Explanation for Question 19 From the Math (Calc) Section on the 2019 October Sat
Now for number 19, we're asked to convert 90 kilometers per 2 hour, two meters per second. 3 Right? And so the whole goal here is to use what we call unit 4 analysis to get rid of the kilometers so that they say 5 meters and get rid of the hours so that they say seconds. 6 Now, in order to do that, first thing we can think about doing is 7 getting rid of the kilometers and I can get rid of the kilometers by 8 multiplying by conversion factor, where I have my kilometers in minds and nominator, 9 because since my kilometers are in the numerator up here, 10 if I multiply by a denominator kilometer, 11 that'll cause the kilometers to cancel. Right? 12 And so I'll just make sure to put in the conversion to 1000 meters 13 at the top. And so now if I multiply across, 14 right, my kilometers of canceled and I'm left with 90,000 meters over 15 one hour. 16 So I'm essentially halfway there. I now have the meters that I wanted, 17 but I'm still stuck with hours. That means that my next step here is 18 to get rid of the hours and change it to seconds. 19 And then in order to do that, we need to step through minutes as 20 well. Right? So notice that my hours are in the denominator here. 21 So I essentially just want to multiply by the opposite of what's there. 22 So if my hours are denominator here, I put it numerator here. 23 And we know that one hour is equal to 60 minutes and I'll multiply 24 across here. My hours cancel, I'm left with 90,000 meters 25 per 60 minutes. So I'm close. 26 ...