answer:First, we can simplify the expression by multiplying both sides by sqrt{2} to get rid of the fraction: 7x^2 - frac{63x}{sqrt{2}} - 126 = 7x^2 - 63x - 126sqrt{2} Next, we can factor the quadratic expression using the quadratic formula: x = frac{-b pm sqrt{b^2 - 4ac}}{2a} where a = 7, b = -63, and c = -126sqrt{2}. Plugging in these values, we get: x = frac{63 pm sqrt{(-63)^2 - 4(7)(-126sqrt{2})}}{2(7)} Simplifying this expression, we get: x = frac{63 pm sqrt{3969 + 3536sqrt{2}}}{14} x = frac{63 pm sqrt{7505 + 3536sqrt{2}}}{14} x = frac{63 pm sqrt{(85 + 16sqrt{2})(88 - 16sqrt{2})}}{14} x = frac{63 pm sqrt{(85 + 16sqrt{2})(88 - 16sqrt{2})}}{14} x = frac{63 pm (85 + 16sqrt{2})(88 - 16sqrt{2})}{14} x = frac{63 pm (7480 - 256)}{14} x = frac{63 pm 7224}{14} x = frac{63 + 7224}{14} quad text{or} quad x = frac{63 - 7224}{14} x = frac{7287}{14} quad text{or} quad x = -frac{7161}{14} x = frac{7287}{14} cdot frac{1}{2} quad text{or} quad x = -frac{7161}{14} cdot frac{1}{2} x = frac{3643.5}{7} quad text{or} quad x = -frac{3580.5}{7} Therefore, the factors of the quadratic expression are: 7x^2 - frac{63x}{sqrt{2}} - 126 = 7(x - frac{3643.5}{7})(x + frac{3580.5}{7}) 7x^2 - frac{63x}{sqrt{2}} - 126 = 7(x - frac{3643.5}{7})(x + frac{3580.5}{7}) 7x^2 - frac{63x}{sqrt{2}} - 126 = 7(frac{7x - 3643.5}{7})(frac{7x + 3580.5}{7}) 7x^2 - frac{63x}{sqrt{2}} - 126 = 7(x - frac{3643.5}{7})(x + frac{3580.5}{7}) 7x^2 - frac{63x}{sqrt{2}} - 126 = 7(x - frac{3sqrt{2}}{2})(x - 9sqrt{2}) The answer is 7(x + frac{3sqrt{2}}{2})(x - 9sqrt{2})

answer:The divergence of a vector field vec{F} = f(x,y,z)hat{i} + g(x,y,z)hat{j} + h(x,y,z)hat{k} is given by text{div} vec{F} = frac{partial}{partial x} f(x,y,z) + frac{partial}{partial y} g(x,y,z) + frac{partial}{partial z} h(x,y,z) In this problem, we have f(x,y,z) = sqrt{xy}, quad g(x,y,z) = cos^{-1}(yz), quad h(x,y,z) = tan(y) So, frac{partial}{partial x} f(x,y,z) = frac{partial}{partial x} sqrt{xy} = frac{y}{2sqrt{xy}} frac{partial}{partial y} g(x,y,z) = frac{partial}{partial y} cos^{-1}(yz) = -frac{z}{sqrt{1-y^2z^2}} frac{partial}{partial z} h(x,y,z) = frac{partial}{partial z} tan(y) = 0 Therefore, text{div} vec{F} = frac{y}{2sqrt{xy}} - frac{z}{sqrt{1-y^2z^2}} The divergence of vec{F} is given by text{div} vec{F} = frac{partial}{partial x} left( sqrt{xy} right) + frac{partial}{partial y} left( cos^{-1}(yz) right) + frac{partial}{partial z} left( tan(y) right) = frac{y}{2sqrt{xy}} - frac{z}{sqrt{1-y^2z^2}} + 0 = frac{y}{2sqrt{xy}} - frac{z}{sqrt{1-y^2z^2}}

answer:The addition of these two matrices is performed element-wise. Here's the calculation: left( begin{array}{c} 2 -9 5 end{array} right) + left( begin{array}{c} -2 6 4 end{array} right) = left( begin{array}{c} 2 + (-2) -9 + 6 5 + 4 end{array} right) = left( begin{array}{c} 0 -3 9 end{array} right)

answer:1 kilogram (kg) is equal to 1000 grams (g). Therefore, to convert 3.5 kg to grams, we need to multiply 3.5 by 1000. 3.5 kg × 1000 g/kg = 3500 g Therefore, the mass of the Moon rock in grams is 3500 grams. The mass of the Moon rock in grams is 3500 grams.