Apotter forms a piece of clay into a right circular cylinder. as she rolls it, the height h of the cylinder increases and the radius r decreases. assume that no clay is lost in the process. suppose the height of the cylinder is increasing by 0.5 centimeters per second. what is the rate at which the radius is changing when the radius is 3 centimeters and the height is 11 centimeters?

  dr/dt = -3/44 cm/s

Step-by-step explanation:

The volume of a cylinder is given by ...

  V = πr²h

Differentiating with respect to t (for constant volume), we get ...

  0 = π(2rh·dr/dt + r²·dh/dt)

Solving for dr/dt, we have ...

  dr/dt = dh/dt(-r²/(2rh)) = (dh/dt)(-r/(2h))

Filling in the given numbers gives ...

  dr/dt = (0.5 cm/s)(-3 cm)/(2·11 cm)

  dr/dt = -3/44 cm/s

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.

no

step-by-step explanation: