hw1so - Create assignment 57321 Homework 1 Jan 22 at 5:43...

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Create assignment, 57321, Homework 1, Jan 22 at 5:43 pm 1 This print-out should have 34 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. The due time is Central time. CalC2a01a 48:01, calculus3, multiple choice, > 1 min, normal. 001 A tank holds 1000 gallons of water, which drains from the bottom of the tank in half an hour. The values in the table t (min) 5 10 15 20 25 30 V (gal) 659 441 230 159 18 0 show the volume, V ( t ), of water remaining in the tank (in gallons) after t minutes. If P is the point (15 , V (15)) on the graph of V as a function of time t , find the slope of the secant line PQ when Q = (25 , V (25)). 1. slope = - 21 . 2 correct 2. slope = - 42 . 9 3. slope = - 21 . 1 4. slope = - 7 . 1 5. slope = - 42 . 4 Explanation: When P = (15 , V (15)) , Q = (25 , V (25)) the slope of the secant line PQ is given by rise run = V (25) - V (15) 25 - 15 . From the table of values, therefore, we see that slope = 18 - 230 25 - 15 = - 21 . 2 . keywords: slope, table of values, secant line CalC2a02b 48:01, calculus3, multiple choice, < 1 min, wording-variable. 002 The position as a function of time t of a car initially heading due north on IH35 is shown in 2 4 6 2 4 time position List the values of m 1 = average velocity on [3 , 4] , m 2 = average velocity on [4 , 6] , m 3 = instantaneous velocity at t = 4 , m 4 = instantaneous velocity at t = 2 , in increasing order. 1. m 2 , m 3 , m 1 , m 4 correct 2. m 1 , m 2 , m 3 , m 4 3. m 2 , m 1 , m 4 , m 3 4. m 3 , m 4 , m 2 , m 1 5. m 3 , m 1 , m 2 , m 4 6. m 4 , m 1 , m 2 , m 3 Explanation: If s ( t ) denotes the position of the car at time t , then the average velocity over the time
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Create assignment, 57321, Homework 1, Jan 22 at 5:43 pm 2 interval [ a, b ] is the slope s ( b ) - s ( a ) b - a of the secant line from ( a, s ( a )) to ( b, s ( b )), while the instantaneous velocity at t = a is the slope of the tangent line at the point ( a, s ( a )) on the graph of s . A positive value for the slope indicates that the car is heading north- wards, while a negative value indicates that it is heading southwards. Thus by inspection, average velocity on [4 , 6] < instantaneous velocity at t = 4 < average velocity on [3 , 4] < instantaneous velocity at t = 2 . For the given values of m 1 , . . . , m 4 , therefore, m 2 < m 3 < m 1 < m 4 . keywords: position v. time graph, instanta- neous velocity, average velocity, CalC2a04b 48:01, calculus3, multiple choice, > 1 min, wording-variable. 003 At which point on the graph U T S R Q P (i) is the slope greatest ( i.e. , most positive)? 1. S correct 2. T 3. U 4. P 5. Q 6. R Explanation: By inspection the point is S . 004 (ii) is the slope smallest ( i.e. , most negative)? 1. U correct 2. P 3. Q 4. R 5. S 6. T Explanation: By inspection the point is U . 005 (iii) does the slope change from positive to negative? 1. T correct 2. U 3. P 4. Q 5. R
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Create assignment, 57321, Homework 1, Jan 22 at 5:43 pm 3 6. S Explanation: By inspection the point is T . 006 (iv) does the slope change from negative to positive? 1. Q correct 2. R 3. S 4. T 5. U 6. P Explanation: By inspection the point is Q .
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