Water is flowing into a large spherical tank at a constant rate. Let V (t) be the volume of water in the tank at time t, and h(t) be the height of the water level at time t.

a) Give a physical interpretation of dV/dt and dh/dt.
b) Which of dV dt and dh dt is constant? Explain your answer.
c) Is dV dt positive, negative, or zero when the tank is one quarter full?
d) Is dh dt positive, negative, or zero when the tank is one quarter full?

See solutions for detail.

Step-by-step explanation:

a.   is the instantaneous rate of change of volume given with respect to time, t.

The volume's rate of change is written as a function of time.

- is the rate of change in the height of water in the tank with respect to time, t.

b.   is the only constant. Water flows into the constant at a constant rate, say per minute.

c. is positive. Volume water in the take  is increasing from time to time.

-The volume at time t=1 is greater than the volume at t=0, hence, it's a positive rate of change.

d. is a positive rate. The initial height of water in the tank is zero.

-The final height at time t is 0.25h. The height is increasing with time.

Hence, it is positive.

none of the above.

for one of the equations to be used in the process, there has to be a term in the equation since squared is .

since there is only a term in the first equation, we cannot derive a from completing the square.

solving with completing the square

options a,b,c are the right answer.

step-by-step explanation:

a linear parent function is always represented as y = x

if we write this function in the form of y=mx+c

⇒

or  

now if we plot a graph we will find these characteristics:

1) y intercept of the graph is zero so its a straight line passing through origin.

2) as we can see in both the forms of function written, values of x and y may be either positive or negative for the positive slope means points on the graph are either in first quadrant or in third one.

3) it's slope is one.