answer:To complete the square, we start with the standard form of a quadratic expression: ax^2 + bx + c. Here, a = -frac{14}{3}, b = -frac{23}{3}, and c = frac{1}{3}. The process involves adding and subtracting the square of half of the coefficient of x to the expression. First, find left(frac{b}{2a}right)^2: left(frac{-frac{23}{3}}{2 cdot -frac{14}{3}}right)^2 = left(frac{23}{14}right)^2 = frac{23^2}{14^2} = frac{529}{196}. Now, add and subtract this value inside the expression: -frac{14 x^2}{3} - frac{23 x}{3} + frac{1}{3} + frac{529}{196} - frac{529}{196}. Group the perfect square trinomial and the constant terms separately: -frac{14}{3} left(x^2 + frac{23}{14}xright) + frac{529}{196} - frac{1}{3} - frac{529}{196}. Complete the square by factoring the perfect square trinomial: -frac{14}{3} left(x^2 + frac{23}{14}x + left(frac{23}{28}right)^2right) + frac{529}{196} - frac{1}{3} - frac{529}{196}. Simplify the expression: -frac{14}{3} left(x + frac{23}{28}right)^2 + frac{529}{196} - frac{196}{196} - frac{529}{196}. Combine the constants: -frac{14}{3} left(x + frac{23}{28}right)^2 + left(frac{529 - 196 - 529}{196}right). Simplify the constant term: -frac{14}{3} left(x + frac{23}{28}right)^2 + frac{0}{196}. The final expression after completing the square is: -frac{14}{3} left(x + frac{23}{28}right)^2. So, the revised answer is correct as initially provided: frac{195}{56}-frac{14}{3} left(x+frac{23}{28}right)^2.

answer:The reduced row echelon form (RREF) of the given matrix is: left( begin{array}{ccccc} 1 & 0 & 0 & frac{1}{26} & -frac{64}{39} 0 & 1 & 0 & -frac{116}{91} & frac{145}{273} 0 & 0 & 1 & frac{118}{91} & -frac{11}{273} end{array} right)

answer:The divergence of a vector field vec{F}(x, y, z) = f(x, y, z)uvec{i} + g(x, y, z)uvec{j} + h(x, y, z)uvec{k} is given by nabla cdot vec{F} = frac{partial f}{partial x} + frac{partial g}{partial y} + frac{partial h}{partial z}. Let's compute the partial derivatives: 1. frac{partial f}{partial x} = frac{1}{2sqrt{x}} 2. frac{partial g}{partial y} = -frac{2(x-y)}{z^2} 3. frac{partial h}{partial z} = 1 Now, we sum these up to find the divergence: nabla cdot vec{F} = frac{1}{2sqrt{x}} - frac{2(x-y)}{z^2} + 1 Thus, the divergence of the given vector field is frac{1}{2sqrt{x}} - frac{2(x-y)}{z^2} + 1.

answer:Protein synthesis is the process by which cells create proteins, which are essential for various cellular functions. The first step of protein synthesis is transcription, which occurs in the nucleus of eukaryotic cells. During transcription, an enzyme called RNA polymerase binds to a specific region of DNA called the promoter and separates the DNA strands. One of the DNA strands, known as the template strand, is used to synthesize a complementary mRNA strand. The mRNA strand is then transported out of the nucleus and into the cytoplasm, where it serves as a template for protein synthesis. Transcription is the first step of protein synthesis, where a DNA strand is used as a template to create a complementary mRNA strand.