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1 Calculus Multivariable, 8e (Hughes-Hallett) Chapter 12 Functions of Several Variables 12.1 Functions of Two Varia bles 1) You are in a nicely heated cabin in the winter.Deciding that it's too warm, you open a small window. Le t T be the temperature in the room, t minutes after the window was opened, x feet from the window. I s T an increasing or decreasing function of x?
- Increasing
- Decreasing
- Neither
Answer: A
Diff: 1 Type: BI Learning Objective: LO 12.1.1 Represent functions of two variables graphically, numerically and algebraically.
Section: 12.1
2) The following table gives the number f (x, y) of grape vines, in thousands, of age x in year y.In one year a fungal disease killed most of the older grapevines, and in the following year a long freeze killed most of the young vines. Which are these years?
- 1982 and 1983
- 1980 and 1981
- 1981 and 1982
- 1983 and 1984
Answer: A
Diff: 1 Type: BI Learning Objective: LO 12.1.1 Represent functions of two variables graphically, numerically and algebraically.
Section: 12.1
Calculus, Multivariable (Chapter 12-21), 8e Deborah Hughes-Hallett, Andrew Gleason, William McCallum (Wiley) (Test Bank All Chapters, 100% original verified, A+ Grade)
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2 3) The following table gives the number f (x, y) of grape vines, in thousands, of age x in year y.In 1986 a successful advertising campaign led to a dramatic increase in demand for premium wines. The growers followed by adding many more plants. Suppose a vine (the plant) produces the first harvestable grapes at age five, and is removed after sixteen years. How many (thousand) grape vines that bear fruit were there in the year 1986 and how many will be there in the year 1993 (assuming that no current vines die before 1993)?Enter your answers separated by a semi-colon.
Answer: 11,000; 40,000
Diff: 2 Type: SA Learning Objective: LO 12.1.1 Represent functions of two variables graphically, numerically and algebraically.
Section: 12.1
4) You are at (3, 4, -2) facing the yz-plane. You walk 5 units, turn right and walk for another 2 units. What are your coordinates now? Are you above or below the xy-plane?
- My coordinates are (-2, 6, -2) and I am below the xy-plane.
- My coordinates are (-2, 6, 2) and I am above the xy-plane.
- My coordinates are (2, 2, 2) and I am above the xy-plane.
- My coordinates are (2, 2, -2) and I am below the xy-plane.
Answer: A
Diff: 1 Type: BI
Learning Objective: LO 12.1.2 Interpret properties of multivariable functions.
Section: 12.1 2 / 4
3 5) (i) Find an equation of the largest sphere that can fit inside the cubical space enclosed by the planes and (ii) If we replace the plane z = 9 in part (a) with what will be the new equation of the largest sphere?
- (i) + + = 25
- (i) + + = 25
- (i) + + = 100
- (i) + + = 100
(ii) + + = 25, 4 ≤ c ≤ 6
(ii) + + = 25
(ii) + + = 100
(ii) + + = 100, 4 ≤ c ≤ 6
Answer: A
Diff: 2 Type: BI
Learning Objective: LO 12.1.3 Graph equations in 3-space.
Section: 12.1
6) Consider the sphere
+ + = 25
(i) What are the center and radius of this sphere?(ii) Find an equation of the circle (if any) where the sphere intersects the plane
- (i) Center (5, -3, -1), Radius 5.
(ii) Substituting gives ( + = -11 so there is no such circle.
- (i) Center (-5, 3, 1), Radius 5.
(ii) ( + = 11.
- (i) Center (5, -3, -1), Radius 25.
(ii) Substituting gives ( + = -11 so there is no such circle.
- (i) Center (-5, 3, 1), Radius 25.
(ii) ( + = 11.
Answer: A
Diff: 2 Type: BI
Learning Objective: LO 12.1.5 Explain how to navigate in 3-space.
Section: 12.1
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4 7) The points A = (3 , 2, 1), B = (-2, -4, 3), and C = (-1, 3, -2) are the vertices of a triangle in space. Which of the vertices is closest to the xz-plane?
- A
- C
- B
Answer: A
Diff: 1 Type: BI
Learning Objective: LO 12.1.5 Explain how to navigate in 3-space.
Section: 12.1
8) The points A = (1, 3, 2), B = (0, -5, 4), and C = ( -2, 2, 1) are the vertices of a triangle in space.Which of the vertices is closest to the origin?
- C
- A
- B
Answer: A
Diff: 1 Type: BI
Learning Objective: LO 12.1.5 Explain how to navigate in 3-space.
Section: 12.1
9) The points A = (3, -5, -4), B = (-1, 4, -5), and C = (-2, -4, 5) are the vertices of a triangle in space. What is the length of the longest side of the triangle?A) B) C) D)
Answer: A
Diff: 1 Type: BI
Learning Objective: LO 12.1.5 Explain how to navigate in 3-space.
Section: 12.1
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