# X y 10 7 12 points a load must be suspended 6 meters

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7. (12 points) A load must be suspended 6 meters below a high ceiling using cables attached to two supports that are 2 meters apart (see figure). How far below the ceiling (labeled x ) should the cables be joined to minimize the total length of cable used? What is the minimum amount of cable needed? (Leave your answers in exact form and make sure to justify your minimum in some way.) 2m 6m cable joined here LOAD ceiling x 11
8. (12 points) A particle moves through the plane along the curve C defined by the parametric equations x ( t ) = 3 t 2 - 4 t , y ( t ) = t 2 + 4 t + 4, where t 0. Let P ( t ) = ( x ( t ) , y ( t )) be the location of the particle at time t . (a) [6pts] Find the equation of the tangent line to the curve C at time t = 1. (b) [6pts] Find the time(s) when a tangent line to the curve at P ( t ) passes through the point (2 , 0). 12
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