the rate of change of pressure The atmospheric pressure at sea level is approximately 14.7 psi. The pressure changes as altitude increases and can be calculated using the relation P(h)=14.7⋅e^(−0.21h), where P is pressure in psi and h is altitude above sea level in miles. Find an expression for the rate of change of pressure as altitude changes and estimate the rate of change in Denver, CO (h=1 mile).

Lisantiom 2022-09-29 Answered
the rate of change of pressure
The atmospheric pressure at sea level is approximately 14.7 psi. The pressure changes as altitude increases and can be calculated using the relation P ( h ) = 14.7 e 0.21 h , where P is pressure in psi and h is altitude above sea level in miles.
Find an expression for the rate of change of pressure as altitude changes and estimate the rate of change in Denver, CO (h=1 mile).
You can still ask an expert for help

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Solve your problem for the price of one coffee

  • Available 24/7
  • Math expert for every subject
  • Pay only if we can solve it
Ask Question

Answers (1)

Bleha7s
Answered 2022-09-30 Author has 11 answers
Take the derivative of P(h)
P ( h ) = 14.7 × 0.21 e 0.21 h
then substitute h with the h of Denver. You will get your answer. I don’t know if you have ever tried to solve this simple question...
Did you like this example?
Subscribe for all access

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

You might be interested in

asked 2022-11-20
How to find average rate of change
How would I find the average rate of change over 8 minutes, of a person that runs at a rate of v ( t ) = x sin ( x 2 7 x ) ft/min? I missed when this was taught and I have no clue on how to do it. Help is greatly appreciated.
asked 2022-08-10
Rate of change of surface area of a sphere given the rate of change of the radius
Air is pumped into a spherical balloon such that the radius of the balloon increases at the rate of 1 20 π cm/s when the radius is 8.5cm. Find the rate of change of the surface area of the balloon at this instant.
How do I do this? I still don't really understand how rate of change works here.
asked 2022-09-23
Cylindrical tank rate of change
Water is pouring into a cylinder with a radius of 5m and height of 20m at a rate of 3 cubic metres a minute. Find the rate of change of height when the tank is half full.
Now the Volume V = π r 2 h and I can determine the rate of change in Volume is d V / d t = π r 2 d h / d t and the rate of change of height is d h / d t = 1 / π r 2 × d V / d t
Using that formula I can determine that the water is rising at a rate of 3 / 25 π m/min. But I cannot seem to figure out how to factor in height so that it is half full. Or is this wrong?
asked 2022-10-31
Relative rate of change
Problem: Volume of a cubic box is V = L 3 . How are the relative rates of change of V and L related?
This problem seems really simple, but I can't understand the concept of a relative rate of change. Here are my workings:
Original equation
V = L 3
I write it in form of differential equation
V = 3 L 2 L
then I divide the 2nd line by the 1st
V V = 3 L 2 L L 3
V V = 3 L L
Expression of the form f ( x ) f ( x ) is called a relative rate of change. And it can be thought of as percentage change. So as I see it by knowing the percentage change in L we can work out the respective percentage change in V, right? Wrong. I tried to make sense of it by putting values into the equation but no success. E.g. we increase L from 2 to 3 (by 50%) thus according to the last formula we should have a respective increase in V of 150% (50% times 3) which is not true ( 3 3 2 3 2 3 is a 237.5% increase). Can you help me out? I'm definitely missing something either in computation or more likely in understanding the concept.
asked 2022-08-12
What is the Rate of change of f ( x 2 ) given rate of change of f (x)
Find the average rate of change of f ( x 2 ) on the interval [1,4] given that the average rate of change of f ( x ) equals 9 on interval [1,16]?
This question has two different "answers" according to two different teachers
The first give answer of 9 by assuming y = x 2 and applying the formula of rate of change as following Let y = x 2 with I= [1,4] then f ( 1 )=1, f ( 4 )=16
f ( 16 ) f ( 1 ) ( 16 1 )
The second give the answer of 45 as following
f ( 16 ) f ( 1 ) 16 1 = 9
f ( 16 ) f ( 1 ) 15 = 9
f ( 16 ) f ( 1 ) = 9 15
Now we find rate of change of f ( x 2 ) following f ( 16 ) f ( 1 ) 4 1 = 9 15 3 = 45 what is the right answer?
Can we ensure the either answers geometrically? Thank you for helping
asked 2022-11-13
Calculating Rate of Change
At the point (0,1,2) in which direction does the function f ( x , y , z ) = x y 2 z increase most rapidly? What is the rate of change of f in this direction? At the point (1,1,0), what is the derivative of f in the direction of the vector 2 i ^ + 3 j ^ + 6 k ^ ?
I assumed that the rate of change is the same as the gradient of the function, namely f. Calculating this gave me:
f = ( x y 2 z ) x i ^ + ( x y 2 z ) y j ^ + ( x y 2 z ) z k ^
            = y 2 z   i ^ + 2 x z   j ^ + x y 2   k ^
Evaluating at point:
f ( 0 , 1 , 2 ) = 2   i ^
Hence, the function increases most rapidly in the x direction.
I am uncertain of how to approach solving the third part of the question, should I evaluate the rate of change at (1,1,0) and then find the difference between that and the vector 2 i ^ + 3 j ^ + 6 k ^ ?
asked 2022-08-11
Rates of change
I’m having some trouble with part c) of the following questions,
a) What is the rate of change of the area A of a square with respect to its side x?
b) What is the rate of change of the area A of a circle with respect to its radius r?
c) Explain why one answer is the perimeter of the figure but the other answer is not.
So, knowing that if we have a square with side length x, then the area of the square as a function of its side is A ( x ) = x 2 . The perimeter as a function of the side is P ( x ) = 4 x. And the rate of change of the area wrt its side is d A d x = 2 x. With a circle, the area as a function of the radius is A ( r ) = π ( r 2 ). And the rate of change of the area wrt its radius is d A d r = 2 π ( r ). The circumference as a function of the radius is also C ( r ) = 2 π ( r ). Therefore it’s the circle that’s the figure with the rate of change of the area wrt its radius equal to its perimeter, and what I saw was that the square had a rate of change of area wrt its side equal to half the perimeter of the square, d A d x = 2 x = 4 x 2
I inscribed a circle in a square with radius equal to half the square’s side length and went through the same work and then arrived at this, A ( r ) = π ( x 2 ) 2 = π 4 x 2 and C ( x 2 ) = 2 π ( x 2 and that d A d r = π 2 x
Somehow in this example, I don’t think it’s correct because the same fact about the rate of change of area wrt radius being equal to perimeter doesn’t hold. I appreciate any help in explaining this, thank you.

New questions