MAC 2312 Midterm: MAC2312 S04 Test 1
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Instructions: write your complete solutions on your answer sheets. You are not required to simplify your answers. Assume all physical units (length, force, etc. ) are in the mks system, hence are compatible. (1) (40 pts. ) The length of a cable is 50 and the weight is 10. 40 was hanging over the edge of a tall building and was pulled to the top. How much work was done? (3) (30 pts. ) Let c denote the curve y = x(4 x), where 0 x 4. In this case, do not evaluate the integrals. (a) the length of c. (b) the area of the surface generated when c is revolved about the (i) x-axis (ii) y-axis (4) (20 pts. ) A tank has the shape of a trapezoidal prism. The top is horizontal and the two ends are vertical. Viewed from an end, the tank looks like the trapezoid shown in the gure below.
