The total number of gallons of water in a tank at time t is modeled by the expression A(t)=30+8t-2/3(t+1)^3/2

193 gallons

Step-by-step explanation:

Given

Required

Determine the maximum amount of water the tank can hold --- Missing from the question

Start by differentiating A w.r.t t

Solving:

Apply power rule:

So:

A'(t) = 0 + 8 + \frac{d}{dt}[-\frac{2}{3}(t+1)^{\frac{3}{2}}]

Equate to 0 to solve for t

Collect Like Term

Square both sides

Make t the subject:

So, the tank is at maximum when t = 63.

Substitute 63 for t in:

Approximate:

4

step-by-step explanation:

6 (donuts) divided by 3 is 2.

so 2/3 means 2 times 2, which is 4/6.

you get two and your friend gets four.