Total solidification times of three casting geometries are to be compared: (1) a sphere, (2) a cylinder, in which the length-to-diameter ratio = 1.0, and (3) a cube. volume = 1000 cm3 for all three shapes, and the same casting alloy is used. (a) determine the relative solidification times for each geometry. (b) based on the results of part (a), which geometric element would make the best riser? (c) if the mold constant = 3.5 min/cm2 in chvorinov's rule, compute the total solidification time for each casting.

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Does the function satisfy the hypotheses of the mean value theorem on the given interval? f(x) = 4x^2 + 3x + 4, [−1, 1] no, f is continuous on [−1, 1] but not differentiable on (−1, 1). no, f is not continuous on [−1, 1]. yes, f is continuous on [−1, 1] and differentiable on (−1, 1) since polynomials are continuous and differentiable on . there is not enough information to verify if this function satisfies the mean value theorem. yes, it does not matter if f is continuous or differentiable; every function satisfies the mean value theorem.

Which equation shows the variable terms isolated on one side and the constant terms isolated on the other side for the equation -1/2x+3=4-1/4x? a. -1/4x=1 b. -3/4x=1 c. 7=1/4x d. 7=3/4x