9/11/2017 Assignment Previewer

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1 41 Multivariable Functions I ( ) Due: Wed Sep :00 PM MDT Question Instructions Notes and Learning Goals Flash Graphing App 1. Question Details SCalcET [ ] The wave heights h in the open sea depend on the speed v of the wind and the length of time t that the wind has been blowing at that speed. Values of the function h = f(v, t) are recorded in feet in the table below. (a) What is the value of f(40, 20) What is its meaning According to the table, f(40, 20) =, which means that if a 40knot wind has been blowing in the open sea for 20 hours, it will create waves with estimated heights of feet. (b) What is the meaning of the function of h = f(30, t) Describe the behavior of this function. We fix v and t, resulting in a constant value. We fix v = 30 and allow t to vary, resulting in an equation of one variable. We fix t = 30 and allow v to vary, resulting in an equation of one variable. We allow v and t to vary, resulting in a function of two variables. (c) What is the meaning of the function h = f(v, 30) Describe the behavior of this function. We fix v and t, resulting in a constant value. We fix v = 30 and allow t to vary, resulting in an equation of one variable. We fix t = 30 and allow v to vary, resulting in an equation of one variable. We allow v and t to vary, resulting in a function of two variables. 1/10

2 2. Question Details SCalcET [ ] The temperaturehumidity index I (or humidex, for short) is the perceived air temperature when the actual temperature is T and the relative humidity is h, so we can write I = f(t, h). The following table of values of I is an excerpt from a table compiled by the National Oceanic & Atmospheric Administration. (a) What is the value of f(85, 20) What is its meaning From the table, f(85, 20) =, which means that when the actual temperature is 85 F and the relative humidity is 20%, the perceived air temperature is approximately F. (b) For what value of h is f(80, h) = 82 % (c) For what value of T is f(t, 50) = 96 F (d) What are the meanings of the functions I = f(85, h) and I = f(100, h) Compare the behavior of these two functions of h. I = f(85, h) means that T is fixed at and h is allowed to vary, resulting in a function of h that gives the humidex values for different relative humidities when the actual temperature is F. Similarly, I = f(100, h) is a function of one variable that gives the humidex values for different relative humidities when the actual temperature is F. Looking at the rows of the table corresponding to T = 85 and T = 100, we see that f(85, h) Select at a relatively constant rate of approximately 2 F per 10% relative humidity, while f(100, h) Select more quickly (at first with an average rate of change of 5 F per 10% relative humidity) and at an Select rate (approximately 12 F per 10% relative humidity for larger values of h). 3. Question Details SCalcET [ ] A manufacturer has modeled its yearly production function P (the monetary value of its entire production in millions of dollars) as a CobbDouglas function P(L, K) = 1.47L 0.65 K 0.35 where L is the number of labor hours (in thousands) and K is the invested capital (in millions of dollars). Find your answers to one decimal place.) P(100, 50) and interpret it. (Round P(100, 50) =, so when the manufacturer invests $ million in capital and thousand hours of labor are completed yearly, the monetary value of the production is about $ million. 2/10

3 4. Question Details SCalcET [ ] f(x, y) = x 2 3/10

5. Question Details SCalcET8 14.1.025. [3799840] f(x, y) = 15 4x 5y https://www.

4 5. Question Details SCalcET [ ] f(x, y) = 15 4x 5y 4/10

5 6. Question Details SCalcET [ ] f(x, y) = sin(x) 5/10

6 7. Question Details SCalcET [ ] f(x, y) = 6 x 2 y 2 6/10

7 8. Question Details SCalcET [ ] Match the function with its graph (labeled IVI). I II III IV V VI (a) f(x, y) = x 2 + y 2 (b) f(x, y) = x 2 y 2 (c) f(x, y) = ln(x 2 + y 2 ) (d) f(x, y) = cos x 2 + y 2 (e) f(x, y) = xy (f) f(x, y) = cos(xy) 7/10

9. Question Details SCalcET8 14.1.507.XP. [3799837] f(x, y) = y 2 + 9 https://www.

8 9. Question Details SCalcET XP. [ ] f(x, y) = y /10

10. Question Details SCalcET8 14.1.508.XP. [3800642] f(x, y) = 9 x 2 9y 2 11. Question Details SCalcET8 14.1.AE.006. [3800620] EXAMPLE 6 Sketch the graph of g(x, y) = 64 x 2 y 2.

We square both sides of this equation to obtain z 2 =, or Video Example x 2 + y 2 + z 2 =, which we recognize as an equation of a sphere

9 10. Question Details SCalcET XP. [ ] f(x, y) = 9 x 2 9y Question Details SCalcET AE.006. [ ] EXAMPLE 6 Sketch the graph of g(x, y) = 64 x 2 y 2. SOLUTION The graph has equation z = 64 x 2 y 2. We square both sides of this equation to obtain z 2 =, or Video Example x 2 + y 2 + z 2 =, which we recognize as an equation of a sphere with center the origin and radius. But, since z 0, the graph of g is just the top half of this sphere. 9/10

10 Assignment Details Name (AID): 41 Multivariable Functions I ( ) Submissions Allowed: 10 Category: Homework Code: Locked: Yes Author: Skriletz, Jaimos ( jaimosskriletz@boisestate.edu ) Last Saved: Sep 11, :43 AM MDT Permission: Protected Randomization: Person Which graded: Last Feedback Settings Before due date Question Score Assignment Score Publish Essay Scores Question Part Score Mark Help/Hints Response Save Work After due date Question Score Assignment Score Publish Essay Scores Key Question Part Score Solution Mark Add Practice Button Help/Hints Response 10/10

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3628&deployment= &UserPass=51c80c11cadbba7fdfd8ac04e92877ef Sections 14.1 and 14.2 (1433628) Question 123456789101112131415161718192021 Due: Wed Sep 22 2010 11:59 PM PDT 1. Question DetailsSCalcET6 14.1.010. [1288541] Consider the function below. g(x, y, z) = ln(18