A diver stands at the very end of a diving board before beginning a dive. The deflecton (d) of the board at a position (s) feet from the stationary end is given by d=cs2(3L-s) for 0 is greater than or equal to s is greater than or equal to L, where L is the length of the board and c is a positive constant that depends on the weight of the diver and on the physica properties of the board. Suppose the board is 10 ft long.
a) If the deflection at the end of the board is 1 ft, find c
b) Show that the deflection is .5 foot somewhere between s=6.5 and s=6.6
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