answer:The ratio of a certain number to the number 8 is found by dividing the certain number by 8. If the certain number is 40, then the ratio is: 40 ÷ 8 = 5 So the ratio of the number 40 to the number 8 is boxed{5:1} .

answer:Solution: (1) Since the parametric equation of line l_1 is begin{cases}x=2+t y=ktend{cases} (t is the parameter), by eliminating the parameter t, we get the standard equation of line l_1: y=k(x-2) quad (1), and the parametric equation of line l_2 is begin{cases}x=2+m y= frac{m}{k}end{cases} (m is the parameter), similarly, we get the standard equation of line l_2: x=-2+ky quad (2); By solving equations (1) and (2) together and eliminating k, we get: x^{2}-y^{2}=4, which is the standard equation of C: x^{2}-y^{2}=4; (2) Since the polar equation of l_3 is rho(cos theta+sin theta)- sqrt{2} =0, its standard equation is: x+y- sqrt{2} =0, By solving begin{cases}x+y= sqrt{2} {x}^{2}-{y}^{2}=4end{cases}, we get: begin{cases}x= frac{3 sqrt{2}}{2} y=- frac{ sqrt{2}}{2}end{cases}, Therefore, rho^{2}=x^{2}+y^{2}= frac{18}{4} + frac{2}{4} =5, Thus, the polar radius of the intersection point M of l_3 and C is rho= sqrt{5}. Therefore, the answers are: (1) The standard equation of C is boxed{x^{2}-y^{2}=4}. (2) The polar radius of M is boxed{sqrt{5}}.

answer:**Analysis** This question examines the conversion of parametric equations to standard equations, the relationship between slope and inclination angle, and the basic trigonometric identities related to the same angle. It tests reasoning and computational skills and is considered a medium-level question. By converting the parametric equation of line l to a standard equation and using the relationship between slope and inclination angle, as well as the basic trigonometric identities, the answer can be obtained. **Solution** Given the problem, let the inclination angle of line l be theta, The parametric equation of line l is begin{cases} & x=1+3t & y=2-4t end{cases} (where t is the parameter), which can be converted to y-2=- dfrac {4}{3}(x-1), Then, tan theta=- dfrac {4}{3}, Since thetain(0,pi), Therefore, cos theta=- dfrac {3}{ sqrt {3^{2}+4^{2}}}=- dfrac {3}{5}, Hence, the correct option is boxed{text{A}}.

answer:1. **Define the angles of the hands**: - For the hour hand, after n minutes past 6:00 PM, the position is 180^circ + frac{n}{2} degrees. - For the minute hand, after n minutes past 6:00 PM, the position is 6n degrees. 2. **Angle formed between the hands**: [ left|180^circ + frac{n}{2} - 6nright| = 130^circ ] Simplifying, we have: [ left|180^circ - frac{11n}{2}right| = 130^circ ] 3. **Solve the equation** for n: [ 180^circ - frac{11n}{2} = 130^circ quad text{or} quad 180^circ - frac{11n}{2} = -130^circ ] Solving these equations: - Case 1: [ 180^circ - 130^circ = frac{11n}{2} implies 50^circ = frac{11n}{2} implies n = frac{100}{11} approx 9.09 text{ minutes} ] - Case 2: [ 180^circ + 130^circ = frac{11n}{2} implies 310^circ = frac{11n}{2} implies n = frac{620}{11} approx 56.36 text{ minutes} ] 4. **Calculate the difference in time**: [ frac{620}{11} - frac{100}{11} = frac{520}{11} approx 47.27 text{ minutes} ] Therefore, the man was away for approximately 47.27 minutes. Conclusion: The man was away for about 47.27 minutes, thus the answer rounds correctly to the nearest minute or choice. The final answer is boxed{C) 47 minutes}