Find the general solution to the given differential equation. (Remember the constant of integration.)dx = x³y dy Cost, revenue, and profit are in dollars and x is the number of units.The average cost of a product changes at the rateT'(x) =4and the average cost of 4 units is $12.00.(a) Find the average cost function.C(x) =(b) Find the average cost of 16 units. (Round your answer to the nearest cent.)$1/4

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Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015

1st Edition

ISBN:9781680331141

Author:HOUGHTON MIFFLIN HARCOURT

Publisher:HOUGHTON MIFFLIN HARCOURT

Chapter8: Graphing Quadratic Functions

Section: Chapter Questions

Problem 17CT

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The cost in dollars of making x items is given by the function Cx)=10x+500. a. The fixed cost is determined when zero items are produced. Find the fixed cost for this item. b.What is the cost of making 25 items? c.Suppose the maximum cost allowed is SI500. What are the domain and range of the cost function, C(x) ?
The demand function for the Viking Boat’s 34-ft Sundancer yacht isp = 200 − 0.01x ln x,where x denotes the number of yachts and p is the price per yacht in hundreds of dollars.(a) Find the revenue function and the marginal revenue function for this model of yacht.(b) Use the result of part (a) to estimate the revenue realized from the sale of the 500-th34-ft Sundance yacht. (Note: This is an estimate, so be careful to use the correct functionfrom part (a) and to evaluate it at the correct value of x.)(c) Now compute the exact revenue realized from the sale of the 500-th 34-ft Sundance yacht. (d) Comment on the approximation provided in part (b).
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A paint store sells 270 pails of paint per month at a price of $32 each. A customer surveyindicates that for each $1.20 decrease in price, sales will increase by 6 pails of paint.a) Determine the demand, or price, function.b) Determine the revenue function.c) Determine the marginal revenue function
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the amount of photosynthesis that takes place in a plant depend on the intensity of light x according to the equation: f(x)=145x2-30x3 i) find the rate of change of photosynthesis with respect to intensity ii)what is the rate of change when x=1 and when x=3? iii)how fast is the rate found in part (a) changing when x=1 when x=3?
The company is conducting set of experiments to maximize the time needed to discharge the battery. It was found that the time (t) is proportional to different powers of acceleration (a) , mass (m), and energy (E) of the battery. Use dimensional homogeneity to find the formula of the time and the value of overall dimensionless proportional constant using t=24 hours, the voltage is 338 V, the Energy is 71 kWh, velocity is= 1D km/hr, and the mass is 14D-pound.
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Find the general solution to the given differential equation. (Remember the constant of integration.) dx = x³y dy