Question

calculus question that I really need answered before 12:30 am tomorrow. Please answer a,b, and c if you can thank you.

Answer 1

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
`(dh)/(dt) = -2`

(a)
`(da)/(dt) = 4(ft^2)/(sec)`

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)
`(dr)/(dt) = -40(cm)/(min)`

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)
`(dv)/(dt) = -10(m^3)/(sec)`

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