Write the general antiderivative of the given rate of change function. (Use C for the constant of integration.) The rate of change of the percentage of the U.S. population that is foreign born is given by p(t) = -0.073t3 + 1.422t2 – 11.34t + 9.236 where output is given in percentage points per decade and t is the number of decades since 1900, data from 0sts 11.t P(t) = percentage points

Q: If f '(x) = x4, what is f(x)? (Use C for the constant of integration.) f(x) =

A: We can make it easier for you.

Q: The increase in carbon dioxide (CO2) in the atmosphere is a major cause of global warming. Using…

A: A(t) = 0.012414t2 + 0.7485t + 313.9 (1 ≤ t ≤ 59) where A(t) is measured in parts per million volume…

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Q: Write expressions for the average rate of change of y with respect to x between a and x and for the…

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Q: |If f(x) = a4 is the parent cubic function, prove that the AVERAGE rate of change of f(x) over the…

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Q: Determine the average rate of change of the function y = sinx from X = 0 to x = 2 O1 2

A: The average rate of change of the function f(x) can be calculated using the formula Average rate of…

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Q: Given that x and y are functions of time, find the indicated rate of change. dx when x 6, y = 3, and…

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Q: Determine the value of the arbitrary constant of the antriderivative of F(x) = x-In(x) given the…

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Q: Find the average rate of change of the function over the given interval. f(t)= 4t+9…

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Q: This is a linear DE. If arranged to its form, what is the integrating factor? * xdy ニ

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Q: a) The marginal profit for a product is modeled by dP -0.0002x + 14. 2 dx Apply the integration to…

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Q: Find the average rate of change of the function over the given interval. f(t) = 6t + 9, [2, 4]…

A: The derivative of the function gives the instantaneous rate of change of the function. since the…

Q: If  f '(x) = x4,  what is f(x)? (Use C for the constant of integration.)

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Q: Find the average rate of change for the function over the given interval. y= 9x +4x+3 between x= -6…

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Q: Let  x(V) = V1/3  be the length of the side of a cube in terms of its volume. As V decreases, does…

A: V is decreasing that is dv/dt is negative  Let dv/dt =-k where k is constant.

Q: Find the average rate of change of f(x) = x2 + 3x + 1from 1 to 2. Use this result to find the…

A: Average rate of change of a function f(x) is calculated as the total change in the function divided…

Q: Let r(t) be the rate at which the world’s oil is consumed,where is measured in years starting at t…

A: Given: Let r(t) be the rate at which the world’s oil is consumed,where is measured in years starting…

Q: For the function y = 4x2: (a) Find the average rate of change of y with respect to a over the…

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Q: Find the average rate of change of the function over the given interval. f(t) = 8t + 9, [7, 8]…

A: Given function is ft=8t+9 and interval 7,8 Average rate of change of function is given as: Average…

Q: Find the average rate of change for the function over the given interval. y =x2 + 9x between x = 4…

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Q: The increase in carbon dioxide (CO2) in the atmosphere is a major cause of global warming. Using…

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Q: If h (x) = x³ + 4æ² – 12x + 7 on the interval [-2, 4]: For what value(s) of C does h' (c) equal the…

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Q: For what function P is the integrating factor α(x) equal to x?

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Q: -√x Q3. Change the order of integration and evaluate f* f* dy dx.

A: We can solve as follows

Q: If f'(x) = 4x°, what is f(x)? (Use C for the constant of integration.) f(x) = %3D

A: It is known that ∫xn dx=xn+1n+1+C provided n≠-1. Given that f'x=4x3. Integrate as follows.

Q: A tank initially holds 10 gal of fresh water. at t=0, a brine solution containing 1/2 lb of salt per…

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Q: For what function P is the integrating factor α(x) equal to ex?

A: Here the given integrating factor

Q: Find the average rate of change over the interval [2, 5], for the function, f(x) = 3 – x

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Suppose a model for the surface area of a human body is given by S = 0.1094w0.425,0.725, where w is…

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Q: What is the period of time ''t'' required for the initial infection rate ''I(t=0)'' to double in…

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Q: If f'(x) = 5x*, what is f(x)? (Use C for the constant of integration.) f(x) =

A: To find the integration

Q: The rate of change of y is proportional to y. When t = 0, y = 2, and when t = 2, y = 4. What is the…

A: Given that rate of change of y is proportional to y that is, dydt=ky        ...(1)

Q: The average rate of change of y with respect to x over the interval [0, 3] for the function y = 3x…

A: The function y=3x+2 over the interval 0,3

Q: Find the average rate of change of g(r) = 5x - 1 from z - 2 to z = 1 =D1 =

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the average rate of change of the function over the given interval. f(t) = 4t2 – 1, [1, 1.1]

A: Given data: The expression for the function is f(t)=4t2-1. The given limit of t is [a, b]=[1, 1.1].…

Q: A whole life policy is issued to (30) with Z=10 for T20. If the force of interest and mortality is…

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Q: Find the average rate of change of the function over the given interval. f(t) = 6t2 – 1, [5, 5.1] -…

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Q: Determine the average rate of change of the function y = cos x from x = 4 77 to x = 4 v2 V2 2 2

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Q: The volume of a cylinder of height 12 inches and radius 7 inches is given by the formula V = 12π².…

A: We have to slove the derivative

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A: Consider the equation

Q: How would I solve for the left endpoint and the right endpoint? Find the average rate of change of…

A: Given :f(t) = 4t2 − 3,      [3, 3.1] formula for average rate of change :

Q: The volume of a cylinder of height 12 inches and radius 7 inches is given by the formula V = 12π².…

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Q: (a) A cougar was found dead in the woods by a ranger, which he assumed was shot by a poacher. The…

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Q: Find the antiderivative of the given derivative. ds = 14t(5t2 – 1)3 dt S=

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Q: Q3. Change the order of integration and evaluate * * dy dx.

A: To evaluate ∫04∫0xdy dx using the change of the order integration. From the limit of integration the…

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.