Water is drained out of tank, shaped as an inverted right circular cone that has a radius of 4cm and a height of 16cm, at the rate of 2 cm3/min. at what rate is the depth of the water changing at the instant when the water in the tank is 8 cm deep? show all work and include units in your answer. give an exact answer showing all work and include units in your answer

cm³/min  

Step-by-step explanation:

Let h = height of water and r = radius of its surface  

At all times,  

So,  

We want

= -2 cm³/min  

When h = 8  cm

cm³/min

The depth of the water is decreasing at a rate of cm³/min

.

The probability that MicroTech will beat the competition with its new computers is 0.994

Step-by-step explanation:

Consider the provided information.

MicroTech has funded three separate design teams to create the new systems.

The Probability of team A will come up with acceptable design is 90% or 0.9

The Probability of team B will come up with acceptable design is 80% or 0.8

The Probability of team C will come up with acceptable design is 70% or 0.7  

The probability of non of them will be able to come up with acceptable design = (1-0.9)×(1-0.8)×(1-0.7) = 0.1×0.2×0.3 = 0.006

Thus, the probability that MicroTech will beat the competition with its new computers is:

1-0.006 = 0.994

Hence, the required probability is 0.994