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- Two towns A and B are 5 km and 7 km, respectively, from a railroad line. The points C and D nearest to A and B are 6 km apart. Where should a station be located to minimize the length of the new road from A to S to B? (grade 12 calculus, use derivatives)A company's market research department recommends the manufacture and marketing of a new headphone. After suitable test marketing, the research department presents the following price-demand equation: x = 10000 - 1000 p. In the price-demand equation, the demand x is given as a function of price p. By solving for p, we obtain an equation in which the price p is given as a function of demand x: p = 10 - 0.001x where * is the number of headphones that retailers are likely to buy at Sp per set. The financial department provides the cost function C (x) = 7000 + 2x where $7000 is the estimate of fixed costs (tooling and overhead) and $2 is the estimate of variable costs per headphone (material, labor, marketing, transportation, storage, etc.). Find the domain of the function defined by the price-demand equation p. Find an interpret the marginal cost function. Find the revenue function as a function of and find its domain. Find the marginal revenue at x = 2000, 5000, 7000. Interpret these…Problem ABC is a right triangle and r is the radius of the inscribed circle. a) Express r in terms of angle x and the length of the hypotenuse h. b) Assume that h is constant and x varies; find x for which r is maximum.
- A certain economy's consumption function is given by the equation C(x) = 0.85x + 9 where C(x) is the personal consumption expenditure in billions of dollars, and x is the disposable personal income in billions of dollars. Find C(0), C(50), and C(100). C(0) = billion dollars C(50) = billion dollars C(100) =A power company burns coal to generate electricity, the cost c(x) to remove x% of the air pollutants is given by c(x)=600,000x/(100-x) determine if each statement is true, false, or cannot be determined a. The cost to remove 25% of the air pollutants is $400,000 b. If the company budgets $900,000 to remove pollutants, the can remove 100% of the pollutants c. The practical domain of the function is x union [0,100)A2. Ms. Whitmell says that the odd degree function she's looking at has a domain of {x∈ℝ} and {y∈ℝ}. If she solves for the turning points of the function, will that change the values for the domain or range Question 1 options: Yes, it will affect the domain Yes, it will affect the range Yes, it will affect the domain and the range No, it will affect neither the domain nor the range
- the point (3,20) on graph y=f(x)Let P=(x,y) be a point on the graph of y=x2-5 a) Express the distance d from P to the origin as a function of x b) what is d if x=0? c) What is d if x=1? I have no idea how to solve this and my book is not very helpful.1.) A packaging company will only accept packages for shipment if the sum of the height and the parameter of the base is not more than 240 inches. a.) Draw a diagram of a box with a square base and label the edges with your choice of variables. b.) Write a function to represent the volume of the box, given that the sum of the height and perimeter of the base is equal to 240 inches. c.) What dimensions (length, width, and height) of such a box will give the maximum volume? d.) What is the maximum volume?
- Provide complete solutions to all the problems given eliminate the arbitrary constant on the given functioncreate and solve an optimization problem involving 2-D or 3-D shapes - solve the following and number it -present an optimization problem of some complexity that involves a 2-D or 3-D shape -define variables used to solve your problem -create an equation for a function related to your problem -state the domain for the x value of your function (and your reasoning behind it) problem example: A soup can of volume 500cm3 is to be constructed. The material for the top costs 0.4 cents/cm2 while the material for the bottom and sides costs 0.2 cents/cm2 . Find the dimensions that will minimize the cost of producing the can - Your problem could be similar to this problem but you cant copy this problem the criteria is Complexity and Suitability of Problem (thinking)-Problem can be solved by optimization-Problem involves a complex 3-D or 2-D shape(eg: a composite shape, hemisphere, etc)-Problem involves an additional component on top of perimeter, surface area, volume, area,…We are constructing a box from a rectangular piece of cardboard. The piece of cardboard which measures 20 inches wide and 58 inches long. We will remove a square of size “x” inches from each corner and turn up the edges. Once we remove the squares of size “x” inches from each corner and turn up the edges, we create a box: Label the dimensions of the newly created box using the variable “x”. h=h= w=w= l=l= What is the equation that represents the Volume of the box as a function of the cutsize of the box? V(x)=Vx= What is the restricted domain of this problem? (That is, what x values "make sense"?) ≤x≤≤x≤ What is the restricted range of this problem? (That is, what V values "make sense"?) ≤V(x)≤≤Vx≤ (round to 1 decimal place) To maximize the volume of the newly created box, how much should be cut from each corner? x=x= inches (round to 1 decimal place) What is the maximum volume the box can hold? V=V= in3 (round to 1 decimal…
