the length of the sequence, just that each term is a positive integer and the total sum of all terms is n. Hint: how many choices are there for the first term in such a sequence, and once it is made, what must be true about the sum of the remaining terms? Derive a recursive formula and then prove inductively.
A cable that weighs 6 lb/ft is used to lift 850 lb of coal up a mine shaft 300 ft deep. Find the work done.
ose the clerk had to stack 200 boxes of cereal in a triangle. how many boxes would be on the bottom row?
question suppose alex wants to kick a ball over a 10 foot fence. assuming that gravity has no effect at what angle
show that in the subgroup-intermediate subfield given in the fundamental theorem of galois theory the subfield
Important information about Mathematics - Poisson Distribution, Metal plates are inspected regularly for flaws and average 2 flaws per square yard. Assume a Poisson process is applicable and calculate the probability of getting
a 17-ft ladder is leaning against a wall. If the bottom of the ladder is pulled alone the ground away from the wall at a constant rate of 5ft/sec, how fast will the top of the ladder be moving away
What is the location of someone standing on the first level in relation to someone standing on the third level?
Use Cylindrical coordinates to evaluate the triple integral SSS_E sqrt(x^2+y^2)dV, where E is the solid bounded by the circular paraboloid z=16-1(x^2+y^2) and the xy-plane.
The area of a parallelogram is 216 square centimeters. The height of the parallelogram is two thirds its base. Find the base and the height.
allison has 5 times as many baseball cards as football cards. in all she has 120 baseball and football cards. how many
A production process contains a machine that deteriorates rapidly in both quantity and output under heavy usage, so it is inspected at the end of each day. Immediately after inspection the condition of the machine is noted and classified into one ..
Consider a bowl containing 36 different slips of paper. Ten of the slips of paper each contain one of the set of digits 0 through 9 and 26 slips each contain one of the 26 letters of the alphabet
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