answer:To calculate the time saved by driving at 60 miles per hour instead of 50 miles per hour for a 1200-mile trip, we follow these steps: 1. Calculate the time it takes to complete the trip at 60 miles per hour: [ text{Time at 60 mph} = frac{text{1200 miles}}{60 , text{miles per hour}} = 20 , text{hours} ] 2. Calculate the time it takes to complete the trip at 50 miles per hour: [ text{Time at 50 mph} = frac{text{1200 miles}}{50 , text{miles per hour}} = 24 , text{hours} ] 3. Determine the time saved by subtracting the time it takes at 60 mph from the time it takes at 50 mph: [ text{Time saved} = 24 , text{hours} - 20 , text{hours} = 4 , text{hours} ] Therefore, Melinda's family would save boxed{4 , text{hours}}.

answer:Rob planned to spend 3 hours reading, but he only spent three-quarters of this time. So, the time he actually spent reading is: 3 hours * (3/4) = 9/4 hours To convert hours to minutes, we multiply by 60 (since there are 60 minutes in an hour): (9/4) hours * 60 minutes/hour = 135 minutes Rob read 9 pages in 135 minutes. To find out how many minutes it took him to read one page, we divide the total time by the number of pages: 135 minutes / 9 pages = 15 minutes/page Therefore, it took Rob boxed{15} minutes to read one page.

answer:Step-by-step Solution: **(1)** Given vectors overrightarrow{m}=(sin A, cos A) and overrightarrow{n}=(1, -sqrt{3}), and overrightarrow{m} cdot overrightarrow{n}=0. Computing the dot product gives: [ sin A cdot 1 + cos A cdot (-sqrt{3}) = 0 ] [ Rightarrow sin A - sqrt{3}cos A = 0 ] [ Rightarrow frac{sin A}{cos A} = sqrt{3} ] [ Rightarrow tan A = sqrt{3} ] So, we have boxed{tan A = sqrt{3}}. **(2)** Given that tan A = sqrt{3} and A is in an acute triangle triangle ABC, we can infer that A = frac{pi}{3}. From the given condition that frac{m}{tan A} = frac{1}{tan B} + frac{1}{tan C}, we express m as: [ m = left(frac{1}{tan B} + frac{1}{tan C}right) tan A ] Substituting the values, we get: [ m = frac{sin A}{cos A} left(frac{cos B}{sin B} + frac{cos C}{sin C}right) ] [ = frac{sin A}{cos A} times frac{sin C cos B + cos C sin B}{sin B sin C} ] [ = frac{sin A}{cos A} times frac{sin A}{sin B sin C} ] Utilizing the law of sines, which states that frac{a}{sin A} = frac{b}{sin B} = frac{c}{sin C}, we can restate m as: [ m = frac{a^2}{bc} times frac{1}{cos A} = frac{2a^2}{bc} ] [ = frac{2(b^2 + c^2 - 2bccos A)}{bc} ] [ = 2left(frac{b}{c} + frac{c}{b} - 1right) geq 2 ] The inequality comes from the AM-GM inequality, where the equality holds if and only if b = c. Thus, the minimum value of the real number m is boxed{2}.

answer:A. The axis of symmetry for y=x^2+2x is x=-1, which means this function is not symmetric about the y-axis, thus it is not an even function; B. y=-x^3 is an odd function; C. The domain of y=|ln x| is (0, +infty), and it is not symmetric about the origin, thus this function is neither odd nor even; D. y=2^{|x|} is an even function, and when x>0, y=2^x is an increasing function, thus this option is correct. Therefore, the answer is: boxed{D}. **Analysis:** It is easy to see that the quadratic function y=x^2+2x is not symmetric about the y-axis, so this function is not an even function. Obviously, option B's function is an odd function, and the function y=|ln x| has a domain of (0, +infty), so this function is not an even function. It is easy to determine that option D is correct.