answer:The sum p(x) + q(x) can be found by combining like terms: begin{align*} p(x) + q(x) &= (-x^2) + (-6x^2) + (-7x) + (-7x) + 3 + 5 &= -x^2 - 6x^2 - 7x - 7x + 3 + 5 &= -(1x^2 + 6x^2) - (7x + 7x) + (3 + 5) &= -7x^2 - 14x + 8 end{align*}

answer:Given the function ( f(x, y) = ye^{2x} + sin(14x) ), we aim to find its total differential. The total differential ( df ) of a function ( f(x, y) ) is given by: [ df = frac{partial f}{partial x}dx + frac{partial f}{partial y}dy ] Using the chain rule to find the partial derivatives: 1. Differentiate with respect to ( x ) while keeping ( y ) constant: [ frac{partial f}{partial x} = frac{partial}{partial x}(ye^{2x}) + frac{partial}{partial x}(sin(14x)) ] [ frac{partial f}{partial x} = ye^{2x} cdot 2 + 14cos(14x) ] [ frac{partial f}{partial x} = 2ye^{2x} + 14cos(14x) ] 2. Differentiate with respect to ( y ) while keeping ( x ) constant: [ frac{partial f}{partial y} = frac{partial}{partial y}(ye^{2x}) + frac{partial}{partial y}(sin(14x)) ] [ frac{partial f}{partial y} = e^{2x} cdot 1 + 0 ] [ frac{partial f}{partial y} = e^{2x} ] Now, substitute these partial derivatives into the total differential formula: [ df = (2ye^{2x} + 14cos(14x))dx + e^{2x}dy ] Hence, the total differential of the given function is: [ df = (2ye^{2x} + 14cos(14x))dx + e^{2x}dy ]

answer:A free market is generally considered more compatible with the capitalist economic system. This is due to the following reasons: 1. Encouragement of innovation: In a capitalist free market, demand and supply are the primary forces that dictate prices, not government regulations. This encourages organizations to innovate and develop new products to meet market demands. Innovation is highly valued in capitalism, and the creators or innovators are fairly rewarded for their contributions. 2. Competition and quality: The absence of price manipulation in a free market, as seen in monopoly and oligopoly structures, fosters competition. This competition in a capitalist system leads to the production of the best products at the most competitive prices, benefiting consumers. In summary, the principles of a free market, such as competition and the incentive to innovate, align more closely with the core tenets of capitalism than with the concentrated market power found in monopoly or oligopoly structures.

answer:Consider the function: g(x)=begin{cases} 0, & text{if the first nonzero digit in the decimal expansion of } x text{ is even} 1, & text{if the first nonzero digit in the decimal expansion of } x text{ is odd} end{cases} This function partitions (0,1) into two disjoint sets: those numbers whose first nonzero digit is even (mapped to 0) and those whose first nonzero digit is odd (mapped to 1). Within any subinterval of (0,1), there are an equal number of even and odd digits, ensuring an equal number of elements mapped to 0 and 1.