Ask Your Teacher If a snowball melts so that its surface area decreases at a rate of 10 cm2/min, find the rate at which the diameter decreases when the diameter is 9 cm.

The diameter decreases at the rate of 0.1768 cm/min when the diameter is 9 cm.

Step-by-step explanation:

A snowball is spherical, so it's area is given by the following formula:

The radius is half the diameter so:

If a snowball melts so that its surface area decreases at a rate of 10 cm2/min, find the rate at which the diameter decreases when the diameter is 9 cm.

This is when

Applying implicit differentiation:

We have to variables(A and d), so:

The diameter decreases at the rate of 0.1768 cm/min when the diameter is 9 cm.

a) one student is chosen from classroom a, then a student is chosen from classroom b.  

step-by-step explanation:

independent events are ones in which the probability of one event does not affect the probability of the second event.

one student is chosen from classroom a; this does not affect the chances of choosing a student from classroom b.   this makes these independent events.

when one card is chosen from a standard deck and then set aside before a second card is chosen, the probability of the second card being chosen changes.   this makes them dependent events.

when one student is chosen from classroom a and then a second student is chosen from classroom a, the probability of choosing the second student changes.   this makes them dependent events.

when a letter is chosen from the alphabet and then a second letter is chosen, the probability of choosing the second letter changes.   this makes them dependent events.