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10c_04f_fs

# 10c_04f_fs - Math 10C Final Exam Solutions Fall 2004 1 It...

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Math 10C Final Exam Solutions Fall 2004 1. It is the amount of money, in cents, that the street vendor takes in (or “collects”, or “earns”, etc.) that day. If you did not give the units (cents), you do not get full credit. 2. The vectors (− 1 , 2 , 0 ) and ( 0 , 0 , 1 ) are parallel to the plane. Therefore a normal to the plane is given by vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle i j k 1 2 0 0 0 1 vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle vextendsingle = 2 i + j . Hence an equation for the plane is 0 = ( 2 , 1 , 0 ) · ( x 1 , y 0 , z 0 ) = 2 x + y 2 . Thus the answer is 2 x + y = 2. Of course, this could be multiplied by a constant; for example, 6 x + 3 y = 6 is acceptable. 3. Calling the vectors u and v and the angle θ , cos θ = u · v | u | | v | = 3 4 + 3 ( 1 2 + 2 2 + 3 2 ) 2 = 2 14 . Thus θ = cos - 1 (1 / 7). 4. Writing F ( x, y ) = x 3 x 2 y + y 3 , we have dy/dx = F x /F y . Since F x = 3 x 2 2 xy and F y = x 2 + 3 y 2 , we have F x (2 , 1) = 8 and F y = 1. Hence the answer is dy/dx = 8.

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