Consider a thick wedge of cheese. One straight cut through the wedge produces two pieces. Two straight cuts produce a maximum of 4 pieces (with one vertical cut and another horizontal cut). Three straight cuts can produce a maximum of 8 pieces (with two vertical cuts that are perpendicular and one horizontal cut). While this pattern seems to indicate a doubling of the pieces with each straight cut, this result is incorrect. In fact, the maximum number of pieces produced by n straight cuts is given by the cubic expression: n3 +5n +6 6 a. Use this expression to predict the maximum number of pieces of cheese that can be produced by six straight cuts. b. Suppose you had 24 confirmed guests coming to your house for a party and purchased a thick wedge of cheese for the occasion. What is the minimal number of straight cuts that you would need to make to this wedge of cheese if you want to make sure that each guest has at least 3 pieces of cheese? Explain your answer.
Consider a thick wedge of cheese. One straight cut through the wedge produces two pieces. Two straight cuts produce a maximum of 4 pieces (with one vertical cut and another horizontal cut). Three straight cuts can produce a maximum of 8 pieces (with two vertical cuts that are perpendicular and one horizontal cut). While this pattern seems to indicate a doubling of the pieces with each straight cut, this result is incorrect. In fact, the maximum number of pieces produced by n straight cuts is given by the cubic expression:
| n3 +5n +6 |
| 6 |
a. Use this expression to predict the maximum number of pieces of cheese that can be produced by six straight cuts.
b. Suppose you had 24 confirmed guests coming to your house for a party and purchased a thick wedge of cheese for the occasion. What is the minimal number of straight cuts that you would need to make to this wedge of cheese if you want to make sure that each guest has at least 3 pieces of cheese? Explain your answer.
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