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BMAD

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  1. Suppose a baseball player runs at a speed of 24 ft/s. He is trying to run on a baseball field where it's 90 feet to each base. Determine the rate of change to second base once the runner reaches halfway to first base.
  2. I still have a different solution
  3. The coins spin at the same rate. The diameter of the coins only matter in this story if we wanted to determine how much sooner one coin would finish before the other one (if there have the same diameter) However, yes, I would think it is safe to assume that x and y are measured in inches. If you recall from a post i made a long time ago, we saw that if two identical coins were spinning around a circle (even if the circle is defined without width) the coin on the inside of the circle would finish the circle sooner relative to the ratio of coin size to the centers of rotation that the coins spin in.
  4. Suppose we have a sine (x) curve over the domain [0,pi]. Two coins will (roll/spin) starting at x=0 and go to pi. The coins have a diameter of 1 inch. If one starts on top of the curve and the other rolls from the bottom side of the curve, which coin would make it to pi first?
  5. Let's say we put up two vertical walls meeting at an 120 degree angle. Then we draw a line on each wall, meeting at the intersection of the walls. Each line makes an angle theta with the horizontal; one goes up from the intersection and the other goes down. What angle theta should there be that the two lines form the angle 137.5?
  6. How many spin-able numbers are there from 0 to 99999 ? This is a no-computer puzzle, only right answers with explanation will be accepted. nevermind
  7. Five people (A,B,C,D,E) each need to complete one task (1,2,3,4,5). The amount of money each person would need to complete each tasks is reported in the matrix below. 1 2 3 4 5 +---------- A | 8 3 5 4 3 B | 2 6 9 4 7 C | 6 1 8 4 3 D | 5 7 9 8 8 E | 5 7 9 4 3 As the assigning manager, who should do which task?
  8. You enter a room with two chests. You know that one chest has a lot of money (but you are unsure as to which). You know the other chest has half as much. Being the greedy person you are you want the most money but the chest are indistinguishable from each other outside of opening and counting the contents. You picked the first chest. Just before you open it, the owner of the chests offers you an opportunity to switch. Should you?
  9. Pretend you have a rectangle that is divided into two smaller rectangles where the area of one rectangle is twice that of the other rectangle. If you were to pick a point at random inside the rectangle, what is the probability that the point is within the larger rectangle?
  10. BMAD

    Star area

    Not until you have raised the question. Clearly their must be an upper bound and lower bound between which the area could exist.
  11. BMAD

    Star area

    my mistake. I did mean to state symmetry. well done!
  12. Suppose we have two congruent equilateral triangles with side length of 8ft. They are on top of each other in the same orientation. Now One triangle is rotated by 180 degrees and is laying on top the other triangle forming a star. The triangles are positioned relative to each other such that the distance from the base of one triangle is 6ft to the base of the other triangle. What is the area of the star?
  13. Assume an exclusive OR.
  14. Why can't a right triangle with an hypotenuse of sqrt(24) have an area of 13 squared inches?
  15. There is an equilateral pentacontagon (a polygon with 50 sides). In one of its vertex stands Dr. Faust. He has three options 1) walk to the diametrically opposed point free of charge; 2) walk counterclockwise to the neighboring vertex by paying $1.05 to Mephistopheles; 3) walk clockwise to the neighboring vertex by receiving a payment of $1.05 from Mephistopheles. If it is given that Dr. Faust has been everywhere at least once, prove that at some point someone paid no less than $25.
  16. Let’s say there is a gathering where among any three people there are two friends. Is it true that people at such gathering can always be divided into two groups in a way that every two people in one group are friends?
  17. Let me see if i can ask my question better. Suppose you have twelve rods of two different sizes. One size is 4 in. The other is 8 in. There are 8 - 4in. Rods and 4 - 8 in rods. Use the 4 in rods to construct two squares. Stand your squares up perpendicular to your table and parallel to each other. Now take one 8 in rod and connect it to the top left of one square (first square) and bottom left of the other. Take your second rod, connect it to the top right of the first square and top left of the other. Third rod, bottom right of first and top right of second. Connect the last rod to the remaining vertices. All rods will remain straight through this process. Find the volume and compare it to the volume of 4x4x8
  18. The square faces are the front and back. If you think of the congruent squares each having vertices abcd in the same clockwise rotation each resting parallel to the other. Then connect 8 inch edges in the following manner, front A to back B, front B to back C, front C to back D, and front D to back A. How does this volume compare to a standard rectangular prism of 4x4x8?
  19. Suppose you have a rectangular prism with dimensions 4x4x8. Lay this shape down with the small square facing you. We are going to distort this rectangular prism. Take the top left corner of the front square and connect it to the bottom left corner of the back corner, take the bottom left corner of the front and connect it to the bottom right corner of the back, and so on. Keep the short edges 4 and the long edges 8, how do the volumes compare?
  20. I'm am curious if maybe I am missing something with my own problem but every time I fold into the center the vertices sum to relatively similar (maybe human error) value. Perhaps this is helpful.
  21. Good question, for this problem I meant for the move to mean always going to the original center.
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