The temperature of a town (in degrees Fahrenheit) can be estimated by the function f(x)=0.035x^4−0.09x^3+5.9x^2−20x+39 where x=1 represents January, x=2 represents February, etc. Find the average temperature from February to May. Round your answer to 4 decimal places.

Q: A radioactive element decays at a rate of 5% annually. There are 40 grams of the substance present.…

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Q: The amount of plutonium remaining from 1 kilogram after x years is given by the function…

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Q: The Loth Cat population grows at a constant relative growth rate. If the population is 400 after 2…

A: Let the constant relative growth rate be 'r' and the time in years be 't'. Let the population at any…

Q: When they invest K dollars, a fishery can produce Q(K) pounds of fish per month, where Q(K) = 104…

A:

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: Proceed as shown below...

Q: 13. a) Determine the average rate of change over the interval x = [1, 5] of the function y = 3x + 1.…

A: To solve the following

Q: 2. Informally explain that a function is considered differentiable, if small changes dx, to the…

A:

Q: What is the rate of change for h(x) = 8x - 9 on the interval [1, 4]?

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Q: A body at a temperature of 0° F is placed in a room whose temperature is kept at 100°F. If after 10…

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Q: Explain the method of fitting of an exponential curves of the form (i)Y = abX and (ii) Y = aebx to…

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Q: The half-life of a certain radioactive substance is 5 days. There are 28.4 g present initially. a.)…

A:

Q: Suppose you are climbing a hill whose shape is given by the equation z = 1000 −0.005x^2 −0.01y^2…

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Q: An article† in The New York Times states, "The number of gas stations [in a city] grows only in…

A: Part (a):To compare the number of gas station.

Q: The population of a certain country has grown at a rate proportional to the number of people in the…

A: Given that: Rate of increase of population is proportional to the number of people in the country.At…

Q: A bacteria colony grows at a rate of 11% per year. If the initial sample has a mass of 500 grams,…

A: We are given that the grow after each year is 11%, that means if the initial value is x, then the…

Q: The duration (time in hours) of dialysis required is modeled by the function y = In(1.5x + 0.5/9x² –…

A:

Q: The number of U.S. citizens aged 65 years and older from 1900 through 2050 is estimated to be…

A:

Q: An articlet in The New York Times states, "The number of gas stations [in a city] grows only in…

A: We will use the given relation between population and gas station.

Q: Total net shipments of aluminum (in billions of pounds) are approximated by g(x)=16.2+2.86ln(x+1)…

A: A) Total net shipments of aluminum (in billions of pounds) are approximated by g(x)=16.2+2.86ln(x+1)…

Q: The half-life of radium-226 is 1590 years. (a) If a sample has a mass of 150 mg, find a function…

A:

Q: 3- Suppose a student carrying a flu virus returns to an isolated college campus of 8000 students. If…

A: let the number of students infected is x, therefore, the number of students not infected is 8000-x…

Q: In a study of a marine tubeworm, scientists developed a model for the time T (measured in years)…

A: Consider the provided question, The time required for the tube worm to reach a length L is given by,…

Q: If a ball is thrown into the air with a velocity of 80ft/s, its height in feet after t seconds if…

A: Given y=80t-16t2 ; V=80 ft/SDifferentiate w.r.t 't'dydx=801-162tdydt=80-32tWe know that ,At…

Q: If the total revenue function for a blender is R(x) = 28x – 0.01x² where x is the number of units…

A: To find The average rate of change of revenue R(x) as x increases from 10 to 20 units.

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A: Given:

Q: Suppose the percent of males who enrolled in college within 12 months of high school graduation is…

A: Given:         Percent of males enrolled in college is    y= -0.126x + 55.72         Percent of…

Q: projected that, t months from now, the population of a certain town will be growing at the rate of…

A:

Q: A sample of 300g of lead-210 decays to polonium-210 according to the function given by A(t)=…

A: A sample of 300g of lead-210 decays to polonium-210 according to the function given by A(t)=…

Q: If the total revenue function for a blender is R(x) = 52x − 0.01x2 where x is the number of units…

A: We have the total revenue function R(x) = 52x − 0.01x2.

