Related Rates

[CarrieRippey]

I have the same assignment. Where problem #2 is concerned, it won't let me complete the problem because I'm having trouble finding the correct unit for the final answer.

Problem #2

The pressure in a cylinder is given byP(t) = 101 + (k/t)

where P is in kilopascals (WebAssign abbreviation kPa) and t is in minutes.
Assume thatt ≥ 1
and k is constant.
At the instant when pressure is 114 kPa, it is changing at−0.85
kPa/min.
When does this happen?
What is the pressure whent = 1
minute.

 

[stapel]

I have the same assignment. Where problem #2 is concerned, it won't let me complete the problem because I'm having trouble finding the correct unit for the final answer.

I will assume that "it" is some sort of online assessment software. I will assume that "completing" means "entering the final answer". If these guesses are incorrect, kindly please provide corrections.

Please reply showing your work, including your units. Thank you.

 

[CarrieRippey]

I will assume that "it" is some sort of online assessment software. I will assume that "completing" means "entering the final answer". If these guesses are incorrectly, kindly please provide corrections.

Please reply showing your work, including your units. Thank you.

The pressure in a cylinder is given byP(t) = 101 +

k

t

where P is in kilopascals (WebAssign abbreviation kPa) and t is in minutes.
Assume thatt ≥ 1
and k is constant.
At timet = 7.5
minutes the pressure is changing at−1.35
kPa/min. Find k.k =

Your answer should be accurate to 1 decimal place and must include units.

so I found that setting P'(t) equal to -1.35 with t being equal to 7.5 minutes leaves me with k=75.9. However I need to plug in units to my answer and no matter what I try the web Assign system I am on continues to tell me that my dimensionallity is incorrect.
I've tried kPa/min, kPa/min^2 and ^3, kPa by itself, min by itself, min/kPa nothing seems to be working. What unit measurement should I be using, and how do I come up with that?

 

[Deleted member 4993]

The pressure in a cylinder is given byP(t) = 101 +

k

t

where P is in kilopascals (WebAssign abbreviation kPa) and t is in minutes.
Assume thatt ≥ 1
and k is constant.
At timet = 7.5
minutes the pressure is changing at−1.35
kPa/min. Find k.k =

Your answer should be accurate to 1 decimal place and must include units.

so I found that setting P'(t) equal to -1.35 with t being equal to 7.5 minutes leaves me with k=75.9. However I need to plug in units to my answer and no matter what I try the web Assign system I am on continues to tell me that my dimensionallity is incorrect.
I've tried kPa/min, kPa/min^2 and ^3, kPa by itself, min by itself, min/kPa nothing seems to be working. What unit measurement should I be using, and how do I come up with that?

k/t must have a unit of kPa.

t has unit of min

What should be the unit of k

 

[Ishuda]

...At timet = 7.5
minutes the pressure is changing at−1.35
kPa/min. Find k.k =

Your answer should be accurate to 1 decimal place and must include units.

so I found that setting P'(t) equal to -1.35 with t being equal to 7.5 minutes leaves me with k=75.9. ...

What does "the pressure is changing at" mean? It means that the rate of change is -1.35 kPa/min and, since rate of change means a derivative, you should be looking at the derivative of P, not P itself.