Q4// The following PDE describes a specific fluid-flow problem in a porous medium. After examining the given mathematical formulation, describe the flow problem to the fullest extent 3²7- Where C>0

6.9 In an electrophoretic fiber-making process, the diameter of the fiber, d, is related to the current flow, 1. The following are measured during production: I (NA) d (μm) 300 22 300 26 350 27 400 30 400 34 500 33 500 33.5 650 37 650 42 The relationship between the current and the diameter can be modeled with an equation of the form d = a + b.I. Use the data to determine the constants a and b that best fit the data.

The points ( – 1.7, 2.1) and (2.5, 8.4) satisfy a linear relationship between two variables, x and y. a. What is the constant rate of change of y with respect to x? 1.5 Preview b. Write a formula that expresses Ay in terms of Ax. deltay=deltax*1.5 Preview c. Write a formula that expresses y in terms of x. y-2.5=1.5(x-8.4) Preview d. What is the value of y when x = 113? = 1.5(113-8.4)+2.5 Preview

Exercise 2. Integrate the following functions. 1. S(3x+2)°dz 2. 3.

Two chemical engineers, A and B, are working independently to develop a model to predict the viscosity of a product (y) from the pH (x1) and the concentration of a certain catalyst (x2). Each engineer has fit the linear model y =A +hr, + B;x; +r The engineers have sent you output summarizing their results: Engineer A Predictor Constant тР Coef SE Coef 199.2 0.5047 394.7 0.000 -1.569 pH Concent. -4.730 0.5857 -8.08 0.000 0.4558 -3.44 0.007 Engineer B Predictor Coef Constant 199.0 0.548 SE Coef T 363.1 0.000 pH Concent. -3.636 1.952 -1.256 1.983 -0.63 0.544 -1.86 0.112 The engineers have also sent you the following scatterplots of pH versus concentration, but forgot to put their names on them. Concentration Concentration Which plot came from which engineer? How do you know? Which engineer's experiment produced the more reliable results? Explain. a. b.

Consider the Cobb-Douglas model for a certain manufacturing plant, 60H0.610.4 W where W is the number of washing machines produced per year, I is the annual investment in capital (in thousands of dollars), and H is the total number of work hours. The annual budget, that pays capital and employees, must be 1 million dollars. Also, employees are paid 10 dollars per hour. Work hours: = Find the number of work hours and annual capital investment that will maximize production. machines. hours. Capital Investment: dollars (in thousands) How many washing machines are produced when production is maximized:

Sandy's main house is a hemispherical glass dome with diameter of 8m. Suppose that the glass is m thick. Use differentials to estimate the volume of the glass material. (Write the answer as kπ m³)

An engineer wants to determine the spring constant for a particular spring. She hangs various weights on one end of the spring and measures the length of the spring each time. A scatterplot of length (y) versus load (x) is depicted in the following figure. Inad a Is the model y = P, +B, x an empirical model or a physical law? b. Should she transform the variables to try to make the relationship more linear, or would it be better to redo the experiment? Explain.

7. t310-3 d dt

Differentiate.