the water in a fish tank is decreasing at a rate of 2 inches per hour
Rate of change is the derivative
Rate of change in height with respect to time is 2 inches per hour
so [tex]\frac{dh}{dt} = -2[/tex]
(a) [tex]\frac{da}{dt} = 4\frac{ft^2}{sec} [/tex]
unit is feet^2 so its area
the unit of area is always units^2
so da/dt is the rate of change in area with respect to time
(b) [tex]\frac{dr}{dt} = -40\frac{cm}{min} [/tex]
r is the radius
so dr/dt is the rate of change in radius with respect to time
Radius is decreasing at the rate of 40 cm per minute
(c) [tex]\frac{dv}{dt} = -10\frac{m^3}{sec} [/tex]
v is the volume . the unit of volume is always cubic units
so dv/dt is the rate of change in volume with respect to time
Volume is decreasing at the rate of 10 meter cube per second
