90^2+60+1

90^2+61

8100+61=8161 i think this is right, i didnt use a cal...

Ok, so for the first one, you have to use an integral. An integral can represent a net accumulation.

This would be a definite integral for the first problem.

Integrate 3t^2 + 2t + 1 from 0 to 30 to get your answer.

The integral would be t^3 + t^2 + t. Don't worry about the constant since you are taking a definite integral. The fundamental theorem of calculus states that you take s(30) - s(0) to solve the definite integral, so that's what you do. For simplicity's sake, it is (30)^3 + (30)^2 + (30), which equals 27,930.

For the next problem, you need to know the volume of a sphere. That is V = (4/3)(pi)r^3. Since the derivative of a function represents the rate of change, we can take the derivative of the function to help us solve the problem.

The derivative is dV/dt = 4(pi)r^2(dr/dt). Now, plug in all the numbers you know.

dV/dt = 4(1/2)^2(pi)(1/pi)

dV/dt = 4(1/4)(pi)(1/pi)

dV/dt = (4/4)(pi/pi)

dV/dt = 1 cubic meter per minute.