Sample Midterm 1 WI 06

# The total interest earned on the 2000 at the end of

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The total interest earned on the \$2,000 at the end of the year was \$155. How much was invested at each rate? (14 points)

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Form A Page 8 of 8 8. An open-topped box is to be made from a 33-inch by 33-inch sheet of aluminum by cutting out x -inch squares from each corner and folding up the sides. What size square should be cut out in order to produce a box of maximum volume? (Round your answer to 1 decimal place.) (14 points) x x
Some useful formulas: log ( uw ) = log ( u ) + log ( w ) log ( u c ) = c log ( u ) A = P (1 + r ) t A = P · e rt A = P (1 + r n ) nt f ( x ) = P · a x d = ( x 1 - x 2 ) 2 + ( y 1 - y 2 ) 2 Area s = θ 360 ( π · r 2 ) cos 2 θ + sin 2 θ = 1 a sin A = b sin B = c sin C a 2 = b 2 + c 2 - 2 bc cos A

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For every point ( x, y ) which is in the first quadrant and is on the graph of y = 11 - x 2 , consider the triangle with corners (0 , 0) , ( x, 0) , and ( x, y ) . For which value of x does this triangle have maximum area? (Round your answer to 2 decimal places.) (x, y) y x (0, 0) (x, 0)
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