[Video] Q20: The mesosphere is the layer of earth’s atmosphere between 50 kilometers and 85 kilometers above earth’s surface. at a distance of 50 kilometers from earth’s surface, the temperature in the mesosphere is −5° celsius, and at a distance of 80 kilometers from earth’s surface, the temperature in the mesosphere is −80° celsius. for every additional 10 kilometers from earth’s surface, the temperature in the mesosphere decreases by k° celsius, where k is a constant. what is the value of k ?

Explanation for Question 20 From the Math (No Calc) Section on the Official Sat Practice Test 4

Now hearing number 20, we've got a really long word problem. 2 So we're going to read it. We're going to break it down and highlight 3 the most important information. And so it tells us that the Mesosphere is a 4 layer of Earth's atmosphere between 50 kilometers and 85 kilometers above 5 the surface at a distance of 50, 6 the temperature is negative five at the distance of 80, 7 the temperatures negative 80 for each additional 10 kilometers. 8 The temperature decreases by K where K is constant. 9 So we need to know what is the value of K so essentially what's 10 happening here is that each time I go up 10 kilometers, 11 my temperature decreases by the same number, 12 which is K right. So K when we say K is a constant, 13 that just means it's a normal number and it's always the same. 14 So I will always be decreasing by the same number. 15 Right. So if I start at 50 and I'm at negative five, 16 and then I go up to 80 and I'm at negative 80, 17 right. Negative 80. Yup. Essentially what I can think about having a constant 18 is that these are really like points on a line, 19 right? I have 80 common, negative 80. 20 They have 50 common negative five. 21 So what I can do here is really solve for the slope of my 22 line. Um, and then make sure I have accounted for the 10 23 kilometers. Right? So we need to be thinking about slope here. 24 And so here, how many times have I gone up 10 kilometers? 25 Right? I went from 50 to 60, from 60 to 70 and from 70 26 to 80. So I had three jump...

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