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Draw a game tree for nim if the starting position consists of three piles with one, two, and three stones, respectively. When drawing the tree represent by the same vertex symmetric positions that result from the same move. Find the value of each vertex of the game tree. Who wins the game if both players follow an optimal strategy?
In what (horizontal) direction should you moce in order to maintain a constant altitude - that is, to niether climb nor descend the hill?
At time t = 0, the police car is 40 km north and the truckis 30 km east of Sioux Falls. Calculate the rate at which the distance between the vehicles is increasing at t = 10 min.
Let R be the region bounded by the graphs of: y = x - sinx, y = pi and x = 0. Use a double integral to calculate the area of the region R
Which of the following would be a valid tensor equation? You should indicate if the equation is valid; and if it is not valid, you should state why.
In each case, sketch the closure of the set: (pi)
UBS Television Company is considering bids submitted by twelve different firms for three different contracts. In how many ways can the contracts be awarded among these firms if no firm is to receive more than two contracts?
Find the equation of the tangent plane to the central conicoid x2 - 4y2 + 3z2 + 2 = 0 at the point (1,2,0). Find whether the plane 2x + 3y + 2z =3 touches the central conicoid 2x2 + 3y2 + z2 = 1 or not.
Use the method of shells to find the volume of the solid obtained by revolving the region bounded by the given curves about the y - axis.
the census figures show that the average income for a family in a rural region is approximately 34860 per year. a
air temperature T varies in a periodic manner, with highs during the day and lows during the night. Assume that the weather pattern is the same for one week, and suppose that T(in degrees Farenheit) at a particular time of day is given by the func..
Prove that the regression line passes through the centroid
A tournament is a directed graph where between every two distinct vertices u and v, there is either an edge from u to v or an edge from v to u, but not both. Prove that every tournament has a Hamiltonian tour. (Hint: use induction on |V |, and sho..
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