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Question: 1. How many chunks of yam can you obtain when using exactly two cuts?
2. What is the largest number of yam chunks obtainable using exactly three cuts? It is much more difficult to draw cut yams than to draw sliced pizza, but attempt it anyway.
3. What is the largest number of pieces of yam you can obtain using exactly four cuts? If you cannot get an exact number, then try to find upper and lower bounds on the number.
(If you have access to a computer and would like a visual aid for your experiments or for communicating your ideas, see Wolfram Demonstration project - Cutting space Into Regions With Four Planes, you can move planes such as those shown in Figure)
A dance team knows 14 routines of which 7 are tap, 5 are ballet, and 2 are modern. The program can consist of any four routines. In how many ways can the manager choose which routines to present if there are no restrictions?
Show that a projectile fired at an angle of theta with initial speed v0 travels a total distance (v02/g) sin 2θ before hitting the ground. What angle will give maximum distance?
The first equation in a system of two equations is x - 2y = 10. The graph of the second equation does not intersect the first. Write a possible second equation for the system and explain your answer. (Note: There are multiple equations that will work..
A savory crepe could have any vegetable (broccoli, mushroom, spinach) and any protein (turkey, cheese, prosciutto). How many different crepes are on the menu?
If Tom Bombadil's house is 16 miles east of Hobbiton and 12 miles south, what is the straight line distance (omit units)?
A right circular cylinder has a radius 3 and height 3. If A and B are two points on its surface, what is the maximum possible straight-line distance between A and B?
At 12pm, ship A is 150 km west of Ship B. Ship A is sailing east at 35 kim/hr and ship B is sailing north at 25 km/hr. How fast is the distance between the two ships changing at 4pm?
Two trains having length of 140 m and 160 m long run at the speed of 60 km/hr and 40 km/hr respectively in opposite directions (on parallel tracks). The time which they take to cross each other
(a) If F : R^n → R^m is a linear transformation and n > m then there exists a nonzero vector x such that F (x) = 0. (b) If F : R^n → R^m and G : R^k → R^n are linear transformations such that ker F = {0} and ker G = {0} then ker F ? G = {0}.
Let D = {z: |z|
Explain how dynamic programming can be used to schedule talks in a lecture hall from a set of possible talks to maximize overall attendance.
In find the elementary row operation that transforms the first matrix into the second.
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