The number of hours needed to paint a house is given by  H(x)=(180/x) + x^2 -10  if 'x' people are working on painting a house. Here, a fraction of a person represents a person working part time.  A. Use calculus to find the min length of time it takes to paint the house. Make sure to use calculus to verify that the time you find is the min. B. The total cost to paint the house is the product of length of time, the number of people working, and the hourly salary ($50/hour). For what number of workers is the total cost minimized?

Q: A factory produces Q(L) = 9L²/3 items each day, where L is the size of the labor force in…

A: The solution is given below in detailed

Q: A mean of 0.074 demands per day is erved for components that can be aired. air takes 30 days. How…

A: Given information: The mean demand per day is 0.074. The number of days is 30.

Q: The rate of growth, in dollars per year, of the net worth, f(t), of a company is given by…

A:

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

Q: The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of…

A:

Q: Solve for x x/12.4=4ft 6in/6ft 3 in

A: 1 ft=12 inch 4 ft 6 inches =4(12)+6=54 inches 6 ft 3 inches =6(12)+3=75 inches

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

A: Proceed as shown below...

Q: he amount of a certain radioactive substance decreases by 15% every hour. If a sample starts with…

A:

Q: 0 and f'(x) > 2 for 1sxs4, how small can

A: It is given that f(1)=10, f'(x)≥2 for 1≤x≤4.

Q: Use differentials to approximate the cube root of 0.009.

A: Approximate  0.00913

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

A:

Q: Find the total income produced by a continuous income stream in the first 10 years if the rate of…

A:

Q: The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of…

A: Explained below

Q: A company estimates that the daily cost (in dollars) of producing x chocolate bars is given by C(x)…

A: Given that  C(x) = 930 + 0.03x + 0.0004x2

Q: A company finds that the total cost of manufacturing a units of a certain product is given by C(x)…

A: We will find the required information as shown below

Q: Suppose that a person learns y items in x hours, as given by y = 40/x, 0sxs4. Find the rate of…

A: Let y represent items and x represent hours Given y=40x To find rate of learning at the end of 1…

Q: The marginal revenue for selling the xth box of light bulbs is  10 + 0.001x2e−x/100.  Find the…

A: Given: The marginal revenue for selling the xth box of light bulbs is given by: 10+0.001x2e-x100 The…

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: The function represents the rate of flow of money in dollars per year. Assume a 10-year period and…

A: Given that,  function f(x) = 0.03 x + 400 Rate r = 8 %  = 0.08 Time period is of 10 years. So time…

Q: The rate of growth of sales (sales per day) for a particular company is predicted to be 25e0.067…

A:

Q: Estimate x² dx using left endpoints for n = 4 approximating rectangles. 3 x² dx is approximately

A: The equation of the integral function is ∫03x2dx. The left endpoints is n=4.

Q: In a study of eating behavior, the cumulative intake (in grams) of one individual was found to vary…

A: In a study of eating behavior, the cumulative intake (in grams) of one individual was found to vary…

Q: The length of a rectangle is increasing at a rate of 4 cm/s and its width is increasing at a rate of…

A:

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

A: Given : A town predicts that its public school population will decrease at the rate of

Q: Based on the graph above, estimate (to one decimal place) the average rate of change from x=1x=1 to…

A:

Q: At time t years an industry consumes fuel at the rate of /(2t + 9) million barrels per year. If the…

A: Linear equation are those equation in which highest power of the variable is 1. The linear equation…

Q: A government agency estimates the number of young adults (ages 18 to 24) in a particular country to…

A: Given that       A Government agency estimates the number of young adults (ages 18 to 24) in a…

Q: The length of a rectangle is increasing at a rate of 8 cm/s and its width is increasing at a rate of…

A:

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

A: We have to find the differential equation for the population growth.

Q: A certain radioactive material is known to decay at a rate proportional to the square root of the…

A: We will find out the required solution.

Q: The length of a rectangle is increasing at a rate of 6 cm/s and its width is increasing at a rate of…

A: Area = length x width A = L x W

Q: The number of bacteria in a liquid culture is observed to grow at a rate proportional to the number…

A: We know that at the beginning of the experiment, number of cells = 104 After 3 hours of the…

Q: With a half life of 36 hours. Suppose a patient receives a  medication of 90 milligrams at midnight.…

A: A=A0e-ktAt t=36,A=A02A02=A0e-36kk=ln236A=A0e-ln236tA0=90At noon on first day…

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: a) What is the maximum amount of the salt that will ever dissolve in the methanol? b) If x = 50 when…

A:

Q: The length of a rectangle is increasing at a rate of 7 cm/s and its width is increasing at a rate of…

A: Given, length of rectangle is increasing at a rate of  7 cm/s width of rectangle is increasing at a…

Q: Solve for x: tanax=-1 -atanx

A:

Q: The marginal revenue for selling the xth box of light bulbs is  10 + 0.001x2e−x/100.  Find the…

A: The marginal revenue is given by 10+0.001x2e-x100 Therefore the total revenue is given by…

Q: Use Newton- Rophson Methad to find th Of the equalion in the range Solution ex t x- 10, ex + X -

A: If an equation is f(x)=0, then according to Newton Raphson method: Xn+1=Xn-f(Xn)f'(Xn)…

Q: Solve for x accurate to three decimal places. ex = 12

A: Given: ex=12.

Q: y = ln (7x³ + 5)* 4

A:

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

A:

Q: Find the average rate of change of g (x) = 2x²-9x from x=2 to x = 6. Simplify your answer as much as…

A: The  average rate of change of function f(x) from the point x=a to x=b is given by:-    (f(b) -…

Q: Find the instantaneous rate of change of g(x)=(x^3-sqrt(x))e^x+(x^5-2x+3)ln(x) when x=3. Round to…

A: The instantaneous rate of change of g(x) is:…

Q: Find the PV of an income stream that pays out continuously at a rate of R(t) = 3000e0.1" dollars per…

A: Given problem:- Find the PV of an income stream that pays out continuously at a rate of R(t) =…

Q: |The amount A(t) of atmospheric pollutants in a certain mountain valley grows naturally and is…

A: Write the naturally growing equation as exponential function A(t). At t = 0, let A (t) be Ao and at…

Q: Suppose you have a clothes dryer that uses 4000 watts of power and run it for an average year f 1…

A: To determine the operational cost of the hair dryer.

Q: A tank with a capacity of 300 litres initially contains 150 liters of pure water. Brine contains 3gm…

A: Solve the question 1 Capacity of tank=300litres Amount of pure water in tank initially=150litres…

Q: A ball is thrown upward so that its height above the ground after time t is h(t) = 20t-5t, where h…

A: Given is : We have to find time when h(t) or height will be maximum And for height , function is :…

Q: he differential to approximate the change in average cost per racket if production is (A) increased…

A: