answer:1. **Write down the thermochemical equations for the reactions:** [ mathrm{C}_6 mathrm{H}_5 mathrm{NO}_2 (text{l}) + 6.25 , mathrm{O}_2 (mathrm{g}) rightarrow 6 , mathrm{CO}_2 (mathrm{g}) + 0.5 , mathrm{N}_2 (mathrm{g}) + 2.5 , mathrm{H}_2 mathrm{O} (text{l}) + 3094.88 , text{kJ} ] [ mathrm{C}_6 mathrm{H}_5 mathrm{NH}_2 (text{l}) + 7.75 , mathrm{O}_2 (mathrm{g}) rightarrow 6 , mathrm{CO}_2 (mathrm{g}) + 0.5 , mathrm{N}_2 (mathrm{g}) + 3.5 , mathrm{H}_2 mathrm{O} (text{l}) + 3392.15 , text{kJ} ] [ mathrm{C}_2 mathrm{H}_5 mathrm{OH} (text{l}) + 3 , mathrm{O}_2 (mathrm{g}) rightarrow 2 , mathrm{CO}_2 (mathrm{g}) + 3 , mathrm{H}_2 mathrm{O} (text{l}) + 1370 , text{kJ} ] 2. **Define variables and write corresponding masses:** Consider the amount of nitrobenzene and aniline in the solution as x moles and y moles respectively. So their masses would be: [ text{Mass of nitrobenzene} = 123x , text{g} ] [ text{Mass of aniline} = 93y , text{g} ] 3. **Express the mass of the solution:** The mass of the solution m(p - p , a) is given by: [ m(p - p , a) = frac{123x}{0.2617} = 470x , text{g} ] 4. **Calculate the amount of ethanol:** The amount of ethanol n(mathrm{C}_2 mathrm{H}_5 mathrm{OH}) is: [ n(mathrm{C}_2 mathrm{H}_5 mathrm{OH}) = frac{470x - 93y - 123x}{46} = 7.54x - 2.02y ] 5. **Set up and simplify the equation for the enthalpy change:** The total heat effect of the combustion reaction is: [ 3094.88x + 3392.15y + 1370(7.54x - 2.02y) = 1467.4 ] Simplifying this equation: [ 3094.88x + 3392.15y + 1370 cdot 7.54x - 1370 cdot 2.02y = 1467.4 ] [ 3094.88x + 10333.8x - 2767.4y = 1467.4 ] Combining terms: [ 13428.68x + 624.75y = 1467.4 quad text{(Equation 1)} ] 6. **Relate the moles of nitrogen gas:** According to the combustion reaction, the moles of nitrogen gas produced were 0.15 moles. Therefore: [ 0.5x + 0.5y = 0.15 ] Solving for y: [ 0.5x + 0.5y = 0.15 ] [ x + y = 0.3 ] [ y = 0.3 - x ] 7. **Substitute y = 0.3 - x into Equation 1 and solve for x:** Substituting y into Equation 1: [ 13428.68x + 624.75(0.3 - x) = 1467.4 ] [ 13428.68x + 187.425 - 624.75x = 1467.4 ] Combining like terms: [ 12803.93x = 1279.975 ] Solving for x: [ x = frac{1279.975}{12803.93} approx 0.1 , text{moles} ] 8. **Calculate the mass result:** Given that: [ m(p - p , a) = 470 cdot 0.1 = 47 , text{g} ] # Conclusion: The final mass is: [ boxed{47 , text{g}} ]

answer:Let the other root be x_1. We first calculate x_1 using the product of the two roots, and then find the value of k using the sum of the two roots. This problem involves the relationship between the roots and coefficients of a quadratic equation ax^{2}+bx+c=0 (a neq 0): if the roots of the equation are x_1 and x_2, then x_1 + x_2 = -frac{b}{a} and x_1 cdot x_2 = frac{c}{a}. Since one root is given as 2, and the product of the roots is frac{c}{a} = -frac{6}{5}, we can find x_1 as follows: x_1 cdot 2 = -frac{6}{5} x_1 = -frac{3}{5} Now that we have both roots, we can find k using the sum of the roots, which is -frac{b}{a} = -frac{k}{5}: x_1 + 2 = -frac{k}{5} -frac{3}{5} + 2 = -frac{k}{5} frac{7}{5} = -frac{k}{5} k = -7 So, the other root is boxed{-frac{3}{5}}, and the value of k is boxed{-7}.

answer:To find the gain percent, we first need to calculate the gain (profit) by subtracting the cost price from the selling price. Gain = Selling Price - Cost Price Gain = Rs. 1080 - Rs. 600 Gain = Rs. 480 Now, to find the gain percent, we use the formula: Gain Percent = (Gain / Cost Price) * 100 Gain Percent = (Rs. 480 / Rs. 600) * 100 Gain Percent = 0.8 * 100 Gain Percent = 80% So, the gain percent is boxed{80%} .

answer:Given the equation x^{2}+y^{2}-4x-2y-4=0, we can rearrange it to form a circle equation. Let's break down the solution step by step: 1. **Rearrange the given equation**: We start by completing the square for both x and y terms. [ x^{2}-4x+y^{2}-2y=4 ] Adding and subtracting the necessary constants inside the equation, we get: [ (x^{2}-4x+4)+(y^{2}-2y+1)=4+4+1 ] Simplifying, we find: [ (x-2)^{2}+(y-1)^{2}=9 ] This represents a circle with center (2,1) and radius 3. 2. **Introduce a new variable**: Let z = x - y. We aim to find the maximum value of z. The equation x - y = z can be rearranged to y = x - z. 3. **Substitute y in the circle's equation**: Substituting y = x - z into the circle equation gives: [ (x-2)^{2}+((x-z)-1)^{2}=9 ] This equation represents the intersection points of the line y = x - z with the circle. 4. **Find the distance from the center to the line**: The distance from the center of the circle (2,1) to the line y = x - z can be calculated using the point-to-line distance formula. The formula for the distance D from a point (x_0, y_0) to a line Ax + By + C = 0 is: [ D = frac{|Ax_0 + By_0 + C|}{sqrt{A^2 + B^2}} ] For our line y = x - z, or -x + y + z = 0, we have A = -1, B = 1, and C = z. Plugging in the center (2,1), we get: [ D = frac{|-2 + 1 + z|}{sqrt{(-1)^2 + 1^2}} = frac{|-1 + z|}{sqrt{2}} ] For the line to intersect the circle, the maximum distance D can be the radius of the circle, which is 3. Therefore, we have: [ frac{|-1 + z|}{sqrt{2}} leqslant 3 ] Simplifying, we find: [ |-1 + z| leqslant 3sqrt{2} ] This leads to two inequalities: [ -1 + z leqslant 3sqrt{2} quad text{and} quad -1 + z geqslant -3sqrt{2} ] Solving these inequalities for z, we get: [ 1 - 3sqrt{2} leqslant z leqslant 1 + 3sqrt{2} ] Therefore, the maximum value of z = x - y is boxed{1 + 3sqrt{2}}, which corresponds to option C.