Please help with this two part question (Calculus)^^

1) -0.016 pounds per square inch per cubic inch.

2)

Step-by-step explanation:

We are given the equation .

Part A)

We want to determine the average rate of change of P as V increases from 200 cubic inches to 250 cubic inches.

To find the average rate of change between two points, we find the slope between them.

Rewrite the given equation as a function of V:

Hence, the average rate of change for V = 200 and V = 250 is:

Therefore, the average rate of change is -0.016 pounds per square inch per cubic inch.

Part B)

We want to express V as a function of P. This can be done through simple division:

We want to show that the instantaneous change of V with respect to P is inversely proportional to the square of P. So, let's take the derivative of both sides with respect to P:  

Differentiate. Note that 1/P is equivalent to P⁻¹. This allows for a simple Power Rule:

Therefore, the instantaneous change of V is indeed inversely proportional to the square of P.

iu

step-by-step explanation:

5.5

step-by-step explanation: