Chapter 7 Test - X ? E Test: Chapter 7 Test Question 1 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K Calculate _ Xkyk for the n = 5 data points (X1,y, ) = (1,3), (X2.y2) = (3,4), (X3,y3) = (5,7), (X4.y4)= (7, 10), and (X5.)5) = (9, 15). O Question 1 E xKyK = (Simplify your answer.) O Question 2 K = 1 O Question 3 O Question 4 O Question 5 O Question 6 O Question 7 Question 8 Next Q Search O WChapter 7 Test - X ? E Test: Chapter 7 Test Question 2 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K Minimize f(x,y) = x2 + xy + yz subject to y = 10 without using the method of Lagrange multipliers; instead, solve the constraint for x or y and substitute into f(x,y). O Question 1 Use the constraint to rewrite f(x,y) = x2 + xy + y2 as a function of one variable, g(x). g(x) = O Question 2 The minimum value of f(x,y) = x2 + xy + yz subject to y = 10 occurs at the point (Type an ordered pair.) O Question 3 The minimum value of f(x,y) = x2 + xy + y2 subject to y = 10 is . (Simplify your answer.) O Question 4 O Question 5 O Question 6 O Question 7 Question 8 Next Q Search O W 15Chapter 7 Test - . X ? E Test: Chapter 7 Test Question 3 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K Find fx(x,y) and fy (x,y), and explain why f(x,y) has no local extrema. f ( x,y) = 2x + 6y +5. O Question 1 fx (x,y) = 0 O Question 2 fy (x, y) = 0 Choose the best explanation below for the reason that f(x,y) has no local extrema. O Question 3 O A. The functions fx (x,y) and fy(x,y) have no local extrema. O B. The functions fx (x,y) and fy (x,y) are non-zero for all (x,y). O Question 4 O C. The second derivative test fails because AC - B2 = 0. O D. The functions fx(x,y) and fy (x,y) are never equal to each other. O Question 5 O Question 6 O Question 7 Question 8 Next Q Search O WChapter 7 Test X ? E Test: Chapter 7 Test Question 4 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K Find f'(0), f"'(0), and determine whether f has a local minimum, local maximum, or neither at x = 0. f(x) = 4x5 - 8x2 + 7 O Question 1 What is f'(0)? O Question 2 f' (0) = What is f"(0)? Question 3 f'' (0) = Does the function have a local minimum, a local maximum, or neither? O Question 4 O A. The function has a local maximum at x = 0. O B. The function has a local minimum at x = 0. O Question 5 O C. The function has neither a local minimum nor a local maximum at x = 0 O Question 6 O Question 7 Question 8 Next Q Search O W 15X ? E Test: Chapter 7 Test Question 5 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K Find the antiderivative. Then use the antiderivative to evaluate the definite integral. (A) (6X + 4y + 7)dx ( B) (6* + 4y + 7) dx O Question 1 - 2 O Question 2 (A) (6x + 4y + 7)dx = (Use C(x) to represent the arbitrary function of x or E(y) to represent the arbitrary function of y.) O Question 3 ( B ) (6x + Ay + 7 ) dx = [ - 2 O Question 4 (Type an expression using y as the variable.) O Question 5 O Question 6 O Question 7 Question 8 Next Q Search O W 15X ? E Test: Chapter 7 Test Question 6 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K Find f'(0), f"(0), and and determine whether f has a local minimum, local maximum, or neither at x = 0. f(x) = (3x +3)2 O Question 1 What is f'(0)? O Question 2 f'(0) = What is f"(0)? O Question 3 f''(0) = Does the function have a local minimum, a local maximum, or neither? O Question 4 O A. The function has a local minimum at x = 0 O B. The function has a local maximum at x = 0. O Question 5 O C. The function has neither a local minimum nor a local maximum at x = 0 Question 6 O Question 7 Question 8 Next Q Search O WX ? E Test: Chapter 7 Test Question 7 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K Find the least squares line. Graph the data and the least squares line. OUI A W X O Question 1 O Question 2 Find the least squares line. y = () x+ (D O Question 3 (Use integers or decimals for any numbers in the expression. Round to the nearest hundredth as needed.) Graph the data and the least squares line. Choose the correct answer below. O Question 4 O A. O B. O c. OD. 12- O Question 5 X O Question 6 12 12 O Question 7 Question 8 Next Q Search O WX ? E Test: Chapter 7 Test Question 8 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K The function S(T,r) = 40(T - 20)(6 -r) gives an ice cream shop's daily sales as a function of temperature T (in F) and rain r (in inches). Find S(90,3) (include the appropriate units) and explain what it means. O Question 7 S(90,3) = (Simplify your Question 8 Explain the m om the previous step. Select the correct choice below and fill in the answer box within your choice. degrees per inch O A. Daily per 1OF in temperature when the temperature is 90 F and rainfall is 3". O Question 9 O B. Daily dollars per inch per inch of rain when the temperature is 90 F and rainfall is 3". O C. Daily degrees when the temperature is 90 F and rainfall is 3". O Question 10 O D. Daily degrees per dollar per 1 F in temperature when the temperature is 90 F and rainfall is 3". O E. Daily inches per dollar per inch of rain when the temperature is 90 F and rainfall is 3". O Question 11 inches O Question 12 dollars O Question 13 O Question 14 Next Q Search O W 15X ? E Test: Chapter 7 Test Question 8 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K The function S(T,r) = 40(T - 20)(6 -r) gives an ice cream shop's daily sales as a function of temperature T (in F) and rain r (in inches). Find S(90,3) (include the appropriate units) and explain what it means. O Question 7 S(90,3) = (Simplify your answer.) Question 8 Explain the meaning of the correct answer from the previous step. Select the correct choice below and fill in the answer box within your choice. O A. Daily sales decrease at a rate of $ per 1'F in temperature when the temperature is 90 F and rainfall is 3". O Question 9 O B. Daily sales increase at a rate of $ per inch of rain when the temperature is 90 F and rainfall is 3". O C. Daily sales are estimated to be $ when the temperature is 90 F and rainfall is 3". O Question 10 O D. Daily sales increase at a rate of $ per 1 F in temperature when the temperature is 90 F and rainfall is 3". O E. Daily sales decrease at a rate of $ per inch of rain when the temperature is 90 F and rainfall is 3". O Question 11 O Question 12 O Question 13 O Question 14 Next Q Search O W 15X ? E Test: Chapter 7 Test Question 9 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K 56 Find the indicated value of the functions f(x,y) = 2x + 7y - 4 and g(x,y) = x 2 + 3y g( - 1,2) O Question 7 Evaluate g( - 1,2). Select the correct choice below and fill in any answer boxes within your choice. O Question 8 O A. g( - 1,2) = (Simplify your answer.) O Question 9 O B. The function g( - 1,2) is undefined. O Question 10 O Question 11 O Question 12 O Question 13 O Question 14 Next Q Search O W 15X ? E Test: Chapter 7 Test Question 10 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K Find the coordinates of the points E and F of the rectangular box shown below. The coordinates of point E are (D) The coordinates of point F are (].) Question 9 O Question 10 Question 11 5 Question 12 O Question 13 O Question 14 O Question 15 Question 16 Next Q Search O W 15X ? E Test: Chapter 7 Test Question 11 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K The equation M(x,y) = 52 + 0.8x - 0.3y gives the mileage (in mpg) of a new car as a function of tire pressure x (in psi) and speed y (in mph). Find M(34,51) (include the appropriate units) and explain what it means. O Question 9 M(34,51) = (Type an intege O Question 10 Explain what th step means. Select the correct choice below and fill in the answer boxes within your choice. (Type integers mpg O A. Increasi O Question 11 and maintaining a tire pressure of psi will increase mileage by mpg. mph per mpg O B. Increasi he psi and maintaining a speed of psi will decrease mileage by mpg mpg per psi O Question 12 O C. Mileage sure of psi and a speed of mph. O D. Increasi psi per mpg he psi and maintaining a speed of mph will increase mileage by mpg. O Question 13 O E. Increasi mph and maintaining a tire pressure of psi will increase mileage by mpg. psi per mph O Question 14 mpg per mph mph per psi O Question 15 psi Question 16 Next Q Search O WX ? E Test: Chapter 7 Test Question 11 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K The equation M(x,y) = 52 + 0.8x - 0.3y gives the mileage (in mpg) of a new car as a function of tire pressure x (in psi) and speed y (in mph). Find M(34,51) (include the appropriate units) and explain what it means. O Question 9 M(34,51) = (Type an integer or a decimal.) O Question 10 Explain what the answer in the previous step means. Select the correct choice below and fill in the answer boxes within your choice. (Type integers or decimals.) O Question 11 O A. Increasing the speed by one mph and maintaining a tire pressure of psi will increase mileage by mpg. O B. Increasing the tire pressure by one psi and maintaining a speed of psi will decrease mileage by mpg O Question 12 O C. Mileage is mpg at a tire pressure of psi and a speed of mph O D. Increasing the tire pressure by one psi and maintaining a speed of mph will increase mileage by mpg. O Question 13 O E. Increasing the speed by one mph and maintaining a tire pressure of psi will increase mileage by mpg. O Question 14 O Question 15 O Question 16 Next Q Search O W 15X ? E Test: Chapter 7 Test Question 12 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K Find the indicated derivative. as if z = In (x8 + e6) O Question 9 O Question 10 dx = 0 O Question 11 Question 12 O Question 13 O Question 14 O Question 15 O Question 16 Next Q Search O W 15X E Test: Chapter 7 Test Question 13 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K Find the volume of a rectangular solid with dimensions of 5 inches by 5 inches by 5.9 inches. O Question 9 v= in.3 (Simplify your answer. Type a whole number or a decimal.) O Question 10 O Question 11 O Question 12 Question 13 O Question 14 O Question 15 O Question 16 Next Q Search O W 15X E Test: Chapter 7 Test Question 14 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K Find the antiderivative. Then use the antiderivative to evaluate the definite integral. (A ) | 18 x 5 y 2 dy (B) / 18x 3 1 2 dy O Question 9 O Question 10 (A ) | 18x5 y 2 dy = [ (Use C(x) to represent the arbitrary function of x or E(y) to represent the arbitrary function of y.) O Question 11 (B) | 18x By2 dy = Question 12 O Question 13 O Question 14 O Question 15 Question 16 Next Q Search O W 15X ? E Test: Chapter 7 Test Question 15 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K Find the volume V of a cone with radius 12 mm and height 3 mm. O Question 9 V cubic millimeters (Round to the nearest hundredth as needed.) O Question 10 O Question 11 Question 12 O Question 13 O Question 14 Question 15 Question 16 Next Q Search O W 15X ? E Test: Chapter 7 Test Question 16 of 16 This test: 16 point(s) possible This question: 1 point(s) possible Submit test Question list K Find the surface area of the cylinder. S in O Question 9 12 in O Question 10 The surface area of the given cylinder is in (Simplify your answer. Type an exact answer in terms of it. Use integers or decimals for any numbers in the expression.) O Question 11 Question 12 O Question 13 O Question 14 O Question 15 Question 16 Submit test Q Search O W