Q: The base x of a triangle is decreasing at the rate of 5 in./sec. and the height y of the triangle is…

A: Given Base = x  Height = y Rate of change of base = dx/dt = - 5 in/s Rate of change of height =…

Q: The monthly output of a certain product isQ(x) = 2400x5/2where x is the capital investment in…

A: The monthly output of a certain product is Q(x) = 2,400x5/2, where x is the capital investment in…

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: On the basis of data for the years 1911 through 1991, the expected life span of people in a country…

A: First find the number of years x from 1908 to date of birth of the person 1966 than put that x in…

Q: Numerically estimate the instantaneous rate of change of f(x)=e-x^2

A:

Q: An article† in The New York Times states, "The number of gas stations [in a city] grows only in…

A: Let N be the population in millions and G be the number of gas stations in a city. Given that the…

Q: y = ln (7x³ + 5)* 4

A:

Q: Solve for x accurate to three decimal places. In(Vx + 9) = 4

A:

Q: An article† in The New York Times states, "The number of gas stations [in a city] grows only in…

A: It is give that population is N and G be the number of gas stations in a city related by G=cN0.77.…

Q: Suppose that the daily profit (in dollars) from the production and sale of x units of a product is…

A:

Q: On the basis of data for the years 1911 through 1994, the expected life span of people in a country…

A: f(x) = 12.469 lnx +17.128x is the number of years from 1906 to person's birth year.expexted life…

Q: What is the average rate of change of f(x)=log2x from 8 to 32. what is the equation of the seant…

A:

Q: What is the instantaneous rate of change at x = 2 of the function f given by 2x f(x) O O 4 -2 H N -…

A: What is instantaneous rate of change at x=2 of the function f given by   f(x)= 2x/x-1

Q: ズ-1 f(x) = X + 3

A: given: f(x)=(x-1)/(x+3) x=4 delta(x)=8

Q: A certain radioactive substance has a half-life of 50 hours. Find how long it will take for 90% of…

A:

Q: There is a relationship between perceived corruption and human development in a country that can be…

A: Given  H(x)=0.3+0.28 In x                 where H(x) is Human development index…

Q: An oil tanker is leaking oil at a rate of L ′ ( x ) = x e ^(− x/2) barrels per hour, where x is the…

A:

Q: Because of job outsourcing, a town predicts that its public school population will decrease at the…

A: .

Q: The duration (time in hours) of dialysis required is modeled by the function y = In(1.5x + 0.5V9x2 –…

A:

Q: Total net shipments of aluminum (in billions of pounds) are approximated by g(x) = 16.2 + 2.86 In(x…

A: Given: The total net shipments of aluminum (in billions of pounds) are approximated by…

Optimization

Optimization comes from the same root as "optimal". "Optimal" means the highest. When you do the optimization process, that is when you are "making it best" to maximize everything and to achieve optimal results, a set of parameters is the base for the selection of the best element for a given system.

Integration

Integration means to sum the things. In mathematics, it is the branch of Calculus which is used to find the area under the curve. The operation subtraction is the inverse of addition, division is the inverse of multiplication. In the same way, integration and differentiation are inverse operators. Differential equations give a relation between a function and its derivative.

Application of Integration

In mathematics, the process of integration is used to compute complex area related problems. With the application of integration, solving area related problems, whether they are a curve, or a curve between lines, can be done easily.

Volume

In mathematics, we describe the term volume as a quantity that can express the total space that an object occupies at any point in time. Usually, volumes can only be calculated for 3-dimensional objects. By 3-dimensional or 3D objects, we mean objects that have length, breadth, and height (or depth).

Area

Area refers to the amount of space a figure encloses and the number of square units that cover a shape. It is two-dimensional and is measured in square units.