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Differential Equations: An Introduction to Modern Methods and Applications
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- Please provide the solution for when x1=1 and y1=0arrow_forwardOn the basis of data from 1990 to 2006, the median income y in year x for men and women is approximated by the equations given below, where x = 0 corresponds to 1990 and y is in constant 2006 dollars. If these equations remain valid in the future, in what year will the median income of men and women be the same? Men: Women: - 237x + 2y = 63,300 - 850x + 3y = 46,199 The median income of men and women will be the same in the yeararrow_forwardWe 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…arrow_forward
- Solve the following graphically. x + 3 = √12x+1 Ox=2 x = -2 or x = -4 Ox=-4 x = 4 or x = 2arrow_forwardEliminate the arbitrary constant in the equation x = Cy2arrow_forward1)The sum of three consecutive multiples of 4 is 444. Find these multiples. [This is a problem on linear equations in one variable] 2.State the steps you will take to transform 3x + n = 7 to x = (1/3)[7- n]arrow_forward
- Suppose C = 45+ 0.5t and L = 9 +2.5t represent the population (in thousands) of two cities, Clarksville and Lanesville, respectively. Determine the number of years it will take for their populations to be (a) equal, and (b) for Clarksville to have twice as many inhabitants as Lanesville. Also report the population of the towns for each situation. (a) In how many years will the population of Clarksville equal that of Lanesville? Number years What will be their populations? Number thousand peoplearrow_forwardPlease find the general solution of the underlined problem.arrow_forward#9,10Please answer these 2 problems with clear and complete solutions.thank youarrow_forward
- Algebra for College StudentsAlgebraISBN:9781285195780Author:Jerome E. Kaufmann, Karen L. SchwittersPublisher:Cengage LearningCollege AlgebraAlgebraISBN:9781305115545Author:James Stewart, Lothar Redlin, Saleem WatsonPublisher:Cengage LearningAlgebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell