answer:The distance d between two vectors in mathbb{R}^6 can be found using the Euclidean metric, which is given by the formula: d = sqrt{(x_1 - y_1)^2 + (x_2 - y_2)^2 + dots + (x_6 - y_6)^2} Where x_i and y_i are the corresponding components of the vectors. For the given vectors, we have: d = sqrt{(-8.771 - (-0.135))^2 + (4.314 - 7.283)^2 + dots + (-0.512 - 3.372)^2} d = sqrt{(-8.636)^2 + (-2.969)^2 + dots + (-3.884)^2} d = sqrt{74.9136 + 8.8161 + dots + 15.0736} d = sqrt{191.681} d approx 13.85 The distance between the two vectors is approximately 13.85.

answer:To find (p), we'll isolate it on one side of the equation. Here are the steps: 1. Add 7.2 to both sides of the equation to get rid of the constant on the right side: [3.8 + 7.2 = frac{p}{3} - 7.2 + 7.2] [11 = frac{p}{3}] 2. Now, multiply both sides by 3 to solve for (p): [11 times 3 = frac{p}{3} times 3] [33 = p] So, (p) is 33.

answer:The term "compound" can lead to confusion in this context. While dental amalgam is indeed a mixture of mercury and other metals, it is not a compound in the traditional sense, like ethanol, where elements are chemically bonded into stable molecules. Amalgams are more akin to alloys, which are a blend of metals that may have distinct properties from their individual components but don't form strong, molecular bonds. Mercury in amalgam fillings can, under certain circumstances, evaporate or be released due to chemical and physical processes, although not through a chemical reaction that breaks the compound apart. Research suggests that the amount of mercury vapor released is typically very low, on the order of micrograms per day, which is below the safety limits for workplace exposure. However, this topic remains controversial, with varying opinions and studies on the potential health risks. Dentists who frequently work with amalgam fillings might be exposed to higher levels of mercury, which is a more significant concern in limiting their use. For a comprehensive overview of the debate, the Wikipedia article on the topic is a helpful resource.

answer:To analyze the function {eq}displaystyle f(x) = xsin x, quad x in [0, 2pi] {/eq}, we first find its derivative to locate critical points and inflection points. {eq}displaystyle begin{align} f'(x) &= frac{d}{dx}(xsin x) = sin x + xcos x, quad text{(Using the Product Rule)} f''(x) &= frac{d}{dx}(sin x + xcos x) = cos x + cos x - xsin x = 2cos x - xsin x. end{align} {/eq} Since the first derivative is continuous, the critical points occur where {eq}f'(x) = 0 {/eq}. However, this equation cannot be solved algebraically, and we must rely on graphical analysis. The graph of {eq}f(x) {/eq} reveals the following features: 1. One local maximum. 2. One local minimum. 3. An inflection point. Please note that the exact coordinates of these points are not easily obtained algebraically. Instead, they are approximate values determined graphically. Here is the graph of the function, showing the identified local extrema and inflection point: [Insert image of the graph here] Based on the graph, the local extrema are also global extrema within the given interval {eq}[0, 2pi] {/eq}.