If the pressure P of the rocketť's gas at an altitude z, temperature T is decaying at a rate proportional to the current pressure. For the given data derive an expression of the pressure as a function of altitude. Explain why you used the positive or negative sign in your derived expression. | produce the data if g=9.81 m/s², R=287 J/(kgK). iii. Find the rate of change of P with respect to T @T=200K.

Q: Find the rate of change. Cube root 3√x with respect to x when x = 1, 8, 27

A: Consider the given: fx=x3ddxfx=ddxx3ddxfx=ddxx13ddxfx=13x13-1ddxfx=13x23

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A: Given: h(x)=x2-2x+3

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A: For 2nd part we need to use total derivative  According to definition: the total differential for  z…

Q: Estimate the instantaneous rate of change at the point indicated. f (x) = ex ; x = e

A: To find the instantaneous rate of change at indicated point:f(x)=ex;x=e. Solution: we know, the…

Q: amount

A: Please refer to the image below

Q: The area of a square with side s is A(s) s². What is the = rate of change of the area of a square…

A:

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A:

Q: Daily crude oil production by one particular oil company for 2008-2013 could be approximated by…

A: Given,          Daily crude oil production by one particular oil company for 2008-2013 could be…

Q: The brain mass of a fetus can be estimated using the total mass of the fetus by the functionb =…

A: To find the rate of change of total mass

Q: Compute the average rate of change of h(x)=Sqrt(x) over the interval [3, 3+x]. Simplify the…

A: To  Compute the average rate of change of h(x)=Sqrt(x) over the interval [3, 3+x].

Q: Find the equation of the graph and estimate the instantaneous rate of change at x = 1

A: From graph we can conclude that the equation of this graph be a parabola i.e., a quadratic equation.…

Q: The rate at which a radioactive chemical is delivered into cells is r(t) (measured in miligrams per…

A: NOTE: As method is not specified, question is solved for Riemann left end point approximation.

Q: The graph shows the depth of water W in a reservoir over a one-year period as a function of the…

A: The graph shows the depth of water W in a reservoir over a one-year period as a function of the…

Q: Q2/ An open cylinder can has an inside radius of 2cm and an inside height of 5cm. use the total…

A:

Q: Find the average rate of change of g(x) = lx -5 from x = - 1 to x = 3

A: Given, gx=1x3-5 from x=-1 to x=3

Q: What is the rate of change of y with respect to rfor this function?

A: Given,           The table represents some points on the graph of a linear function.

Q: find the rate of change. The reciprocal 1/x with respect to x when x = 1, 2, 3

A: The rate of change of a function is the value of the derivative of the function; thus, let the…

Q: Estimate the average rate of change from x = 1 to x = 4. %3D

A: average rate of change of f(x) on a,b=f(b)-f(a)b-aHere a=1 ,  b=4From graph f(1) = 5 ,  f(4) = 4

Q: Assume that the rate of change of air pressure with altitude (distance above the earth) is…

A: Topic:- Differential equation

Q: For a certain animal, the surface area S of the body is related to the body's weight W according toS…

A: The surface area S of the body is related to the body's weight W according to S is:

Q: estimated using the total mass of the fetus by the function b = 0.22m0.87, where m is the mass of…

A:

Q: Find the average rate of change for the given function over the indicated values of xx. If…

A: Given that  y = -2x2 +5x+1   where 'x' goes from -2 to 6 .     we have to find average rate of…

Q: What is the rate of change of y with respect to x for this function?

A:

Q: Find the average rate of change of the function between the given values of x. y = −5x − x2 between…

A:

Q: For a certain animal, the surface area S of the body is related to the body's weight W according to…

A: The surface area S of the body related to the body's weight W is given by S=kW2/3…

Q: If the demand for q units of a product priced at $p per unit is described by the equation 200 V29 +…

A:

Q: Consider the ordered pair of points below. (X1, V1) = (-8, -7) (x2, Y2) = (-5, 2) Find the average…

A:

Q: Suppose x and y are functions of third variable t. In the equation +y²=45, what are the values of…

A: First we will differentiate the given equation with respect to t using the chain rule of…

Q: Find the rate of change of y with respect to x when x=3000 and y=100

A: Given data:   The given expression of the function is 180x0.75y0.25=230,734. The given value of…

Q: Find the rate of change. Area of a square with respect to its side s when s = 5

A: To find the rate of change of the area of square with respect to its side s.

Q: Find x0 given that the rate of change of y =2x2+x-1 with respect to x at x=x0 is 4

A: giveny =2x2+x-1 rate of change=4rate of change=dydxdydx=4x+1

Q: What is the average rate of change of f(x) from x, = 3 to x2 = 5? Please write your answer rounded…

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Q: Find the rate of change of x with respect to p. 500 – X 0 < x < 500 8x

A:

Q: At a temperature of 20°C, the volume V (in liters) of 1.33 g of o, is related to its pressure p (in…

A: As per guideline we have to solve one question Please repost other question again

Q: currently 49 workers, find the instantaneous rate of change of monthly output with respect to the…

A: The monthly output at the Olek Carpet Mill is Q(x) = 15,000 + 2x2 units,    (40 ≤ x ≤ 60)  , where x…

Q: Choose whether the following statement is true or false. Average rate of change of a function…

A:

Q: estimate the instantaneous rate of change at the point indicated.f (x) = ln x; x = 3

A: To find the instantaneous rate of change at x=3 we need f'(3) We find f'(x)

Q: Suppose that the spread of a disease through the student body at an isolated college campus can be…

A: Here we have to find out rate of change of y.

Q: A typical male's body surface area S in square meters is often modeled by the formula S = 0 Vwh ,…

A: S=160wh Here, height of a person is  'h' cm and weight of a person is  'w' cm.

Q: Let f(x) = x/x + 1 (c) What is the average rate of change of f between x = 5 and x = 10?

A:

Q: Suppose that f(x) = 3x² – 3. (A) Find the slope of the line tangent to f(x) at x = 5. (B) Find the…

A: We find f'(x) using the power rule Slope of the line tangent to f(x) at x=5 is given by f'(5) So to…

Q: If a ball is dropped from a height of 2304 feet, then its height in feet above the ground is given…

A: Given that, if a ball is dropped from a height of 2304 feet, then its height in feet above the…

Q: A stuntman estimates the time T, in seconds, for him to fall x meters, 15. is T(x) = 0.54Vx. Find…

A: Instantaneous rate of change – It is the rate of change at each instant in time, not over a long…

Q: The area of a square with side s is A(s) = s². What is the rate of change of the area of a square…

A: We are given :  The Area of a square with  side s is A(s) =s2

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Q: What is the average rate of change of f between x=3 and x=10

A:

Exponential Growth Model

The relation that represents an exponential function is: