Afilter filled with liquid is in the shape of a vertex-down cone with a height of 9 inches and a diameter of 6 inches at its open (upper) end. if the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, how fast is the level of the liquid dropping when the liquid is 2 inches deep?

Level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

Step-by-step explanation:

Since we have given that

Height = 9 inches

Diameter = 6 inches

Radius = 3 inches

So,

Volume of cone is given by

By differentiating with respect to time t, we get that

Now,  the liquid drips out the bottom of the filter at the constant rate of 4 cubic inches per second, ie

and h = 2 inches deep.

Hence, level of the liquid dropping at 28.28 inch/second when the liquid is 2 inches deep.

amount of oatypop that contains the prize = 40%

amount   of oatypop which doesn't contain the prize = (100-40)=60%

probability that hannah will win a prize

    = s +f s +f f s+ff   f s+ff f f s+ infinity.where f= failure,s= success

=   or 60%

probability that hannah only has to buy 3 or less boxes before getting a prize= (s) and ( f s) and (ff s) and (f f f s)

        = = 87.04 %  

step-by-step explanation: