answer:To solve the equation left| frac{71}{3}-frac{34 x}{3}right| =frac{26}{3}, we can first isolate the absolute value expression: left| frac{71}{3}-frac{34 x}{3}right| =frac{26}{3} frac{71}{3}-frac{34 x}{3}=frac{26}{3} quad text{or} quad frac{71}{3}-frac{34 x}{3}=-frac{26}{3} Solving each equation separately, we get: frac{71}{3}-frac{34 x}{3}=frac{26}{3} -frac{34 x}{3}=frac{26}{3}-frac{71}{3} -frac{34 x}{3}=-frac{45}{3} x=frac{45}{34} frac{71}{3}-frac{34 x}{3}=-frac{26}{3} -frac{34 x}{3}=-frac{26}{3}-frac{71}{3} -frac{34 x}{3}=-frac{97}{3} x=frac{97}{34} Therefore, the solutions to the equation left| frac{71}{3}-frac{34 x}{3}right| =frac{26}{3} are x=frac{45}{34} and x=frac{97}{34}. The answer is left{xto frac{45}{34}, xto frac{97}{34}right}

answer:-frac{605}{108}-frac{65}{36 sqrt{3}}-frac{5 sqrt{3}}{4} The original answer provided seems accurate, but to improve formatting and readability, we can express the answer in a more standard mathematical format: -left(frac{605}{108} + frac{65}{36 cdot sqrt{3}} + frac{5 cdot sqrt{3}}{4}right) This format groups the terms and makes it clearer that they are all part of a single sum.

answer:Upon calculation, the estimated values for the polyhedron are as follows: - Solid Angle at vertex left(0.587, 0.356, 0.97right): 1.2 steradians - Surface Area: 1.84 square units - Volume: 0.16 cubic units

answer:Consider a closed, convex, absorbing subset K in a topological vector space X of second category. Form the intersection H = K ∩ (-K), which is also closed, convex, and absorbing. Since X is of second category, H must have non-empty interior. Using the property 2H = H + H = H - H, it can be shown that H contains an open neighborhood of the origin, which is also contained in K.