Height of the woman = 5 ft Rate at which the woman is walking = 7.5 ft/sec Let us assume the length of the shadow = s Le us assume the <span>distance of the woman's feet from the base of the streetlight = x </span>Then s/5 = (s + x)/12 12s = 5s + 5x 7s = 5x s = (5/7)x Now let us differentiate with respect to t ds/dt = (5/7)(dx/dt) We already know that dx/dt = 7/2 ft/sec Then ds/dt = (5/7) * (7/2) = (5/2) = 2.5 ft/sec From the above deduction, it can be easily concluded that the rate at which the tip of her shadow is moving is 2.5 ft/sec.
6/54 times because there are 9 marbles and the orange marble is 1 out of those 9 marbles. If you multiply 6*9= 54 then you notice there is a 6/54 chance of picking any 1 marble out of the 54 times that you decide to pick marbles.
