assignment 1-solutions-1

assignment 1-solutions-1 - Mirzoyeva(tim89 – assignment 1...

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Unformatted text preview: Mirzoyeva (tim89) – assignment 1 – luecke – (58600) 1 This print-out should have 13 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. HINTS. CalC11b16b: sin/cos = tan; CalC11b29s: The slope of a line is the slope of the tangent at any point on the line; CalC11b40a: What is the convention about the square root sign? 001 10.0 points If the constant C is chosen so that the parabolic arc y = x 2 4 from (0 , 0) to (2 , 1) is given parametrically by ( Ct , y ( t ) ) , ≤ t ≤ 3 , find the coordinates of the point P on this arc corresponding to t = 2. 1. P = parenleftBig 4 9 , 4 3 parenrightBig 2. P = parenleftBig 1 9 , 2 3 parenrightBig 3. P = parenleftBig 2 3 , 1 9 parenrightBig 4. P = parenleftBig 2 3 , 4 9 parenrightBig 5. P = parenleftBig 1 9 , 4 3 parenrightBig 6. P = parenleftBig 4 3 , 4 9 parenrightBig correct Explanation: We have to determine y ( t ) and C so that 4 y ( t ) = C 2 t 2 , while x (0) = 0 , y (3) = 1 , 3 C = 2 . Thus C = 2 3 , 4 y ( t ) = parenleftBig 2 3 parenrightBig 2 t 2 . Consequently, when t = 2, P = (2 C, y (2)) = parenleftBig 4 3 , 4 9 parenrightBig . keywords: parametric curve, parabola 002 10.0 points Determine A so that the curve y = 5 x + 8 can be written in parametric form as x ( t ) = t- 2 , y ( t ) = At- 2 . 1. A = 5 correct 2. A = 6 3. A =- 5 4. A =- 7 5. A =- 6 6. A = 7 Explanation: We have to eliminate t from the parametric equations for x and y . Now from the equation for x it follows that t = x + 2. Thus y = 5 x + 8 = A ( x + 2)- 2 . Consequently A = 5 . 003 10.0 points Find a Cartesian equation for the curve given in parametric form by y ( t ) = 1 2 t 2 , x ( t ) = 1 8 t 3 . Mirzoyeva (tim89) – assignment 1 – luecke – (58600) 2 1. y = x 4 / 3 2. y = 2 x 2 / 3 correct 3. y = 2 x 4 / 3 4. y = x 3 / 2 5. y = x 2 / 3 6. y = 2 x 3 / 2 Explanation: We have to eliminate the parameter t from the equations for x and y . But from the equation for x , it follows that t = 2 x 1 / 3 , in which case y = 1 2 parenleftBig 2 x 1 / 3 parenrightBig 2 = 2 x 2 / 3 ....
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assignment 1-solutions-1 - Mirzoyeva(tim89 – assignment 1...

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